This tool calculates the protected area between two lightning rods based on the IEC 62305 standard and the Rolling Sphere Method, suitable for building, tower, and industrial facility lightning protection design. Parameter Description Current Type Select the type of current in the system: - Direct Current (DC): Common in solar PV systems or DC-powered equipment - Alternating Single-Phase (AC Single-Phase): Typical in residential power distribution Note: This parameter is used to distinguish input modes but does not affect the protection zone calculation directly. Inputs Choose input method: - Voltage/Power: Enter voltage and load power - Power/Resistance: Enter power and line resistance Tip: This feature may be used for future extensions (e.g., ground resistance or induced voltage calculation), but it does not influence the geometric protection range. Height of Lightning Rod A The height of the primary lightning rod, in meters (m) or centimeters (cm). Usually the taller rod, defining the upper boundary of the protection zone. Height of Lightning Rod B The height of the second lightning rod, same unit as above. If the rods are of different heights, an unequal-height configuration is formed. Space Between Two Lightning Rods Horizontal distance between the two rods, in meters (m), denoted as (d). General rule: \( d \leq 1.5 \times (h_1 + h_2) \), otherwise effective protection cannot be achieved. Height of the Protected Object The height of the structure or equipment to be protected, in meters (m). This value must not exceed the maximum allowable height within the protection zone. Usage Recommendations Prefer equal-height rods for simpler design Keep spacing less than 1.5 times the sum of rod heights Ensure the protected object's height is below the protection zone For critical facilities, consider adding a third rod or using a meshed air-termination system

Calculate resistance (Ω) from V, I, P, or Z in DC and AC circuits using Ohm’s Law. Includes power factor handling for real-world accuracy. “Tendency of a body to oppose the passage of an electric current.” This is the fundamental definition of resistance: the property of a material that resists the flow of electric current. Accurately calculating resistance is essential for circuit design, troubleshooting, and energy efficiency analysis—whether in direct current (DC) or alternating current (AC) systems. Who Is This Tool For? Electrical engineers: for load modeling, protection coordination, and pre-simulation parameter estimation. Electricians and field technicians: to quickly verify equipment resistance and diagnose short circuits, ground faults, or insulation degradation. Students and electronics hobbyists: to understand practical applications of Ohm’s Law across different circuit conditions. Energy auditors and efficiency consultants: to evaluate operational efficiency using resistance and power factor relationships. Automation and control engineers: for precise impedance matching in sensor loops or PLC input modules. Typical Use Cases Scenario Application Motor winding inspection Measure voltage and current to back-calculate equivalent resistance and detect inter-turn short circuits. Heating element verification Given rated voltage and power (e.g., 220V / 1500W), compute theoretical resistance to assess aging or failure. Lighting system design Calculate equivalent resistance of LED drivers or incandescent loads to ensure voltage drop stays within limits. UPS and inverter testing In single-phase AC output, combine apparent power and power factor to isolate the resistive component of the load. Educational labs Help students visualize why V/I ≠ R in AC circuits due to reactance and phase shift. Calculation Principle The calculator is based on Ohm's Law and its derived forms. Resistance (R) can be computed using any of the following equivalent formulas: R = V / I R = P / (I^2) R = (V^2) / P R = Z / Power Factor Where: R: Resistance (Ω) V: Voltage (V) I: Current (A) P: Power (W) Z: Impedance (Ω) Power Factor: Ratio of active power to apparent power, ranging from 0 to 1 Note: In AC circuits, these formulas are only fully equivalent when the power factor equals 1 (purely resistive load). Parameter Details Current Type Direct Current (DC): Current flows steadily in one direction from positive to negative pole. Frequency is zero. In this case, impedance Z equals resistance R, and power factor is always 1. Alternating Current (AC): Current direction and amplitude vary periodically at a constant frequency. Single-phase system: Two conductors — one phase and one neutral (zero potential). Two-phase system: Two phase conductors; neutral may be present in three-wire configurations. Three-phase system: Three phase conductors; neutral is included in four-wire systems. This calculator currently supports DC and single-phase AC inputs. For three-phase systems, convert line-to-line voltage to phase voltage first: V_phase = V_line / sqrt(3), then treat as single-phase. Voltage Voltage is the difference in electric potential between two points. Input method depends on system type: Single-phase: Enter Phase-Neutral voltage. Two-phase / Three-phase: Enter Phase-Phase voltage. Example: A standard 220V household outlet is single-phase → input 220V. An industrial 380V supply is three-phase → for per-phase calculation, use 380 / sqrt(3) ≈ 220V. Current Current is the flow of electric charge through a conductor, measured in amperes (A). It is one of the most direct inputs for resistance calculation via R = V / I. Power Electric power is the rate at which energy is supplied or consumed by a component, measured in watts (W). In AC systems, distinguish between: Active Power (W): Real power that performs useful work. Reactive Power (VAR): Power used to establish magnetic/electric fields; does no real work. Apparent Power (VA): Vector sum of active and reactive power: S = sqrt(P^2 + Q^2). Important: The "P" in the formulas above refers to active power (W). If you input apparent power (VA), you must also provide the power factor; otherwise, results will be inaccurate. Power Factor Power Factor = cos(phi), where phi is the phase angle between voltage and current. Pure resistive load (e.g., heater, incandescent lamp): Power Factor = 1 Inductive or capacitive loads (e.g., motors, transformers): Power Factor < 1 (typically 0.7–0.95) In AC circuits, resistance is derived from impedance and power factor: R = Z * Power Factor = Z / (1 / Power Factor) Impedance Impedance (Z) is the total opposition to alternating current flow, combining resistance (R) and reactance (X), measured in ohms (Ω). The relationship is: Z = sqrt(R^2 + X^2) Therefore, resistance can only be extracted from impedance if the power factor (or phase angle) is known. People Also Ask (FAQ) Why can’t I use R = V / I directly in AC circuits? Because V / I gives you impedance (Z), not pure resistance (R). To get R, multiply by the power factor: R = (V / I) * cos(phi). Do I need to enter power factor for DC circuits? No. In DC, there is no phase shift, so power factor is always 1, and Z = R. Can I calculate resistance if I only know reactive power (VAR)? No. Resistance relates only to active power. You need either active power (W), or apparent power (VA) plus power factor. Can this tool be used for three-phase motors? Yes, but treat it per phase. Measure phase voltage and phase current, or convert line values using V_phase = V_line / sqrt(3), then apply single-phase formulas. Usage Tips Prefer voltage + current input: Most accurate and least prone to error. Ensure unit consistency: V in volts, I in amps, P in watts. Always enter power factor for AC: If omitted, the calculator assumes cos(phi) = 1, which overestimates resistance. Validate results: Example – a 1000W heater at 220V should have R ≈ (220^2)/1000 = 48.4 Ω. Large deviations suggest input errors. This tool adheres to international electrical standards (IEC 60050) and is suitable for education, engineering design, and field maintenance—helping users quickly and accurately determine the effective resistance in real-world circuits.

Free online calculator for active (real) power in DC and AC circuits. Supports voltage, current, resistance, impedance, power factor, or apparent/reactive power inputs. Active power, also known as real power, is the portion of electrical power that performs useful work in a circuit—such as producing heat, light, or mechanical motion. Measured in watts (W) or kilowatts (kW), active power represents the actual energy consumed by a load and is the basis for electricity billing. This tool calculates active power based on voltage, current, power factor, apparent power, reactive power, resistance, or impedance. It supports both single-phase and three-phase systems, making it ideal for motors, lighting, transformers, and industrial equipment. Parameter Description Parameter Description Current Type Select circuit type: • Direct Current (DC): Constant flow from positive to negative pole • Single-phase AC: One live conductor (phase) + neutral • Two-phase AC: Two phase conductors, optionally with neutral • Three-phase AC: Three phase conductors; four-wire system includes neutral Voltage Electric potential difference between two points. • Single-phase: Enter Phase-Neutral voltage • Two-phase / Three-phase: Enter Phase-Phase voltage Current Flow of electric charge through a material, unit: Amperes (A) Power Factor Ratio of active power to apparent power, indicating efficiency. Value between 0 and 1. Ideal value: 1.0 Apparent Power Product of RMS voltage and current, representing total power supplied. Unit: Volt-Ampere (VA) Reactive Power Energy alternately flowing in inductive/capacitive components without conversion to other forms. Unit: VAR (Volt-Ampere Reactive) Resistance Opposition to DC current flow, unit: Ohm (Ω) Impedance Total opposition to AC current, including resistance, inductance, and capacitance. Unit: Ohm (Ω) Calculation Principle The general formula for active power is: P = V × I × cosφ Where: P: Active power (W) V: Voltage (V) I: Current (A) cosφ: Power factor Other common formulas: P = S × cosφ P = Q / tanφ P = I² × R P = V² / R Example Calculation If voltage is 230V, current is 10A, and power factor is 0.8, then active power is: P = 230 × 10 × 0.8 = 1840 W Usage Recommendations Monitor active power regularly to assess equipment efficiency Use data from energy meters to analyze consumption patterns and optimize usage Consider harmonic distortion when dealing with nonlinear loads (e.g., VFDs, LED drivers) Active power is the basis for electricity billing, especially under time-of-use pricing schemes Combine with power factor correction to improve overall energy efficiency Common Input Combinations The calculator supports multiple input methods depending on available measurements: Voltage/Resistance: Use when current is not directly measurable Voltage/Impedance: For AC circuits with known Z and cosφ Current/Resistance: Direct calculation via P = I² × R Current/Impedance: Requires power factor to extract resistive component Voltage/Current: Most direct method, requires power factor for AC Apparent power/Reactive power: Use trigonometric relationship to find active power Apparent power: Only valid if power factor is known Reactive power: Must be combined with power factor or apparent power Supported Circuit Types Direct Current (DC): No phase shift, power factor = 1, impedance = resistance Single-phase AC: Common in homes and small commercial buildings Two-phase AC: Less common, used in specific industrial applications Three-phase AC: Standard for motors, transformers, and industrial power systems People Also Ask (FAQ) What is the difference between active power and apparent power? Active power (P) is the real power doing useful work (in watts). Apparent power (S) is the vector sum of active and reactive power (in VA). The ratio P/S is the power factor. Why is active power important for electricity billing? Utilities charge based on active power because it represents the actual energy consumed. Reactive power increases current but does no useful work, so it’s not billed directly. Can I calculate active power without knowing the power factor? Only if you know the resistance (for DC or purely resistive AC loads). Otherwise, you need either power factor or a combination of apparent/reactive power. How does this tool handle three-phase systems? For three-phase systems, enter line-to-line voltage and per-phase values. The tool assumes balanced loads and applies the standard three-phase formula: P = √3 × V_line × I_line × cosφ. Is this calculator suitable for non-linear loads like LED drivers? Yes, but keep in mind that non-linear loads may have distorted waveforms and lower power factors. Use measured RMS values and actual power factor for best accuracy. Calculation Example Given: Current type: Direct Current Voltage: 220 V Resistance: 20 Ω Using the formula: P = V² / R P = 220² / 20 = 48400 / 20 = 2420 W = 2.42 kW Result: Active power = 2.42 kW This matches the example shown in the interface screenshot. This tool adheres to international electrical standards (IEC 60050) and is suitable for engineers, technicians, students, and facility managers who need to calculate real power in various electrical systems.

Calculate power factor (PF) in AC circuits using voltage, current, active power, reactive power, resistance, or impedance. Supports single-phase, two-phase, and three-phase systems. Based on IEC standards for electrical efficiency analysis. Input Parameter Symbol Unit Required Combinations Voltage V V (volts) With current → S = V×I Current I A (amperes) With voltage → S = V×I Active Power P W (watts) With S or Q → PF = P/S or P/√(P²+Q²) Reactive Power Q VAR With P → PF = P / √(P² + Q²) Resistance R Ω (ohms) With Z → PF = R / Z Impedance Z Ω (ohms) With R → PF = R / Z Definition and Importance Power factor (PF) is the ratio of active power (P) to apparent power (S): PF = P / S = cosφ PF = 1.0: Purely resistive load (e.g., heater), no reactive power PF < 1.0: Inductive or capacitive load (e.g., motors, transformers) Low PF consequences: Increased line current Higher copper losses Reduced transformer capacity Utility penalties (common if PF < 0.85–0.90) Calculation Methods The calculator uses one of the following equivalent formulas based on available inputs: From P and S: PF = P / (V × I) From P and Q: PF = P / √(P² + Q²) From R and Z: PF = R / Z From phase angle φ: PF = cosφ (if angle is known) Note: DC circuits are not supported — power factor is always 1.0 in DC systems. System Support Single-phase AC Enter Phase-Neutral voltage and per-phase current. Two-phase AC Enter Phase-Phase voltage; assumes balanced load. Three-phase AC Enter Line-to-Line voltage (V LL) and line current (I L). The calculator assumes a balanced system and computes total apparent power as S = √3 × V LL × I L. Typical Applications Industrial motor systems: Verify PF before installing capacitor banks Energy audits: Identify low-efficiency loads for correction Electrical design: Size conductors and protection devices with accurate current estimates Utility compliance: Ensure PF ≥ 0.95 to avoid demand charges Educational labs: Demonstrate relationship between P, Q, S, and PF Usage Guidelines Use RMS values for voltage and current in AC systems For non-linear loads (e.g., VFDs, LED drivers), measured PF may include harmonic distortion effects If only apparent power (VA) is known, active power (W) must also be provided Resistance and impedance inputs assume linear, sinusoidal conditions Frequently Asked Questions (FAQ) What is the power factor and why is it important? The power factor (PF) is the ratio of active power to apparent power in AC circuits, indicating how effectively electrical energy is being used. A high PF means less wasted energy and more efficient use of electrical infrastructure. How do I calculate power factor if I only know voltage and current? To calculate power factor using just voltage and current, you need to measure or estimate the phase angle between them. The formula is: PF = cosφ, where φ is the phase angle. Alternatively, if you can also measure active power (P), then PF = P / (V × I). Can this calculator be used for DC systems? No, power factor is a concept applicable only to AC systems. In DC systems, the power factor is always 1 because there is no phase shift between voltage and current. What does a low power factor indicate about my system? A low power factor indicates that your system has significant reactive power, which means some of the electrical energy is being stored and then released by inductive or capacitive loads without doing useful work. This results in higher currents, increased losses, and possibly utility penalties. How can I improve the power factor in my facility? Improving power factor often involves adding capacitor banks to compensate for reactive power, especially in industrial settings with many motors. Reducing the number of lightly loaded inductive devices and ensuring proper maintenance of existing equipment can also help. Is this tool suitable for three-phase systems? Yes, this calculator supports single-phase, two-phase, and three-phase systems. For three-phase calculations, enter line-to-line voltage and per-phase current values. Ensure balanced load conditions for accurate results. Why might utilities charge extra fees for low power factors? Utilities may impose penalties on customers with low power factors because they require larger capacity infrastructure to deliver the same amount of active power. Low PF increases transmission losses and reduces grid efficiency. This calculator adheres to IEC 60050 terminology and is intended for use by electrical engineers, facility managers, technicians, and students in power systems analysis.

Free online reactive power calculator for AC systems.Calculate reactive power (Q) in VAR for AC systems using voltage, current, active power, apparent power, or power factor. Supports single-phase and three-phase configurations for power quality analysis, capacitor bank design, and energy efficiency optimization. Reactive power is the energy alternately flowing in inductive and capacitive components of an AC circuit without being transformed into other forms of energy. Although it does not perform useful work, reactive power is essential for maintaining voltage stability and system performance. Unit: Volt-Ampere Reactive (VAR). What Is Reactive Power and Why Is It Important? Reactive power (Q) sustains the electric and magnetic fields in motors, transformers, and other inductive loads. Without it, AC systems would collapse due to insufficient voltage support—even though it doesn’t directly consume energy. How Do You Calculate Reactive Power? Reactive power can be calculated using any of these formulas: Q = V × I × sinφ Q = √(S² − P²) Q = P × tanφ Where: V = Voltage (V), I = Current (A), φ = phase angle, P = Active power (W), S = Apparent power (VA) What Is the Unit of Reactive Power? The unit is Volt-Ampere Reactive (VAR). Larger systems use kVAR (kilovar) or MVAR (megavar). Does Reactive Power Consume Energy? No. Reactive power oscillates between source and load without net energy consumption. However, it increases current flow, causing higher losses and voltage drops in distribution lines. Can Reactive Power Be Negative? Yes. By convention: • Inductive loads (motors, transformers): Q > 0 (absorb VAR) • Capacitive loads (capacitor banks, cables): Q < 0 (supply VAR) How Does Reactive Power Affect Power Factor? Power factor (PF) = P / S = cosφ. Higher reactive power reduces PF, leading to inefficient power usage. Utilities often penalize low PF in industrial billing. Why Is Reactive Power Needed in AC Systems? It enables electromagnetic devices to function by establishing magnetic fields. Without reactive power, motors wouldn’t start, and transformers couldn’t transfer energy. How to Reduce Reactive Power in Industrial Systems? Use power factor correction via capacitor banks or synchronous condensers. This offsets inductive VAR with capacitive VAR, bringing PF closer to 1.0 and reducing line losses. Parameter Description Parameter Description Current Type Select the type of current: • Direct Current (DC): Constant flow; no reactive power • Alternating Current (AC): Reverses direction periodically System configurations: – Single-phase: Phase + neutral – Two-phase: Two phases (± neutral) – Three-phase: Three phases (± neutral) Voltage Electric potential difference. • Single-phase: Enter Phase-Neutral voltage • Two/Three-phase: Enter Phase-Phase voltage Current Flow of charge, measured in amperes (A) Active Power Useful power consumed (W). Formula: P = V × I × cosφ Apparent Power Total power supplied (VA). Formula: S = V × I Power Factor PF = P / S = cosφ. Ranges from 0 to 1. Resistance Opposition to DC current. R = ρ × l / A (Ω) Impedance Total AC opposition: Z = √(R² + (XL − XC)²) (Ω) Reactive Power Calculation Principle Reactive power \( Q \) is calculated as: Q = V × I × sinφ or Q = √(S² − P²) If the circuit is inductive, Q > 0 (absorbs reactive power); if capacitive, Q < 0 (supplies reactive power). Usage Recommendations Low power factor increases line losses and voltage drop in power systems Capacitor banks are commonly used in industrial plants to compensate reactive power Use this tool to calculate reactive power from known voltage, current, and power factor values Monitor Q to optimize transformer loading and avoid utility penalties Who Should Use This Tool? Electrical engineers: for load flow studies and PF correction design Plant maintenance teams: to audit motor efficiency and capacitor bank performance Students: to visualize the relationship between P, Q, and S in power triangles Energy consultants: to recommend cost-saving reactive power compensation strategies This calculator adheres to IEC 60050 standards and supports accurate reactive power analysis in real-world AC power systems.

Calculate impedance (Ω) in AC circuits using voltage, current, power, or resistance. Supports single, two, and three-phase systems for electrical engineering and power analysis. Impedance is the total opposition of a circuit to the flow of alternating electric current, measured in ohms (Ω). It includes resistance, inductive reactance, and capacitive reactance. Impedance is a key parameter in AC circuit analysis and affects voltage drop, current flow, and protection coordination. What Is Impedance and How Is It Different from Resistance? Resistance opposes DC current and is due to material properties. Impedance opposes AC current and includes resistance plus reactive components (inductive and capacitive). In DC, impedance equals resistance; in AC, they differ. How Do You Calculate Impedance in an AC Circuit? Use one of these formulas: Z = V / I Z = √(R² + (XL − XC)²) Z = S / (V × I) → when apparent power is known Where: Z = Impedance (Ω), V = Voltage (V), I = Current (A) R = Resistance (Ω), XL = Inductive reactance, XC = Capacitive reactance Parameter Description Parameter Description Current Type Select the type of current: • Direct Current (DC): Constant flow; impedance = resistance • Alternating Current (AC): Reverses direction periodically System configurations: – Single-phase: Phase + neutral – Two-phase: Two phases (± neutral) – Three-phase: Three phases (± neutral) Voltage Electric potential difference. • Single-phase: Enter Phase-Neutral voltage • Two/Three-phase: Enter Phase-Phase voltage Current Flow of charge, measured in amperes (A) Active Power Useful power consumed (W). Formula: P = V × I × cosφ Reactive Power Energy oscillation in inductors/capacitors (VAR). Formula: Q = V × I × sinφ Apparent Power Total power supplied (VA). Formula: S = V × I Power Factor PF = P / S = cosφ. Ranges from 0 to 1. Resistance Opposition to DC current. R = ρ × l / A (Ω) Impedance Calculation Principle Impedance \( Z \) is defined as: Z = V / I For a series RLC circuit: Z = √(R² + (XL − XC)²) If XL > XC, the circuit is inductive; if XC > XL, it is capacitive. What Is the Unit of Impedance? The unit is ohm (Ω), same as resistance. Larger values may be expressed in kΩ or MΩ. Can Impedance Be Negative? No. Impedance is always a positive value because it represents magnitude of opposition. However, phase angle can be negative if the circuit is capacitive. How Does Impedance Affect AC Circuits? Impedance determines the amount of current flowing for a given voltage. High impedance reduces current, while low impedance increases it. It also affects power factor, voltage regulation, and fault current levels. What Is the Formula for Total Impedance in a Series RLC Circuit? In a series RLC circuit: Z = √(R² + (XL − XC)²) Where: XL = 2πfL XC = 1/(2πfC) f = Frequency (Hz), L = Inductance (H), C = Capacitance (F) Why Is Impedance Important in Power Systems? Impedance affects short-circuit current magnitude, voltage drop under load, transformer loading, and protective device settings. Accurate impedance values are essential for system design, relay coordination, and stability studies. Usage Recommendations Impedance affects short-circuit current, voltage drop, and protection device selection Low power factor increases line losses; consider reactive power compensation Use this tool to back-calculate unknown impedance values from measured voltage and current Verify impedance values during commissioning and maintenance to ensure system reliability This calculator adheres to IEC 60050 standards and supports accurate impedance analysis in real-world AC power systems.

Calculate apparent power (VA) in AC/DC circuits using voltage, current, power factor, resistance, or impedance. Supports single, two, and three-phase systems for electrical engineering. Apparent power is the vector sum of active and reactive power, representing total power supplied by the source. It is measured in Volt-Ampere (VA) and is crucial for sizing transformers, generators, and circuit breakers. What Is Apparent Power and How Is It Calculated? Apparent power (S) is the total power flowing in a circuit, regardless of whether it performs useful work. It is calculated as: S = √(P² + Q²) S = V × I (single-phase) S = √3 × V × I (three-phase) Where: P = Active power (W), Q = Reactive power (VAR) V = Voltage (V), I = Current (A) What Is the Unit of Apparent Power? The unit is Volt-Ampere (VA). Larger systems use kVA (kilovolt-ampere) or MVA (megavolt-ampere). How Do You Calculate Apparent Power in a Three-Phase System? In a three-phase system: S = √3 × VL-L × IL Where: VL-L = Line-to-line voltage IL = Line current Note: This assumes balanced loads. For unbalanced systems, sum individual phase powers. Is Apparent Power the Same as Real Power? No. Real (active) power (P) is the power that performs useful work (e.g., heat, motion). Apparent power (S) includes both real and reactive components. They are equal only when power factor = 1. What Is the Relationship Between Apparent, Active, and Reactive Power? They form a right triangle known as the **power triangle**: Active power (P) = S × cosφ Reactive power (Q) = S × sinφ Apparent power (S) = √(P² + Q²) Where φ is the phase angle between voltage and current. Why Is Apparent Power Important in Electrical Systems? Apparent power determines the capacity of electrical equipment like transformers, cables, and switchgear. Utilities use it to bill commercial/industrial customers and assess system loading. Parameter Description Parameter Description Current Type Select the type of current: • Direct Current (DC): Constant flow; S = V × I • Alternating Current (AC): Reverses direction periodically System configurations: – Single-phase: Phase + neutral – Two-phase: Two phases (± neutral) – Three-phase: Three phases (± neutral) Voltage Electric potential difference. • Single-phase: Enter Phase-Neutral voltage • Two/Three-phase: Enter Phase-Phase voltage Current Flow of charge, measured in amperes (A) Active Power Useful power consumed (W). Formula: P = V × I × cosφ Reactive Power Energy oscillation in inductors/capacitors (VAR). Formula: Q = V × I × sinφ Power Factor PF = P / S = cosφ. Ranges from 0 to 1. Resistance Opposition to DC current. R = ρ × l / A (Ω) Impedance Total AC opposition: Z = √(R² + (XL − XC)²) (Ω) Apparent Power Calculation Principle Apparent power \( S \) is defined as: S = √(P² + Q²) Alternatively: S = V × I (single-phase) S = √3 × V × I (three-phase) S = V² / R (for DC or purely resistive AC) S = I² × Z Usage Recommendations Use this tool to size transformers, generators, and UPS systems Monitor apparent power to prevent overloading equipment Enter any two known values (e.g., V & I, P & PF) to compute missing parameters For three-phase systems, ensure line-to-line voltage is used This calculator adheres to IEC 60050 standards and supports accurate apparent power analysis in real-world electrical systems.

Calculate torque (N·m, ft·lbf) or power (kW, HP) from RPM using the mechanical power-torque-speed relationship. Supports motors, engines, pumps, turbines, and gear systems for engineering design and analysis. This tool calculates torque (T) in rotating mechanical systems using power (P) and rotational speed (n). It is commonly used in mechanical engineering for sizing drives, gears, couplings, and transmission components. Commonly used in mechanical engineering and motor selection for sizing drives, gears, and transmission systems. How Do You Calculate Torque from Power and RPM? Use the following formula: T = P × 9549 / n Where: T = Torque (N·m) P = Power (kW) n = Rotational speed (rpm) For power in horsepower (HP), use: T = P × 5252 / n Where P is in HP. What Is the Formula for Motor Torque? The standard formula for calculating torque in rotating machinery is: SI units: T = P × 9549 / n (N·m) Imperial units: T = P × 5252 / n (ft·lbf) Where P is power in kW or HP, and n is RPM. What Is the Unit of Torque? The SI unit is Newton-meter (N·m). Other common units include: kgf·m (kilogram-force meter) ft·lbf (foot-pound force) in·lbf (inch-pound force) This calculator supports all four units for easy conversion. Is Torque Directly Proportional to Power? Yes, but only when speed is constant. Torque is directly proportional to power and inversely proportional to speed. For a given power output, increasing speed reduces torque, and vice versa. How Does Torque Relate to Speed in an Electric Motor? In electric motors, torque and speed have an inverse relationship at constant power: At low speed: high torque (e.g., startup) At high speed: low torque (e.g., steady-state operation) This is why motors are often designed with specific torque-speed curves for different applications. What Is Rated Torque vs Peak Torque? Rated torque is the continuous torque a motor can deliver at full load without overheating. It corresponds to the rated power and speed. Peak torque is the maximum torque a motor can produce momentarily (e.g., during acceleration). It is typically higher than rated torque but not sustainable. Parameter Description Parameter Description Calculation Mode Select whether to calculate torque from power and RPM, or power from torque and RPM. Power Mechanical power output of the motor. Units: kW, HP, W Revolutions (RPM) Rotational speed of the motor shaft in revolutions per minute. Torque Rotational force produced by the motor. Units: N·m, kgf·m, ft·lbf, in·lbf Torque Calculation Principle The fundamental relationship between torque, power, and speed is: T = P × 9549 / n Where: T = Torque (N·m) P = Power (kW) n = Rotational speed (rpm) Note: This assumes constant power output and ideal conditions. For AC motors, this typically represents the rated torque at full load. Usage Recommendations Use this tool to size motors, gearboxes, and couplings Convert between metric and imperial units for international projects Verify motor specifications before installation Ensure torque values match application requirements (e.g., conveyor, pump, fan) This calculator adheres to ISO standards and supports accurate torque analysis in real-world mechanical systems.

Calculate accurate battery runtime using Peukert effect, depth of discharge (DoD), and series/parallel configurations. Supports lead-acid, AGM, gel, and lithium-ion for solar, EV, UPS, and off-grid systems. This tool estimates the theoretical runtime of a battery under a given load by considering configuration, capacity, discharge rate, and battery chemistry. Ideal for off-grid systems, backup power, electric vehicles, and portable electronics. How Do You Calculate Battery Runtime? The basic formula is: Runtime (hours) = (Total Capacity × DoD) / Load Current Where: - Total Capacity = Number of Batteries × Capacity per Battery × Connection Factor - DoD = Depth of Discharge (% or Ah) - Load Current = Load Power / Voltage (if in watts) Peukert Equation for Realistic Runtime The accurate runtime is calculated using: t = (C₀ × Tᵏ) / Iᵏ Where: t = Actual runtime (hours) C₀ = Rated capacity of a single battery (Ah, e.g., 100 Ah @ 20h) T = Rated discharge time (hours, typically 20 h for lead-acid) I = Total load current (A) = Load Power (W) / System Voltage (V) k = Peukert constant (see table below) Note: For multi-battery systems, total capacity and voltage are first computed based on series/parallel configuration before applying this formula. What Is the Peukert Effect and How Does It Affect Battery Life? The Peukert effect describes how battery capacity decreases as discharge rate increases. Higher currents reduce usable capacity, especially in lead-acid batteries. Peukert constant (k) > 1.0 indicates capacity loss at high rates Lithium-ion batteries have k ≈ 1.0 → less affected Older batteries have higher k values due to internal resistance increase This calculator uses the Peukert equation to provide more accurate runtime estimates than simple division. How Does Battery Connection (Series vs Parallel) Affect Runtime? Battery connections change total voltage and capacity: Series: Voltages add up, capacity stays the same → higher voltage, same runtime Parallel: Voltage stays the same, capacities add up → same voltage, longer runtime Series-Parallel: Combines both effects → higher voltage and longer runtime Example: Two 12V 100Ah batteries in parallel = 12V 200Ah → doubles runtime. What Is Depth of Discharge (DoD) and Why Is It Important? Depth of Discharge (DoD) is the percentage of battery capacity used during a cycle: DoD = (Used Capacity / Total Capacity) × 100% Higher DoD = longer runtime but shorter battery lifespan Lead-acid: typically limited to 50% DoD to extend cycle life Lithium-ion: can safely reach 80–100% DoD Exceeding recommended DoD reduces battery health and performance Always consider manufacturer recommendations for optimal battery longevity. How Does Battery Age Affect Runtime? As batteries age, their internal resistance increases and capacity degrades: Capacity drops by 10–20% per year in lead-acid batteries Peukert constant increases with age → faster capacity loss at high loads Efficiency decreases → more energy lost as heat This calculator assumes new battery conditions. For aged batteries, reduce rated capacity by 10–20% for realistic estimates. Can I Use This Calculator for Lithium-Ion Batteries? Yes! The calculator supports all battery types, including lithium-ion: Use Peukert constant ≈ 1.0–1.28 (closer to 1.0 than lead-acid) Allow higher DoD (up to 100%) without significant damage Less sensitive to discharge rate → Peukert effect is minimal However, always check manufacturer specs for temperature limits and charge/discharge cycles. Parameter Description Parameter Description Connection Select battery configuration: • Series: Voltages add, capacity unchanged • Parallel: Voltage unchanged, capacities add • Single: One battery Number of Batteries Total number of batteries in the system. Voltage (V) Nominal voltage of a single battery (e.g., 12V, 24V). Capacity (Ah) Rated capacity of a single battery in ampere-hours (Ah). Load (W or A) Power consumption of connected device: • In watts (W): suitable for most appliances • In amperes (A): when operating current is known Peukert Constant (k) Coefficient for capacity correction at different discharge rates: • Lead-Acid: 1.1–1.3 • Gel: 1.1–1.25 • Flooded: 1.2–1.5 • Lithium-Ion: 1.0–1.28 Depth of Discharge (DoD) Percentage of capacity discharged relative to full charge. • Can be entered as % or Ah • Typical values: 50% (lead-acid), 80–100% (lithium-ion) Rated Discharge Time Time (in hours) over which the rated capacity is measured (usually 20h for lead-acid). Battery Runtime Calculation Principle The calculator uses the following steps: Compute total system voltage and capacity based on connection type Apply Peukert equation to correct capacity for actual discharge rate Calculate available energy: E = V × C × DoD Divide by load power to get runtime: t = E / P For DC systems, efficiency is assumed 100%. Real-world losses (wires, inverters) may reduce actual runtime by 10–20%. Usage Recommendations Use for sizing UPS, solar systems, EVs, and portable power stations Consider safety margins: multiply runtime by 0.8–0.9 for real-world conditions Limit DoD to preserve battery life (especially for lead-acid) Account for temperature effects: cold reduces capacity by 20–30% Regularly recalibrate based on observed performance This calculator adheres to IEEE standards and supports accurate battery runtime estimation in real-world applications.

Calculate heat energy (joules) dissipated in resistors using Joule's Law: Q = I²Rt. Essential for circuit design, thermal safety, and power loss analysis in electrical systems. This tool calculates the heat energy (Q) dissipated as thermal energy in resistive elements of an electrical circuit using Joule’s Law. Essential for thermal management, component selection, and fire risk prevention in electronics and power systems. What Is Joule’s Law of Heating? Joule’s Law states that the heat energy generated in a resistor is directly proportional to: The square of the current (I²) The resistance (R) The time the current flows (t) The formula is: Q = I² × R × t Alternatively, since power P = I²R, we can also write: Q = P × t Where: Q = Heat energy (joules, J) I = Current (amperes, A) R = Resistance (ohms, Ω) t = Time (seconds, s) P = Power (watts, W) How Do You Calculate Heat Energy from Current and Resistance? Use Q = I² × R × t when you know: Current flowing through the resistor Resistance value Duration of current flow Example: I = 2 A, R = 10 Ω, t = 5 s → Q = (2)² × 10 × 5 = 200 J Why Does a Resistor Get Hot When Current Flows Through It? As electrons move through a resistive material: They collide with atoms in the lattice Kinetic energy is converted into vibrational energy This manifests as heat (thermal energy) This process is irreversible — electrical energy is permanently lost as heat. Is Heat Proportional to Current or Current Squared? Heat is proportional to the square of the current. This means: Doubling current → 4× more heat Tripling current → 9× more heat This quadratic relationship makes overcurrent a major cause of overheating and component failure. What Is the Unit of Heat Energy in Circuits? The SI unit is the joule (J). Since 1 watt = 1 joule/second: A 1W resistor running for 1 second dissipates 1 J For larger systems, kilojoules (kJ) or watt-hours (Wh) may be used How Is Power Related to Heat Dissipation? Electrical power consumed by a resistor is entirely converted into heat: P = I²R = V²/R = VI Therefore, total heat energy over time is simply: Q = P × t This is why power rating (e.g., ¼W, 1W, 5W) is critical when selecting resistors. Parameter Definitions Parameter Description Resistance (R) Opposition to current flow, measured in ohms (Ω). Higher R → more heat for same current. Example: 100 Ω resistor limits current and generates heat. Current (I) Flow of electric charge, in amperes (A). Heat ∝ I² — doubling current quadruples heat! Example: 1 A vs. 2 A → 4× more heat. Power (P) Rate of energy conversion, in watts (W). 1 W = 1 J/s. Can be calculated as P = I²R or P = V × I. Example: A 5W LED dissipates 5 J every second. Time (t) Duration of current flow, in seconds (s). Longer time → more total heat. Example: 60 s produces 60× more heat than 1 s. Application Scenarios Designing heating elements (e.g., electric stoves, hair dryers, space heaters) Estimating power loss in transmission lines and connectors Predicting temperature rise in PCB traces, ICs, and resistors Selecting resistors with adequate power ratings to avoid burnout Performing safety analysis to prevent overheating and fire hazards Understanding thermal behavior in battery packs and motor windings Important Notes This model assumes all electrical energy is converted to heat (ideal resistor) For AC circuits, use RMS current values in the formula Always include a safety margin (e.g., operate at ≤70% of max power rating) This calculator adheres to fundamental principles of electromagnetism and thermodynamics, providing reliable estimates for educational and engineering purposes.