Electrical Power Calculator for DC and AC Circuits
Calculate real electrical power, voltage, current or power factor for DC, single-phase AC and balanced three-phase AC systems. Convert metric prefixes and review apparent power, reactive power and every formula step.
- DC and AC modes
- Single and three phase
- Solve P, V, I or PF
- W, VA and var results
Online Electrical Power Calculator
Select a circuit model and the unknown quantity. The calculator converts every magnitude to coherent SI units before applying the matching DC or AC power equation.
DC load power calculated from voltage and current magnitudes.
Equivalent Result Units
| Unit | Equivalent value |
|---|---|
| milliwatts (mW) | 24000 mW |
| watts (W) | 24 W |
| kilowatts (kW) | 0.024 kW |
Calculation Steps
- Convert the entered values to 12 V and 2 A.
- Use the DC load formula P = VI.
- Substitute P = 12 × 2 = 24 W.
- Convert the answer to the selected display unit.
This is a nonnegative DC load-power magnitude. Signed source and generation conventions, transient behavior and equipment ratings remain outside the calculation.
How to Use This Electrical Power Calculator
- Choose the circuit model. Select DC, single-phase AC or balanced three-phase AC.
- Choose the unknown. Select real power, voltage, current or, in an AC mode, power factor.
- Enter the known values. Use nonnegative magnitudes. For AC, use RMS values and the line quantities named beside the fields.
- Set power factor for AC. Enter a decimal from 0 to 1 or a percentage from 0% to 100%, then choose a reactive-power direction if known.
- Choose units and precision. Set the answer, apparent-power and reactive-power units plus the displayed significant digits.
- Calculate and review. Check the formula, conversions, power quantities, assumptions and warnings before using the result.
What Is Electrical Power?
Electrical power is the rate at which a circuit transfers or converts energy. The SI unit is the watt. One watt equals one joule per second. A 24 W load therefore converts 24 joules of electrical energy each second while its operating conditions remain steady.
For a DC load using nonnegative magnitudes, power P in watts equals voltage V in volts multiplied by current I in amperes. The calculator also rearranges this equation to V = P/I and I = P/V when the divisor is nonzero.
This page uses a load-consumption magnitude model. It does not attach positive and negative signs to power flow between sources and loads. Regeneration, exported power and passive-sign-convention analysis need declared current and voltage directions and sit outside this tool.
DC, Single-Phase and Three-Phase Power Formulas
Use RMS voltage and current for AC. In the three-phase mode, voltage means line-to-line RMS voltage and current means line current. The three-phase equation assumes equal balanced phases.
| Circuit model | Real power | Apparent power | Required convention |
|---|---|---|---|
| DC load | P = VI | Not used | Steady nonnegative magnitudes |
| Single-phase AC | P = VrmsIrmsPF | S = VrmsIrms | RMS values for one phase |
| Balanced three-phase AC | P = √3 VLLILPF | S = √3 VLLIL | Line-to-line RMS voltage and line current |
For sinusoidal AC, the ordinary power triangle gives the reactive-power magnitude as |Q| = S√(1 − PF2) and the phase-angle magnitude as |φ| = cos−1(PF). The direction selector applies the common load convention: positive Q for a lagging load and negative Q for a leading load.
Worked Electrical Power Examples
Example 1: DC power from volts and amps
A 12 V DC load draws 2 A. Multiply the two magnitudes:
If the same operating point lasts for two hours, energy use is 48 Wh. Time and energy are separate from instantaneous or average power, so use the Energy Consumption Calculator for that next step.
Example 2: Single-phase AC real power
A sinusoidal single-phase load uses 230 V RMS, 10 A RMS and a power factor of 0.8:
The corresponding reactive-power magnitude is 1380 var and the phase-angle magnitude is about 36.87 degrees. Power factor does not state whether Q is leading or lagging, so the calculator shows a magnitude unless you choose a direction.
Example 3: Balanced three-phase power
A balanced load has 400 V line-to-line RMS voltage, 20 A line current and a 0.9 power factor:
The apparent power is about 13.8564 kVA. This is total three-phase power, not the power of one phase. The same line-value equation applies to balanced wye and delta loads.
Example 4: Solve power factor
A single-phase load takes 920 W at 230 V RMS and 5 A RMS. Its apparent power is 1150 VA, so PF = P/S = 920/1150 = 0.8, or 80%. A calculated power factor above 1 would be inconsistent with this model and is rejected.
Real, Apparent and Reactive Power
AC calculations use three related quantities. Real power P, measured in watts, is the average rate of net energy transfer to the load. Apparent power S, measured in volt-amperes, is the RMS voltage-current product. Reactive power Q, measured in var, describes the alternating exchange associated with ideal inductive and capacitive energy storage under the sinusoidal power-triangle model.
| Quantity | Symbol | Unit | Meaning in this calculator |
|---|---|---|---|
| Real power | P | watt (W) | Average power transferred to a load |
| Apparent power | S | volt-ampere (VA) | RMS voltage-current capacity |
| Reactive power | Q | var | Signed value or magnitude from the sinusoidal power triangle |
| Power factor | PF | dimensionless | P/S, constrained from 0 through 1 |
Power factor is not efficiency. A motor may have a 0.85 power factor and a different energy-conversion efficiency. Electrical input power is also not automatically the same as shaft output, heat output or useful delivered power.
Three-Phase Voltage and Current Convention
The balanced three-phase mode expects the RMS voltage measured between two lines, written VLL, and the RMS current in a line conductor, written IL. With those line quantities, total apparent power is S = √3 VLLIL. Total real power is that value multiplied by power factor.
Do not enter line-to-neutral voltage into the field labelled line-to-line. In a balanced wye system, line-to-line voltage is √3 times line-to-neutral voltage. Delta and wye phase relationships differ, but their total balanced-power formula in line quantities is the same.
An unbalanced load needs phase-by-phase voltage, current and power measurement or a suitable polyphase power analyzer. Averaging a severely unbalanced system into one line-value formula may hide neutral current, phase overload and unequal power.
Electrical Power Units and Prefixes
The calculator converts SI prefixes as exact powers of ten. A kilowatt is 1000 watts, a megawatt is 1,000,000 watts and a milliwatt is 0.001 watt. The same prefixes scale volt-amperes and var.
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| pico | p | 10−12 | 1 pW = 10−12 W |
| nano | n | 10−9 | 1 nA = 10−9 A |
| micro | µ | 10−6 | 1 µV = 10−6 V |
| milli | m | 10−3 | 1 mW = 0.001 W |
| kilo | k | 103 | 1 kVA = 1000 VA |
| mega | M | 106 | 1 Mvar = 1,000,000 var |
| giga | G | 109 | 1 GW = 1,000,000,000 W |
| tera | T | 1012 | 1 TW = 1,000,000,000,000 W |
Symbols are case-sensitive. Use kW, not KW, for kilowatts. A kilowatt-hour is energy, not power. For example, a steady 2 kW load operating for three hours uses 6 kWh.
Zero Values and Indeterminate Results
Direct power calculation accepts zero. Zero voltage or zero current gives zero DC power. In AC mode, a zero power factor also gives zero real power even when apparent power is positive.
Inverse equations need a nonzero denominator. If real power is positive while current, voltage or the required AC power factor is zero, no finite solution exists. If both the numerator and denominator are zero, the unknown is not unique. For example, P = 0 and I = 0 do not determine one voltage.
When solving power factor, apparent power must be positive. P = 0 with S = 0 does not determine PF. A positive real power with zero apparent power is impossible in this model. The calculator also rejects P greater than S instead of clamping the result to 1.
Accuracy, Waveforms and Practical Limits
- Use RMS readings. Do not mix peak, peak-to-peak and RMS values in an AC calculation.
- Match the operating point. Voltage, current and power factor should describe the same load at the same time.
- Check phase balance. Use the three-phase mode only when the balanced line-value model is reasonable.
- Distinguish power factor types. For distorted waveforms, true power factor includes harmonic effects and need not equal cos φ.
- Use measured power when needed. A power analyzer accounts for waveform shape and phase relationships that simple nameplate multiplication misses.
- Match precision to evidence. Extra displayed digits do not remove meter uncertainty or equipment variation.
The displayed power triangle and phase angle assume sinusoidal steady-state behavior. For distorted voltage or current, calculate average real power from simultaneous waveform samples or use a true-power instrument. Use the Percent Error Calculator to compare a measured result with an expected value.
Resistive Power Forms
For a passive ohmic resistor, combine P = VI with V = IR to obtain P = I2R. When resistance is greater than zero, P = V2/R is also valid. These forms describe ideal resistive dissipation at the stated operating point.
Do not apply the resistance forms to a general motor, transformer, capacitor, inductor, switching supply or nonlinear load. Use the Ohm's Law Calculator when voltage, current and resistance are the main quantities.
Electrical Safety and Rating Limits
A calculated watt value does not select a conductor, breaker, fuse, contactor, transformer, resistor rating or enclosure. Real designs also depend on duty cycle, temperature, insulation, fault current, inrush, harmonics, ventilation, derating, protection coordination and local electrical requirements.
Do not work on energized mains, panels or exposed conductors from a calculator result. De-energize and verify equipment using approved procedures and suitable instruments. Energized work and consequential designs belong to qualified persons following current rules and equipment instructions.
Related Calculators
Frequently Asked Questions
What is the formula for electrical power?
For a DC load using magnitudes, P = VI. For single-phase AC, P = VrmsIrmsPF. For balanced three-phase AC using line quantities, P = √3 VLLILPF.
How do I calculate watts from volts and amps?
For a DC load, multiply volts by amperes. For single-phase purely resistive AC, use RMS values and PF = 1. Balanced three-phase power needs the separate line-value formula.
How is single-phase AC power calculated?
Multiply RMS voltage by RMS current and power factor: P = VrmsIrmsPF. The voltage-current product without PF is apparent power S in volt-amperes.
How is balanced three-phase power calculated?
Use P = √3 VLLILPF with line-to-line RMS voltage and line current. The result is total power for a balanced three-phase system.
What does power factor mean?
Power factor is real power divided by apparent power, P/S. It ranges from 0 to 1 in this magnitude model. It is not efficiency, and its value alone does not identify leading or lagging current.
What is the difference between watts, VA and var?
Watts measure real power, volt-amperes measure apparent power and var measures reactive power. They are related but should not be labelled as the same quantity when power factor is below 1.
How do I calculate power factor?
Divide real power by apparent power: PF = P/S. For single phase, S = VI. For balanced three phase, S = √3 VI using line values. Apparent power must be positive.
What is the difference between kW and kWh?
A kilowatt is power, or energy transfer rate. A kilowatt-hour is energy. A steady 2 kW load operating for three hours uses 6 kWh.
Can I enter peak AC voltage or current?
No. Enter RMS voltage and RMS current in the AC modes. Mixing RMS and peak values produces an inconsistent real-power result.
Does calculated power determine a safe circuit or component rating?
No. A formula result does not account for inrush, duty cycle, temperature, harmonics, derating, insulation, fault current, protection rules or installation requirements.
Method and Review Basis
DC power and resistor forms were checked against OpenStax electrical energy and power. RMS and single-phase AC relationships were checked against OpenStax AC power guidance. Balanced line-value formulas, W, VA and var relationships were checked against the U.S. Department of Energy Electrical Science Handbook and DOE motor-load guidance. SI units and prefixes were checked against the BIPM SI Brochure. Safety scope was reviewed against NIOSH electrical safety guidance.
Educational and electrical-safety disclaimer: This calculator provides equation-based load estimates for the selected idealized circuit model. It does not verify measurements, waveform quality, equipment ratings, installation design, protection, code compliance or a safe work condition. Confirm units, assumptions and applicable requirements independently. Only qualified persons should work on or near energized electrical equipment.