Electrical Power Calculator
Calculate electrical power from voltage, current, phase, and power factor for DC, single-phase AC, and three-phase AC systems.
This calculator separates DC power from AC real, apparent, and reactive power and uses RMS voltage/current for AC calculations.
Calculation Results
What Is Electrical Power?
Electrical power is the rate at which electrical energy is transferred, converted, or used. The SI unit of power is the watt (W). Larger systems often use kilowatts (kW) or megawatts (MW), while AC apparent power uses volt-amperes and reactive power uses volt-amperes reactive.
DC Power Formula
For basic DC power calculations, voltage in volts multiplied by current in amperes gives power in watts. Real equipment may also involve efficiency, converter losses, waveform effects, or transient behavior that are outside this simplified relationship.
Single-Phase AC Power
For sinusoidal single-phase AC, use RMS voltage and current. Voltage and current determine apparent power, while power factor determines how much of that apparent power is real power.
Three-Phase AC Power
These relations apply to a balanced three-phase system using line-to-line voltage and line current. If line-to-neutral voltage is entered for a balanced wye system, the calculator converts it to line-to-line voltage before using the √3 relationship.
Real, Apparent, and Reactive Power
| Quantity | Meaning | Common Units |
|---|---|---|
| Real Power, P | Average power converted to useful work, heat, mechanical output, or other net energy transfer. | W, kW, MW |
| Apparent Power, S | RMS voltage-current product for AC equipment and system loading. | VA, kVA, MVA |
| Reactive Power, Q | Power associated with periodic energy exchange in reactive elements. | VAR, kVAR, MVAR |
Power Factor
Power factor describes the relationship between real power and apparent power. At PF = 1, real and apparent power are numerically equal. At lower PF, a larger apparent power is required for the same real-power transfer.
Lagging power factor is commonly associated with inductive behavior, while leading power factor can occur with capacitive behavior. The magnitude of S = VI is not changed by choosing leading or lagging.
RMS Voltage and Current
AC power equations normally use RMS voltage and RMS current. For a sinusoidal waveform:
Do not enter a peak value into an RMS-based power equation unless it has first been converted appropriately.
kW vs kVA
kW measures real power, while kVA measures apparent power. Their relationship is:
For example, 100 kW at PF = 0.80 corresponds to 125 kVA.
kW vs kVAR
kW represents real power and kVAR represents reactive power. They are different components of the power triangle. The apparent-power magnitude combines both:
Power vs Energy
Power describes the rate of energy transfer, while energy describes how much energy is transferred over time.
A 2 kW load operating for 5 hours uses 10 kWh of energy. kW and kWh should not be treated as interchangeable quantities.
Efficiency vs Power Factor
Power factor and efficiency are different quantities. Power factor relates real power to apparent power. Efficiency relates useful output power to input power.
A motor can have PF = 0.85 and efficiency = 0.92 at the same operating point. One value cannot be substituted for the other.
Resistive Loads
For an ideal purely resistive AC load, power factor is approximately 1, so real power is approximately equal to V × I. Real equipment may include inductive, capacitive, electronic, harmonic, or control effects that change the relationship.
Motor Loads
Motor systems commonly involve real power, reactive power, power factor, and efficiency. Electrical input power and mechanical output power should not be confused.
For a balanced three-phase motor input, the electrical real-power relationship is typically P = √3VI·PF when the applicable RMS line values and power factor are known.
Engineering Applications
- Motors and pumps
- HVAC equipment
- Transformers
- Generators
- Industrial equipment
- Electrical panels
- Building loads
- Power distribution
2026 Engineering Reference
Updated for 2026. The electrical power equations used by this calculator are established engineering relationships. The 2026 reference update concerns current SI definitions and unit-conversion references used by this page rather than a new annual version of the power equations.
Engineering References
SI units, prefixes, and unit-conversion reference.
NIST Special Publication 811Reference for SI base-unit definitions including the ampere and related derived electrical units.
NIST SI Base UnitsReference for electricity, magnetism, and power-unit conversion factors.
NIST Appendix B.9Limitations
This calculator provides electrical power estimates based on user-supplied values and simplified circuit relationships. It does not replace load studies, short-circuit studies, protection coordination, harmonic analysis, transformer sizing, conductor sizing, voltage-drop studies, code compliance, manufacturer data, or professional electrical engineering design.
Frequently Asked Questions
1. How do I calculate electrical power from voltage and current?
For DC, multiply voltage by current: P = VI. For single-phase AC, multiply RMS voltage, RMS current and power factor. For balanced three-phase AC using line-to-line voltage and line current, multiply √3 × V × I × PF. Select the matching system before calculating.
2. What is the formula for watts?
For basic DC power, watts equal volts times amperes. In AC systems, real watts also depend on power factor. Single-phase real power is VI·PF, while balanced three-phase real power using line-to-line voltage is √3VI·PF.
3. How do I calculate AC power?
Use RMS voltage and current. For single-phase AC, apparent power is VI and real power is VI·PF. For balanced three-phase AC, apparent power is √3VI and real power is √3VI·PF when V is line-to-line voltage and I is line current.
4. What is the difference between single-phase and three-phase power?
Single-phase AC uses one alternating voltage waveform for the load. Three-phase systems use three phase-displaced waveforms and are common for larger motors and industrial distribution. Their power formulas differ, including the √3 factor when balanced line-to-line voltage and line current are used.
5. Why is √3 used in three-phase power calculations?
The √3 factor comes from the vector relationship between phase and line quantities in a balanced three-phase system. When line-to-line voltage and line current are used, total apparent power is √3VI. The calculator handles line-to-neutral input separately for a balanced wye system.
6. What power factor should I use?
Use the measured, manufacturer-published, or design power factor for the actual operating condition. Do not assume one universal power factor for all motors or equipment. Power factor can vary with load, controls, harmonics, and equipment type.
7. What happens when the power factor is 1?
At unity power factor, real power and apparent power are numerically equal and reactive power magnitude is zero in the simplified sinusoidal power triangle. This is an idealized condition; many AC loads operate with a power factor below 1.
8. What is the difference between kW and kVA?
kW is real power, while kVA is apparent power. The relationship is kW = kVA × PF. A load drawing 100 kW at 0.80 power factor requires 125 kVA of apparent power.
9. What is the difference between kW and kVAR?
kW represents real power transferred to net work or heat. kVAR represents reactive power associated with energy exchange in reactive elements. Together they form the apparent power relationship kVA² = kW² + kVAR².
10. Can I calculate power without knowing power factor?
You can calculate apparent power from RMS voltage and current without power factor. To calculate real AC power, you need power factor or another way to determine the relationship between real and apparent power. DC basic power does not use AC power factor.
11. Should I use RMS voltage for AC power calculations?
Yes for the standard AC power equations used here. If you only know sinusoidal peak voltage or peak current, divide the peak value by √2 to obtain RMS before using the calculator.
12. What is apparent power?
Apparent power is the RMS voltage-current product for an AC load or system. It is measured in VA, kVA, or MVA. Apparent power combines the effects of real and reactive power and is important for equipment and conductor loading.
13. What is reactive power?
Reactive power represents the periodic exchange of energy associated with inductive and capacitive behavior in AC systems. It is measured in VAR or kVAR. The calculator reports reactive-power magnitude and identifies whether the selected power factor is leading or lagging.
14. Is power factor the same as efficiency?
No. Power factor is real power divided by apparent power. Efficiency is useful output power divided by input power. A motor can have a high efficiency but a lower power factor, or vice versa.
15. How do I calculate current from electrical power?
For DC, I = P/V. For single-phase AC, I = P/(V·PF). For balanced three-phase AC using line-to-line voltage, I = P/(√3V·PF). Make sure the power input is real power and use consistent units.
16. How do I calculate voltage from power and current?
For DC, V = P/I. For single-phase AC, V = P/(I·PF). For balanced three-phase AC using line-to-line voltage, V = P/(√3I·PF). If line-to-neutral voltage is the desired result, the calculator converts from the line-to-line result for a balanced wye system.
17. How do I calculate three-phase current from kW?
Convert kW to watts, then use I = P/(√3V·PF) when V is balanced line-to-line voltage. If your voltage is line-to-neutral, use the calculator's voltage-type selector so the correct line-to-line relationship is applied.
18. Can this calculator be used for motors?
It can estimate motor electrical input quantities when voltage, current, power factor, and phase configuration are known. It does not replace motor efficiency calculations, starting-current analysis, conductor sizing, overload protection, or manufacturer motor data.
19. Does electrical power equal electrical energy?
No. Power is a rate, measured in W or kW. Energy is power accumulated over time, commonly measured in Wh or kWh. A 2 kW load running for 5 hours uses 10 kWh.
20. Can this calculator size a circuit breaker or wire?
No. Breaker and conductor sizing requires code rules, continuous-load treatment, insulation and temperature ratings, installation method, ampacity, voltage drop, fault current, coordination, equipment requirements, and other project-specific considerations.
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Engineering Disclaimer
This calculator provides estimates based on simplified electrical power relationships and user-supplied inputs. Actual electrical-system design may require consideration of equipment characteristics, harmonics, unbalanced loads, transient conditions, conductor limitations, protection requirements, applicable electrical codes, manufacturer specifications, and qualified engineering review.