How the AC Power Calculator works

The AC Power Calculator converts voltage, current and power factor into real power in kilowatts, apparent power in kilovolt-amperes and reactive power in kilovolt-amperes reactive. It supports a single-phase supply and a balanced three-phase supply. When operating time is entered, the AC Power Calculator also estimates real energy in kilowatt-hours and apparent energy in kilovolt-ampere-hours.

The AC Power Calculator uses standard relationships between RMS voltage, current and power factor. The NIST electrical SI unit guidance explains the ampere and related derived units. Equipment nameplates, utility rules and qualified electrical design should take priority.

AC Power Calculator formulas

For single-phase power, apparent power is S = V × I and real power is P = V × I × PF. For balanced three-phase power using line-to-line voltage, S = √3 × V × I and P = √3 × V × I × PF. When line-to-neutral voltage is selected, the multiplier is 3 instead of √3. Reactive power is Q = S × √(1 − PF²). Phase angle is cos⁻¹(PF). Real energy equals kilowatts multiplied by hours.

Powerful AC Power Calculator example

A 230-volt single-phase load drawing 10 amperes at a 0.90 power factor has 2.30 kVA of apparent power and 2.07 kW of real power. Reactive power is approximately 1.00 kVAR and the phase angle is about 25.84 degrees. If the load operates for 8 hours, it uses approximately 16.56 kWh of real energy and 18.40 kVAh of apparent energy.

Real, apparent and reactive power

Real power performs useful work and is measured in watts or kilowatts. Apparent power combines the effect of real and reactive power and is used when sizing generators, transformers, cables and other equipment. Reactive power represents energy exchanged with inductive or capacitive fields. These values form a right-triangle relationship: apparent power squared equals real power squared plus reactive power squared.

Single-phase and three-phase systems

Single-phase calculations use one voltage-current relationship. Balanced three-phase calculations combine three phase conductors and require the correct voltage definition. Line-to-line voltage is the common nameplate value for many three-phase systems. If line-to-neutral voltage is entered, the calculator applies three times phase voltage and line current. Unbalanced systems require separate phase measurements and cannot be represented accurately by one balanced calculation.

Power factor and equipment sizing

Power factor is real power divided by apparent power. A value closer to 1 means current is being converted into useful real power more effectively. Motors, transformers and power electronics may have lower or varying power factor. Equipment must usually be sized for current and apparent power, not only kilowatts. Startup current, harmonics, duty cycle, temperature and applicable electrical codes may require additional capacity.

Accuracy and limitations

The AC Power Calculator assumes sinusoidal RMS values, a constant power factor and a balanced load for three-phase calculations. It does not model harmonics, distorted waveforms, phase imbalance, voltage drop, demand peaks, motor starting current or generator transient response. Use measured average values when estimating energy, and use manufacturer and code requirements for conductor or protection sizing.

Do not use the AC Power Calculator as the sole basis for installation, maintenance or energized electrical work. Electrical systems can cause shock, fire, arc-flash injury and equipment damage. Critical designs require a qualified electrician or engineer.

Frequently asked questions

Should I enter line-to-line or line-to-neutral voltage?

For balanced three-phase systems, select the definition that matches your measurement. Most equipment nameplates show line-to-line voltage.

What if the power factor is unknown?

Use a measured or manufacturer value. Entering 1 gives the theoretical maximum real power but may overestimate real power for motors and other reactive loads.

Does this calculate electricity cost?

The result includes kWh. Multiply real energy by your electricity rate, or use an electricity cost tool when tariffs include demand charges or multiple rates.

Can it calculate an unbalanced three-phase load?

No. Calculate each phase separately from its measured voltage, current and power factor, then combine the real and reactive components.

Why are kW and kVA different?

kW measures useful real power, while kVA measures total apparent power. They are equal only when power factor is 1.