This web-based tool converts battery charge capacity from Amp-hours (Ah) to Kilowatt-hours (kWh), and vice versa. It is ideal for use in electric vehicles, home energy storage systems, off-grid solar setups, and industrial battery applications. How Battery Energy Is Calculated The fundamental formula used by this calculator is: kWh = Ah × Voltage (V) ÷ 1000 Ah (Amp-hours): Measure of charge capacity — how much current a battery can deliver over time. Voltage (V): Electrical potential difference across the battery terminals. kWh (Kilowatt-hours): Unit of energy representing total stored or delivered power. For example: A 50 Ah battery at 48 V has an energy capacity of: 50 × 48 ÷ 1000 = 2.4 kWh Key Parameters Explained Parameter Description Capacity Battery capacity in Amp-hours (Ah), indicating how much current it can deliver over time. Voltage (V) Electrical potential difference between two points, measured in volts (V). Essential for energy calculation. Depth of Discharge (DoD) Percentage of battery capacity that has been discharged relative to total capacity. - Complementary to State of Charge (SoC): SoC + DoD = 100% - Can be expressed as % or in Ah - Actual capacity may exceed nominal, so DoD can go beyond 100% (e.g., up to 110%) State of Charge (SoC) Remaining battery charge as a percentage of total capacity. 0% = empty, 100% = full. Depleted Capacity Total amount of energy drawn from the battery, in kWh or Ah. Example Calculation Battery: 50 Ah, 48 V Depth of Discharge (DoD): 80% Total Energy = 50 × 48 ÷ 1000 = 2.4 kWh Depleted Energy = 2.4 × 80% = 1.92 kWh Remaining Energy = 2.4 − 1.92 = 0.48 kWh State of Charge (SoC) = 100% − 80% = 20% Use Cases Estimating EV driving range based on battery size and average consumption Designing home energy storage systems with accurate kWh capacity planning Calculating available energy in off-grid solar setups with battery backup Analyzing battery cycle life and efficiency under different DoD levels Comparing battery specs across manufacturers using consistent units Frequently Asked Questions How do I convert Ah to kWh? To convert Amp-hours (Ah) to Kilowatt-hours (kWh), multiply the Ah value by the battery voltage (in volts), then divide by 1000: kWh = Ah × V ÷ 1000 For example: 100 Ah × 220 V ÷ 1000 = 22 kWh What is the difference between Ah and kWh? Ah (Amp-hours) measures charge capacity — how long a battery can supply current. kWh (Kilowatt-hours) measures energy — how much power it can deliver over time. They are related through voltage: kWh = Ah × V ÷ 1000 Can I use this calculator for lithium batteries? Yes. This calculator works for all battery types including lithium-ion, lead-acid, LiFePO₄, and NiMH, as long as you know the nominal voltage and Ah rating. What does Depth of Discharge (DoD) mean? Depth of Discharge (DoD) is the percentage of battery capacity that has been used. For example, a 50 Ah battery discharged to 10 Ah has a DoD of 80%. Higher DoD means more usable energy but may reduce battery lifespan. Is 100% DoD safe for my battery? No. Most batteries should not be regularly discharged to 100% DoD. Recommended limits are: Lithium-ion: 80–90% DoD Lead-acid: 50% DoD LiFePO₄: Up to 100% DoD (with caution) Deep cycling reduces cycle life. How many kWh is a 100 Ah battery? It depends on the voltage. For example: 100 Ah × 12 V ÷ 1000 = 1.2 kWh 100 Ah × 24 V ÷ 1000 = 2.4 kWh 100 Ah × 48 V ÷ 1000 = 4.8 kWh Reference Standards IEC 61960: Secondary cells and batteries containing alkaline or other non-acid electrolytes UL 1973: Standard for Stationary Batteries IEEE 1188: Guide for Maintenance, Testing, and Replacement of Valve Regulated Lead-Acid Batteries

This web-based tool converts between reactive power (VAR) and capacitance (µF) for both single-phase and three-phase AC systems. It supports power factor correction calculations, capacitor sizing, and electrical system commissioning. Core Formulas The calculator uses the following standard electrical engineering formulas: Single-Phase System Q (VAR) = 2π × f × C (µF) × V² × 10⁻⁶ Three-Phase System Q (VAR) = 3 × 2π × f × C (µF) × V² × 10⁻⁶ Q: Reactive power in VAR f: Frequency in Hz (typically 50 or 60 Hz) C: Capacitance in microfarads (µF) V: Voltage in volts (V) 10⁻⁶: Conversion factor from µF to farads Input Parameters Parameter Description Reactive Power (VAR) Reactive power supplied by the capacitor, in VAR. Used to calculate required capacitance (µF). Voltage (V) - Single-phase: Phase-to-neutral voltage - Three-phase: Line-to-line (phase-to-phase) voltage Unit: Volts (V) Frequency (Hz) Number of cycles per second. Common values: 50 Hz (Europe), 60 Hz (North America). Example Calculation Single-phase system: Voltage V = 230 V Frequency f = 50 Hz Capacitance C = 40 µF Reactive power: Q = 2π × 50 × 40 × (230)² × 10⁻⁶ ≈ 6.78 kVAR Reverse calculation: Given Q = 6.78 kVAR, V = 230 V, f = 50 Hz Solve for C: C = Q / (2π × f × V² × 10⁻⁶) ≈ 40 µF Use Cases Power factor correction in industrial plants and commercial buildings Capacitor bank sizing for motor loads, transformers, and lighting circuits Electrical system commissioning and performance verification Academic learning and exam preparation in electrical engineering Energy efficiency audits to reduce utility penalties Frequently Asked Questions How do I convert VAR to µF? To convert reactive power (VAR) to capacitance (µF), use the formula: C (µF) = Q (VAR) ÷ (2π × f × V² × 10⁻⁶) For three-phase: multiply denominator by 3. Example: For 1000 VAR at 230 V, 50 Hz → C ≈ 1000 ÷ (2π × 50 × 230² × 10⁻⁶) ≈ 61.4 µF What is the difference between VAR and µF? VAR (Volt-Ampere Reactive) is a unit of reactive power — the amount of energy stored and released by capacitors or inductors. µF (microfarad) is a unit of capacitance — a physical property of the capacitor. They are related through voltage and frequency via the formula above. Can I use this calculator for three-phase systems? Yes. The calculator supports both single-phase and three-phase systems. For three-phase, select the appropriate option and input line-to-line voltage. The formula automatically multiplies by 3. Why is power factor correction important? Power factor correction improves system efficiency by reducing reactive current, which: Lowers electricity bills (reduces demand charges) Reduces losses in cables and transformers Increases available capacity in existing systems Improves voltage stability How many µF is needed for 1 kVAR? It depends on voltage and frequency. For example: At 230 V, 50 Hz: ~61.4 µF At 480 V, 60 Hz: ~14.4 µF At 240 V, 60 Hz: ~33.5 µF Use this calculator to get precise values for your system. What happens if I install too large a capacitor? Over-correction leads to overcompensation, where the power factor becomes leading (greater than 1). This can cause: Voltage rise Resonance with system inductance Damage to equipment Possible tripping of protection devices Always size capacitors based on actual load requirements. Reference Standards IEC 60831: Specifications for shunt power capacitors for AC systems IEEE 141: Recommended Practice for Electric Power Distribution for Industrial Plants NEC Article 460: Capacitors BS EN 60831: Power capacitors for AC systems

Convert delta (Δ) to wye (Y) or vice versa using the standard Δ-Y transformation formulas. Calculate equivalent resistances for circuit simplification in three-phase systems, bridge networks, and academic problems. Supports both directions with step-by-step results. Core Formulas (Δ → Y) The Δ-Y transformation preserves terminal voltages and currents while replacing the delta network with an equivalent star network: Ra = (Rab × Rbc) / (Rab + Rbc + Rac) Rb = (Rbc × Rac) / (Rab + Rbc + Rac) Rc = (Rac × Rab) / (Rab + Rbc + Rac) Where: Rab, Rbc, Rac: Resistances in the delta configuration (Ω) Ra, Rb, Rc: Equivalent resistances in the wye configuration (Ω) Reverse Formula (Y → Δ) To convert from star to delta: Rab = (Ra × Rb + Rb × Rc + Rc × Ra) / Rc Rbc = (Ra × Rb + Rb × Rc + Rc × Ra) / Ra Rac = (Ra × Rb + Rb × Rc + Rc × Ra) / Rb Input Parameters Parameter Description Rab Resistance between terminals a and b in delta configuration (Ω) Rbc Resistance between terminals b and c in delta configuration (Ω) Rac Resistance between terminals a and c in delta configuration (Ω) Example Calculation Given: Rab = 10 Ω Rbc = 20 Ω Rac = 30 Ω Calculate equivalent star resistances: Ra = (10 × 20) / (10 + 20 + 30) = 200 / 60 ≈ 3.33 Ω Rb = (20 × 30) / 60 = 600 / 60 = 10 Ω Rc = (30 × 10) / 60 = 300 / 60 = 5 Ω Result: The delta network with resistances 10 Ω, 20 Ω, 30 Ω is equivalent to a star network with Ra = 3.33 Ω, Rb = 10 Ω, Rc = 5 Ω. Use Cases Circuit simplification in complex networks with multiple loops Power system analysis for balanced and unbalanced loads Electronics design of impedance matching and filter circuits Academic learning in electrical engineering courses (e.g., Circuit Theory, Network Analysis) Exam preparation for competitive exams like GATE, IIT JAM, IEEE Frequently Asked Questions What is the difference between delta and wye connection? Delta (Δ): Three resistors connected end-to-end forming a triangle. Each resistor connects two terminals. Wye (Y): Three resistors connected at a common central node (star). Each resistor connects one terminal to the center. Both configurations can be made electrically equivalent through transformation. Why is Δ-Y transformation important? It allows engineers to simplify complex circuits by replacing a delta network with a star (or vice versa), making analysis easier using series/parallel rules or nodal/mesh methods. It’s especially useful in three-phase systems and symmetric networks. Can I use this calculator for AC circuits? Yes, but only if the components are purely resistive. For AC circuits with inductance or capacitance, you must use impedance (Z) instead of resistance (R), and the same transformation formulas apply using complex numbers. How do I convert Y to Δ? Use the reverse formulas: Rab = (Ra × Rb + Rb × Rc + Rc × Ra) / Rc Rbc = (Ra × Rb + Rb × Rc + Rc × Ra) / Ra Rac = (Ra × Rb + Rb × Rc + Rc × Ra) / Rb This calculator supports both directions: Δ → Y and Y → Δ. When should I use Δ-Y transformation? Use it when: You have a bridge-like network that cannot be simplified by series/parallel combinations You need to analyze three-phase systems with unbalanced loads You're solving problems involving symmetry or equivalence You want to reduce the number of nodes in a circuit Is Δ-Y transformation valid for all resistor values? Yes, as long as the total resistance sum (Rab + Rbc + Rac) is not zero. If any resistance is zero or infinite, special care is needed. The transformation assumes linear, time-invariant components. Reference Standards IEEE Std 145-2017: Standard for Electric Power Systems and Equipment IEC 60034: Rotating electrical machines Textbooks: "Electric Circuits" by James W. Nilsson, "Network Analysis" by M.E. Van Valkenburg Related Tools Y to Delta (Y-Δ) Conversion Three-Phase Power Calculator Impedance (Z) to Resistance (R) & Reactance (X) Mesh Current Method Solver

Convert between power units: Watt (W), Kilowatt (kW), Horsepower (HP), BTU/h, and kcal/h. Ideal for HVAC systems, motor selection, automotive engineering, and energy efficiency analysis. Includes conversion formulas, real-world examples, and support for both mechanical and metric horsepower. Supported Units & Conversion Factors Unit Full Name Relation to Watt (W) W Watt 1 W = 1 W kW Kilowatt 1 kW = 1000 W HP Horsepower - Mechanical HP: 1 HP ≈ 745.7 W - Metric HP: 1 HP ≈ 735.5 W BTU/h British Thermal Unit per hour 1 BTU/h ≈ 0.000293071 W 1 W ≈ 3.600 BTU/h kcal/h Kilocalorie per hour 1 kcal/h ≈ 1.163 W 1 W ≈ 0.8598 kcal/h Example Calculations Example 1: Air Conditioner Cooling Capacity An air conditioner has a cooling capacity of 3000 kcal/h. Power in watts: 3000 × 1.163 ≈ 3489 W Or about 3.49 kW Example 2: Engine Output Power An engine produces 200 HP (mechanical). Power in watts: 200 × 745.7 = 149,140 W Or 149.14 kW Example 3: Heating System Power A heater outputs 5 kW of power. BTU/h: 5 × 3600 = 18,000 BTU/h kcal/h: 5 × 859.8 ≈ 4299 kcal/h Use Cases Motor and generator selection based on required output power HVAC system design — sizing AC units, boilers, heat pumps Automotive engine rating — comparing horsepower and kilowatts Energy efficiency evaluation — converting between thermal and electrical power Academic learning — physics, engineering, and thermodynamics exams Frequently Asked Questions How many watts is 1 horsepower? One mechanical horsepower (HP) is approximately 745.7 watts. In metric systems, 1 HP ≈ 735.5 watts. So, 1 HP = 0.7457 kW. How do I convert kW to BTU/h? To convert kilowatts to BTU per hour: BTU/h = kW × 3600 Example: 2 kW × 3600 = 7,200 BTU/h What is the difference between mechanical and metric horsepower? Mechanical HP (US): Defined as 550 ft·lbf/s or ~745.7 W. Metric HP (PS): Defined as 75 kgf·m/s or ~735.5 W. They are slightly different but often used interchangeably in practice. How many BTU/h is 1 kW? 1 kilowatt equals 3,600 BTU/h. This is because 1 watt = 3.6 BTU/h, so 1000 watts = 3,600 BTU/h. Why is BTU/h used in HVAC systems? BTU/h (British Thermal Unit per hour) measures the amount of heat energy delivered or removed per hour. It's widely used in HVAC because it directly relates to heating and cooling performance. For example, a 12,000 BTU/h AC unit can cool a small room effectively. Can I use this calculator for electric motors? Yes. Electric motors are rated in both horsepower (HP) and kilowatts (kW). This calculator helps convert between them for comparison, selection, or efficiency analysis. Is 1 kW equal to 1 HP? No. 1 kW ≈ 1.341 HP (mechanical). So, 1 HP ≈ 0.746 kW. They are not equal, but commonly compared in industrial and automotive contexts. Reference Standards ISO 80000-13: Quantities and units — Physical chemistry and molecular physics ASHRAE Standard 90.1: Energy Standard for Buildings Except Low-Rise Residential Buildings IEEE 145-2017: Standard for Electric Power Systems and Equipment SAE J1140: Motor Vehicle Power Rating

Convert torque between Newton-metre (N·m), Kilogram-meter (kgf·m), Foot-pound (ft·lbf), and Inch-pound (in·lbf). Essential for automotive engineering, mechanical design, bolt tightening, and academic applications. Includes conversion formulas and real-world examples. Core Formula The relationship between angular velocity (ω) and frequency (f) is: ω (rad/s) = 2π × f (Hz) Or equivalently: f (Hz) = ω (rad/s) ÷ (2π) ω: Angular velocity in radians per second (rad/s) f: Frequency in Hertz (Hz) π: Pi ≈ 3.14159 Example Calculations Example 1: Motor Rotation A motor rotates at 100 rad/s. Frequency: f = 100 ÷ (2π) ≈ 15.915 Hz Rotation speed: ~15.9 revolutions per second Example 2: AC Power System Standard AC frequency is 50 Hz. Angular velocity: ω = 2π × 50 = 314.16 rad/s Used in voltage equations: V(t) = V₀ × sin(ωt) Use Cases Motor and generator design — calculating rotational speed from electrical frequency AC circuit analysis — determining angular frequency for sinusoidal signals Rotating machinery dynamics — vibration analysis, resonance studies Physics and engineering education — understanding rotational motion Control system design — feedback loops for servo motors Frequently Asked Questions How do I convert rad/s to Hz? Divide the angular velocity by 2π: f (Hz) = ω (rad/s) ÷ (2π) Example: 100 rad/s ÷ (2×3.14159) ≈ 15.915 Hz What is the difference between angular velocity and frequency? Angular velocity (ω) measures how fast an object rotates in radians per second. Frequency (f) measures how many full rotations occur per second (in Hz). They are related by: ω = 2πf. Why is angular velocity used in AC systems? In AC circuits, voltage and current vary sinusoidally over time. The rate of change is described by angular frequency (ω), which appears in the equation: V(t) = V₀ × sin(ωt). This simplifies mathematical modeling of oscillations. How many rad/s is 60 Hz? ω = 2π × 60 ≈ 376.99 rad/s This is common in North American power systems (60 Hz). Can I use this calculator for RPM? Yes, but you need to convert RPM to rad/s first: 1 RPM = 2π/60 rad/s ≈ 0.1047 rad/s Then use the calculator to find frequency. Is angular velocity the same as angular frequency? Yes, in most contexts, “angular velocity” and “angular frequency” refer to the same quantity: ω = 2πf, measured in rad/s. They describe the rate of rotation or oscillation. Reference Standards IEEE 145-2017: Standard for Electric Power Systems and Equipment ISO 80000-3: Quantities and units — Space and time Textbooks: "Engineering Mechanics" by Hibbeler, "Electric Circuits" by Nilsson

Convert torque between Newton-metre (N·m), Kilogram-meter (kgf·m), Foot-pound (ft·lbf), and Inch-pound (in·lbf). Ideal for automotive engineering, mechanical design, bolt tightening, and academic applications. Includes conversion formulas and real-world examples. Supported Units & Conversion Factors Unit Full Name Relation to Newton-metre (N·m) N·m Newton-metre 1 N·m = 1 N·m kgf·m Kilogram-meter 1 kgf·m ≈ 9.80665 N·m ft·lbf Foot-pound 1 ft·lbf ≈ 1.35582 N·m in·lbf Inch-pound 1 in·lbf ≈ 0.112985 N·m Example Calculations Example 1: Engine Torque An engine produces 300 N·m of torque. kgf·m: 300 ÷ 9.80665 ≈ 30.6 kgf·m ft·lbf: 300 × 0.73756 ≈ 221.3 ft·lbf Example 2: Bolt Tightening A bolt requires 40 in·lbf of torque. N·m: 40 × 0.112985 ≈ 4.52 N·m ft·lbf: 40 ÷ 12 = 3.33 ft·lbf Use Cases Automotive engine torque specification — comparing performance across regions Motor and gearbox selection — matching output torque to load requirements Bolt tightening torque setting — ensuring proper clamping force in assemblies Mechanical design and dynamics analysis — calculating forces in rotating systems Academic learning and exams — physics, engineering mechanics, thermodynamics Frequently Asked Questions How many ft·lbf is 1 N·m? 1 N·m ≈ 0.73756 ft·lbf So, 1 ft·lbf ≈ 1.35582 N·m. What is the difference between N·m and kgf·m? N·m is the SI unit of torque, based on Newtons and meters. kgf·m uses kilogram-force (a gravitational force), so 1 kgf·m ≈ 9.80665 N·m. It's commonly used in older European and Asian machinery specs. How do I convert in·lbf to N·m? Multiply by 0.112985: N·m = in·lbf × 0.112985 Example: 100 in·lbf × 0.112985 = 11.2985 N·m Is 1 ft·lbf equal to 12 in·lbf? Yes! Since 1 foot = 12 inches, 1 ft·lbf = 12 in·lbf. This is a direct linear relationship, not a conversion factor. Why is torque important in engines? Torque measures the rotational force an engine can produce. Higher torque means better acceleration and pulling power, especially at low speeds. It’s crucial for trucks, tractors, and heavy machinery. Can I use this calculator for wrench settings? Yes! Many torque wrenches are calibrated in ft·lbf or N·m. Use this tool to convert between them when following manufacturer specifications. Reference Standards ISO 80000-3: Quantities and units — Space and time SAE J1140: Motor Vehicle Power Rating ASTM E1003: Standard Test Method for Measurement of Torque Textbooks: "Mechanics of Materials" by Ferdinand Beer, "Engineering Mechanics" by Hibbeler

Convert between peak, peak-to-peak, and RMS voltage values in AC signals. Ideal for electrical engineering, circuit design, oscilloscope analysis, and academic studies. Includes formulas, examples, and a visual waveform diagram. Core Formulas Conversion Formula RMS → Peak V_peak = V_rms × √2 ≈ V_rms × 1.414 Peak → RMS V_rms = V_peak / √2 ≈ V_peak / 1.414 Peak → Peak-to-Peak V_pp = 2 × V_peak Peak-to-Peak → Peak V_peak = V_pp / 2 RMS → Peak-to-Peak V_pp = 2 × V_rms × √2 ≈ V_rms × 2.828 Peak-to-Peak → RMS V_rms = V_pp / (2 × √2) ≈ V_pp / 2.828 Parameters Peak (Vpeak): The maximum instantaneous voltage in one cycle of an AC waveform, unit: Volts (V) Peak-to-Peak (Vpp): The difference between the maximum and minimum voltage values, representing the total swing of the signal RMS (Vrms): Root-Mean-Squared value, equivalent to the DC voltage that would produce the same heating effect. Mains electricity (e.g., 230V) is specified as RMS Visual Waveform Diagram Example Calculations Example 1: Household AC Voltage Household mains voltage RMS = 230 V Peak: 230 × 1.414 ≈ 325.2 V Peak-to-Peak: 325.2 × 2 ≈ 650.4 V Example 2: Signal Generator Output Signal generator output Peak-to-Peak = 10 V Peak: 10 ÷ 2 = 5 V RMS: 5 ÷ 1.414 ≈ 3.54 V Use Cases Electrical measurements and instrument calibration — ensuring accuracy of multimeters and oscilloscopes Circuit design and component selection — choosing diodes, capacitors, and transformers based on peak voltage Signal analysis and oscilloscope interpretation — reading waveforms from test equipment Academic learning and exams — understanding AC theory, power systems, and electronics Frequently Asked Questions (Based on Google "People Also Ask") What is the difference between peak and RMS voltage? Peak voltage is the maximum amplitude of the AC waveform. RMS voltage is the effective value, equivalent to the DC voltage that delivers the same power. For sine waves: Vrms = Vpeak / √2 ≈ Vpeak / 1.414. Why is household voltage given as RMS? Because RMS represents the equivalent heating effect of DC. A 230V RMS AC supply delivers the same power as a 230V DC source, making it easier to compare and use in practical applications. How do I convert RMS to peak voltage? Multiply RMS by √2 (≈1.414): V_peak = V_rms × 1.414 Example: 120V RMS → 120 × 1.414 ≈ 169.7 V peak Is peak-to-peak voltage twice the peak voltage? Yes! For a symmetric AC waveform: V_pp = 2 × V_peak This is because the signal swings from +V_peak to -V_peak. Can this calculator be used for non-sinusoidal waves? No. These formulas are only accurate for sinusoidal waveforms. For square or triangular waves, different RMS relationships apply. What does RMS stand for? RMS stands for Root Mean Square. It is calculated as: V_rms = √(average of V² over one cycle) It gives the effective value of an AC signal. Reference Standards IEC 60050: International Electrotechnical Vocabulary IEEE 145-2017: Standard for Electric Power Systems and Equipment Textbooks: "Electric Circuits" by Nilsson & Riedel, "Fundamentals of Electric Circuits" by Alexander & Sadiku

Convert between Joule (J), kilowatt-hour (kWh), British Thermal Unit (BTU), and Calorie (cal) instantly. Ideal for electrical engineering, building energy analysis, nutrition, and academic studies. Includes conversion formulas, examples, and real-world applications. Supported Units & Conversion Factors Unit Full Name Relation to Joule (J) J Joule 1 J = 1 J kJ Kilojoule 1 kJ = 1,000 J MJ Megajoule 1 MJ = 1,000,000 J Wh Watt-hour 1 Wh = 3,600 J kWh Kilowatt-hour 1 kWh = 3,600,000 J MWh Megawatt-hour 1 MWh = 3.6 × 10⁹ J BTU British Thermal Unit 1 BTU ≈ 1,055.06 J cal Calorie 1 cal ≈ 4.184 J kcal Kilocalorie 1 kcal = 4,184 J Mcal Megacalorie 1 Mcal = 4,184,000 J Example Calculations Example 1: Electrical Energy to Nutrition A household uses 1 kWh of electricity. Joules: 1 kWh = 3,600,000 J Kilocalories: 3,600,000 ÷ 4,184 ≈ 860 kcal So, 1 kWh ≈ 860 kcal — equivalent to the energy in ~200 grams of sugar Example 2: Nutritional Energy to Electricity A meal contains 30,000 kcal. Joules: 30,000 × 4,184 = 125,520,000 J kWh: 125,520,000 ÷ 3,600,000 ≈ 34.9 kWh That’s enough to power a 1,000W heater for ~35 hours Use Cases Power system energy analysis — comparing electricity consumption across different sources Building energy efficiency design — calculating HVAC loads and insulation performance Nutritional label interpretation — understanding food energy content in kcal vs. joules Engineering energy balance calculations — thermodynamics, heat transfer, and mechanical systems Academic learning and exams — physics, chemistry, and engineering courses Frequently Asked Questions (Based on Google "People Also Ask") How many joules are in 1 kWh? 1 kilowatt-hour (kWh) = 3,600,000 joules (J) This is because 1 watt = 1 joule/second, and 1 hour = 3,600 seconds. What is the difference between calorie and kilocalorie? 1 calorie (cal) = 4.184 joules — the energy to heat 1 gram of water by 1°C. 1 kilocalorie (kcal) = 1,000 calories = 4,184 joules. On food labels, “Calorie” with a capital C means kilocalorie. How do I convert BTU to kWh? Divide BTU by 3,412: kWh = BTU ÷ 3,412 Example: 10,000 BTU ÷ 3,412 ≈ 2.93 kWh Why is energy measured in both kWh and BTU? kWh is used for electrical energy (e.g., electricity bills). BTU is used for thermal energy (e.g., heating, cooling, fuel). They are interchangeable via conversion factors, but context determines which is more appropriate. Can I use this calculator for food energy? Yes! Food energy is typically labeled in kilocalories (kcal). You can convert it to joules or kWh using this tool. For example: 1,000 kcal = 4,184,000 J ≈ 1.16 kWh. Is 1 kWh equal to 1,000 watts? No. 1 kWh is 1,000 watts × 1 hour — a measure of energy, not power. Power is measured in watts (W), while energy is measured in watt-hours (Wh) or kilowatt-hours (kWh). Reference Standards ISO 80000-13: Quantities and units — Physical chemistry and molecular physics ASHRAE Standard 90.1: Energy Standard for Buildings Except Low-Rise Residential Buildings IEC 60050: International Electrotechnical Vocabulary Textbooks: "Thermodynamics" by Yunus Cengel, "Introduction to Heat Transfer" by Incropera

Convert between magnetic field units: Tesla (T), Gauss (G), microtesla (μT), millitesla (mT), kilogauss (kG), and megagauss (MG). Ideal for MRI, motor design, geophysics, electromagnetic research, and academic studies. Includes conversion formulas, real-world examples, and scientific notation support. Key Conversion Formulas Conversion Formula Tesla → Gauss 1 T = 10⁴ G Gauss → Tesla 1 G = 10⁻⁴ T mT → Gauss 1 mT = 10 G μT → Gauss 1 μT = 0.01 G kG → Tesla 1 kG = 0.1 T MG → Tesla 1 MG = 100 T Example Calculations Example 1: Earth's Magnetic Field The Earth's magnetic field is about 0.5 Gauss. Tesla: 0.5 × 10⁻⁴ T = 5 × 10⁻⁵ T Microtesla: 5 × 10⁻⁵ T = 50 μT Example 2: MRI Magnet Field A typical MRI scanner uses a 1.5 Tesla magnet. Gauss: 1.5 × 10⁴ G = 15,000 G Kilogauss: 15,000 G ÷ 1,000 = 15 kG Example 3: Neodymium Magnet A strong neodymium magnet has a surface field of 12,000 Gauss. Tesla: 12,000 × 10⁻⁴ T = 1.2 T Millitesla: 1.2 T × 1,000 = 1,200 mT Example 4: Lab Pulsed Magnetic Field High-power pulsed magnets can reach 1 Megagauss. Gauss: 1 MG = 10⁶ G = 1,000,000 G Tesla: 1,000,000 G × 10⁻⁴ T/G = 100 T Example 5: Sensor Reading A magnetic sensor reads 800 microtesla. Tesla: 800 × 10⁻⁶ T = 8 × 10⁻⁴ T Gauss: 8 × 10⁻⁴ T ÷ 10⁻⁴ = 8 G Use Cases Medical devices — MRI, NMR spectroscopy, and biomedical imaging systems Motor and generator design — calculating magnetic flux density in electric machines Magnetic material testing — evaluating performance of permanent magnets, soft magnets, and superconductors Geophysics and geology — measuring Earth's magnetic field and mineral exploration Electromagnetic compatibility (EMC) — assessing interference from electromagnetic fields Research — high-field magnets in plasma physics, fusion energy, and particle accelerators Education and teaching — electromagnetism, physics, and engineering courses Frequently Asked Questions What is the difference between Tesla and Gauss? Tesla (T) is the SI unit of magnetic flux density. Gauss (G) is a CGS unit, commonly used in older literature and some industries. 1 T = 10,000 G — so 1 Gauss = 0.0001 Tesla. How strong is a typical MRI magnet? Most clinical MRI scanners use magnets with fields between 1.5 T and 3.0 T, which equals 15,000 to 30,000 Gauss. Research MRI systems can go up to 7 T or higher. Is 1 microtesla equal to 100 Gauss? No! 1 μT = 0.01 G So, 100 μT = 1 G. Common mistake: people confuse μT and mT. Can this calculator handle scientific notation? Yes! You can input values like 1.5e-5 for 15 microtesla or 3e4 for 30,000 Gauss. The tool supports real-time bidirectional calculation. Why do some labs still use Gauss instead of Tesla? Historical reasons: many older instruments and textbooks use Gauss. Also, Gauss is more convenient for small fields (e.g., Earth’s field ≈ 0.5 G), while Tesla is better for large fields (e.g., MRI). What is the strongest magnetic field ever created? The strongest continuous magnetic field is around 45 T (450,000 G), achieved using hybrid magnets. Pulsed fields can exceed 100 T (10 MG) for very short durations. Reference Standards ISO 80000-3: Quantities and units — Space and time IEC 60050: International Electrotechnical Vocabulary NIST Special Publication 811: Guide for the Use of the International System of Units (SI) Textbooks: "Introduction to Electrodynamics" by David J. Griffiths, "Electromagnetism" by John R. Reitz Related Tools Energy Unit Converter AC Voltage Converter Torque Unit Converter Power Unit Converter

Convert between angular velocity (RPM, rad/s) and linear velocity (m/s, ft/s) using radius. Ideal for motor design, car tire speed, wind turbines, robotics, and physics education. Supports real-time bidirectional calculation with scientific accuracy. Key Formulas Conversion Formula RPM → rad/s ω = (2π / 60) × RPM ≈ 0.10472 × RPM rad/s → RPM RPM = (60 / 2π) × ω ≈ 9.5493 × ω Angular → Linear (m/s) v = ω × r m/s → ft/s v_ft/s = v_m/s × 3.28084 ft/s → m/s v_m/s = v_ft/s ÷ 3.28084 Example Calculations Example 1: Motor Speed to Angular Velocity A motor runs at 3000 RPM. Angular velocity: ω = (2π / 60) × 3000 ≈ 314.16 rad/s Example 2: Angular Velocity to RPM A shaft rotates at 100 rad/s. RPM: RPM = (60 / 2π) × 100 ≈ 954.93 RPM Example 3: Wheel Radius and Angular Velocity to Linear Speed A wheel has a radius of 0.1 m and rotates at 100 rad/s. Linear velocity: v = 100 × 0.1 = 10 m/s In feet per second: 10 × 3.28084 ≈ 32.81 ft/s Example 4: Linear Velocity to Angular Velocity A car moves at 20 m/s. The tire radius is 0.3 m. Angular velocity: ω = v / r = 20 / 0.3 ≈ 66.67 rad/s RPM: 66.67 × 9.5493 ≈ 637.2 RPM Use Cases Motor and generator selection — matching speed and torque requirements Car tire RPM to speed conversion — calculating vehicle speed from wheel rotation Wind turbines, pumps, fans design — optimizing blade tip speed and efficiency Robot joint control and motion planning — converting servo angles to end-effector velocity Physics education — teaching circular motion, centripetal acceleration, and rotational kinematics Frequently Asked Questions How do I convert RPM to m/s? You need the radius of rotation. First, convert RPM to rad/s: ω = (2π / 60) × RPM Then, calculate linear speed: v = ω × r Example: 3000 RPM, r = 0.1 m → v = 314.16 × 0.1 = 31.42 m/s What is the relationship between RPM and rad/s? One revolution equals 2π radians, and 1 minute has 60 seconds. So: 1 RPM = 2π / 60 ≈ 0.10472 rad/s To convert: rad/s = RPM × 0.10472 Can I use this calculator for car wheels? Yes! Enter the tire radius (e.g., 0.3 m) and input either RPM or speed (m/s or ft/s). The tool will calculate the other values, helping you understand how fast your car is moving based on wheel rotation. Why does the result depend on radius? Because linear velocity depends on both angular speed and distance from the center. A point farther from the axis moves faster than one closer, even if they rotate at the same RPM. This is why larger wheels travel faster at the same RPM. Is there a difference between angular velocity and angular speed? Yes. Angular velocity is a vector quantity (has magnitude and direction), while angular speed is scalar (only magnitude). In most practical applications, we use the term interchangeably when direction isn't critical. How accurate is this converter? The calculations use standard SI units and exact mathematical constants (π, 3.28084 for ft/m). Results are precise to 4–6 significant digits, suitable for engineering and academic purposes. Reference Standards ISO 80000-3: Quantities and units — Space and time IEC 60050: International Electrotechnical Vocabulary NIST Special Publication 811: Guide for the Use of the International System of Units (SI) Textbooks: "Engineering Mechanics: Dynamics" by Hibbeler, "Physics for Scientists and Engineers" by Serway