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 using voltage, current, power, or impedance in AC/DC circuits. “Tendency of a body to oppose the passage of an electric current.” Calculation Principle Based on Ohm's Law and its derivatives: ( R = frac{V}{I} = frac{P}{I^2} = frac{V^2}{P} = frac{Z}{text{Power Factor}} ) Where: R: Resistance (Ω) V: Voltage (V) I: Current (A) P: Power (W) Z: Impedance (Ω) Power Factor: Ratio of active to apparent power (0–1) Parameters Current Type Direct Current (DC): Current flows steadily from positive to negative pole. Alternating Current (AC): Direction and amplitude vary periodically with constant frequency. Single-phase system: Two conductors — one phase and one neutral (zero potential). Two-phase system: Two phase conductors; neutral is distributed in three-wire systems. Three-phase system: Three phase conductors; neutral is included in four-wire systems. Voltage Difference in electric potential between two points. Input method: • Single-phase: Enter Phase-Neutral voltage • Two-phase / Three-phase: Enter Phase-Phase voltage Current Flow of electric charge through a material, measured in amperes (A). Power Electric power supplied or absorbed by a component, measured in watts (W). Power Factor Ratio of active power to apparent power: ( cos phi ), where ( phi ) is the phase angle between voltage and current. Value ranges from 0 to 1. Pure resistive load: 1; inductive/capacitive loads: < 1. Impedance Total opposition to alternating current flow, including resistance and reactance, measured in ohms (Ω).

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), it 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: 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

Power Factor Calculation The power factor (PF) is a critical parameter in AC circuits that measures the ratio of active power to apparent power, indicating how efficiently electrical energy is being used. An ideal value is 1.0, meaning voltage and current are in phase with no reactive losses. In real systems, especially those with inductive loads (e.g., motors, transformers), it is typically less than 1.0. This tool calculates the power factor based on input parameters such as voltage, current, active power, reactive power, or impedance, supporting single-phase, two-phase, and three-phase systems. 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) Active Power Actual power consumed by the load and converted into useful work (heat, light, motion). Unit: Watts (W) Reactive Power Energy alternately flowing in inductive/capacitive components without conversion to other forms. Unit: VAR (Volt-Ampere Reactive) Apparent Power Product of RMS voltage and current, representing total power supplied. Unit: VA (Volt-Ampere) 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 Power factor is defined as: PF = P / S = cosφ Where: - P: Active power (W) - S: Apparent power (VA), S = V × I - φ: Phase angle between voltage and current Alternative formulas: PF = R / Z = P / √(P² + Q²) Where: - R: Resistance - Z: Impedance - Q: Reactive power Higher power factor means better efficiency and lower line losses Low power factor increases current, reduces transformer capacity, and may incur utility penalties Usage Recommendations Industrial users should monitor power factor regularly; target ≥ 0.95 Use capacitor banks for reactive power compensation to improve PF Utilities often charge extra fees for power factors below 0.8 Combine with voltage, current, and power data to assess system performance

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, it is essential for maintaining voltage stability and system performance. Unit: Volt-Ampere Reactive (VAR). Parameter Description Current Type Select the type of current: - Direct Current (DC): Constant flow from positive to negative pole; no reactive power - Alternating Current (AC): Reverses direction and amplitude periodically at constant frequency System configurations: - Single-phase: Two conductors (phase + neutral) - Two-phase: Two phase conductors; neutral may be distributed - Three-phase: Three phase conductors; four-wire system includes neutral Note: Reactive power only exists in AC circuits. Voltage Electric potential difference between two points. - For single-phase: Enter Phase-Neutral voltage - For two-phase or three-phase: Enter Phase-Phase voltage Current Flow of electric charge through a material, measured in amperes (A). Active Power The power actually consumed by a load and converted into useful energy (e.g., heat, motion). Unit: Watts (W) Formula: P = V × I × cosφ Apparent Power The product of RMS voltage and current, representing total power supplied by the source. Unit: Volt-Ampere (VA) Formula: S = V × I Power Factor Ratio of active power to apparent power, indicating efficiency of power usage. Formula: PF = P / S = cosφ where φ is the phase angle between voltage and current. Value ranges from 0 to 1. Resistance Opposition to current flow due to material properties, length, and cross-sectional area. Unit: Ohm (Ω) Formula: R = ρ × l / A Impedance Total opposition of a circuit to alternating current, including resistance, inductive reactance, and capacitive reactance. Unit: Ohm (Ω) Formula: Z = √(R² + (XL - XC)²) Reactive Power Calculation Principle Reactive power \( Q \) is calculated as: Q = V × I × sinφ or: Q = √(S² - P²) Where: - S: Apparent power (VA) - P: Active power (W) - φ: Phase angle between voltage and current 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

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, and is a key parameter in AC circuit analysis. Parameter Description Current Type Select the type of current: - Direct Current (DC): Constant flow from positive to negative pole - Alternating Current (AC): Reverses direction and amplitude periodically at constant frequency System configurations: - Single-phase: Two conductors (phase + neutral) - Two-phase: Two phase conductors; neutral may be distributed - Three-phase: Three phase conductors; four-wire system includes neutral Note: Impedance is only meaningful in AC circuits; in DC, impedance equals resistance. Voltage Electric potential difference between two points. - For single-phase: Enter Phase-Neutral voltage - For two-phase or three-phase: Enter Phase-Phase voltage Current Flow of electric charge through a material, measured in amperes (A). Active Power The power actually consumed by a load and converted into useful energy (e.g., heat, motion). Unit: Watts (W) Formula: P = V × I × cosφ Reactive Power Power that alternately flows in inductors or capacitors without being transformed into other forms of energy. Unit: Volt-Ampere Reactive (VAR) Formula: Q = V × I × sinφ Apparent Power The product of RMS voltage and current, representing total power supplied by the source. Unit: Volt-Ampere (VA) Formula: S = V × I Power Factor Ratio of active power to apparent power, indicating efficiency of power usage. Formula: PF = P / S = cosφ where φ is the phase angle between voltage and current. Value ranges from 0 to 1. Resistance Opposition to current flow due to material properties, length, and cross-sectional area. Unit: Ohm (Ω) Formula: R = ρ × l / A Impedance Calculation Principle Impedance \( Z \) is defined as: Z = V / I For a series RLC circuit: Z = √(R² + (XL - XC)²) Where: - R: Resistance - XL = 2πfL: Inductive reactance - XC = 1/(2πfC): Capacitive reactance - f: Frequency (Hz) - L: Inductance (H) - C: Capacitance (F) If XL > XC, the circuit is inductive; if XC > XL, it is capacitive. Usage Recommendations Impedance affects short-circuit current, voltage drop, and protection device selection in power systems Low power factor increases line losses; consider reactive power compensation Use this tool to back-calculate unknown impedance values from measured voltage and current

This tool calculates the apparent power (S) in an electrical circuit based on voltage, current, and power factor. It also supports calculation using resistance, impedance, or reactive power depending on available data. Apparent power is the vector sum of active and reactive power: S = √(P² + Q²) Where: - S = Apparent power (VA) - P = Active power (W) - Q = Reactive power (VAR) Alternatively: S = V × I × √3 (for three-phase systems) S = V × I (for single-phase systems) Input Parameters: • Current type – Select the type of electrical current: - Direct Current (DC): Constant flow from positive to negative pole. - Alternating Current (AC): - Single-phase: One phase conductor and one neutral. - Two-phase: Two phase conductors. - Three-phase: Three phase conductors (three-wire or four-wire with neutral). • Voltage – Electric potential difference between two points. - For single-phase: Enter Phase-Neutral voltage. - For two-phase or three-phase: Enter Phase-Phase voltage. • Current – Flow of electric charge through a material (A). • Active power (P) – Real power consumed by the load (W). • Reactive power (Q) – Power that oscillates in reactive components (inductors/capacitors) without doing work (VAR). • Power factor (cos φ) – Ratio of active power to apparent power. - Value between 0 and 1. - cos φ = φ = phase angle between voltage and current. • Resistance (R) – Opposition to DC current flow (Ω). • Impedance (Z) – Total opposition to AC current flow, including resistance and reactance (Ω). Note: You only need to enter two known values to calculate the rest. The tool will automatically compute missing parameters.

This tool calculates the maximum torque (T) of an electric motor based on its rated power (P) and nominal rotational speed (n). It is commonly used in mechanical engineering and motor selection. The relationship between torque, power, and speed is: T = P × 9549 / n Where: - T = Torque (Nm) - P = Power (kW) - n = Rotational speed (rpm) Note: - This formula assumes constant power output. - Torque is inversely proportional to speed: higher speed means lower torque for the same power. - For AC motors, this typically represents the rated torque at full load.

This calculator estimates the theoretical runtime of a battery under a given load. By entering battery configuration and load parameters, you can determine the expected duration of power supply. Parameter Description Connection -Select the battery connection type: --Series: Voltages add up, capacity remains unchanged --Parallel: Voltage remains constant, capacities add up Number of Batteries -Total number of batteries in the system. The total voltage and capacity are calculated based on the connection type. Voltage (V) -Nominal voltage of a single battery, in volts (V). Capacity (Ah) -Rated capacity of a single battery, in ampere-hours (Ah). Load (W or A) -Power consumption of the connected device. Two input options: --Power (W): In watts, suitable for most appliances --Current (A): In amperes, when operating current is known Peukert Constant (k) -A coefficient used to correct for capacity loss at higher discharge rates. Typical values by battery type: --Lead-Acid: 1.1 – 1.3 --Gel: 1.1 – 1.25 --Flooded: 1.2 – 1.5 --Lithium-Ion: 1.0 – 1.28 -An ideal battery has a Peukert constant of 1.0. Real batteries have values greater than 1.0, which typically increase with age. Depth of Discharge (DoD) -The percentage of battery capacity that has been discharged relative to full capacity.DoD = 100% - SoC (State of Charge). -Can be expressed in percent (%) or ampere-hours (Ah). In some cases, actual capacity exceeds rated capacity, so DoD may exceed 100%.

Calculate the heat energy dissipated in resistive elements of a circuit. "Power dissipated in the form of heat in the resistive elements of the circuit." Key Formula: Joule's Law Q = I² × R × t or 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) Note: Both formulas are equivalent. Use $ Q = I^2 R t $ when you know current and resistance. Parameter Definitions 1. Resistance (R) The tendency of a material to oppose the flow of electric current, measured in ohms (Ω). Higher resistance leads to more heat generation for the same current. Example: A 100 Ω resistor limits current and produces heat. 2. Power (P) Electrical power supplied or absorbed by a component, measured in watts (W). 1 watt = 1 joule per second. You can calculate it as: P = I² × R or P = V × I Example: A 5W LED uses 5 joules every second. 3. Current (I) The flow of electric charge through a material, measured in amperes (A). Heat is proportional to the square of the current — doubling current quadruples heat! Example: 1 A, 2 A, 10 A — each produces vastly different heat levels. 4. Time (t) Duration for which current flows, measured in seconds (s). Longer time → more total heat generated. Example: 1 second vs. 60 seconds → 60x more heat. How It Works When current flows through a resistor: Electrons move through the material They collide with atoms, losing kinetic energy This energy is transferred as vibrational energy → heat Total heat depends on: current, resistance, and duration The process is irreversible — electrical energy is lost as heat. Application Scenarios Designing heating elements (e.g., electric stoves, hair dryers) Calculating power loss in transmission lines Estimating temperature rise in PCB traces and components Selecting appropriate resistors based on power rating Understanding why devices get hot during operation Safety analysis in circuits (preventing overheating and fire risk)