What this calculator does
In an AC circuit with inductance or capacitance, current and voltage do not peak at the same instant. That phase difference means some of the current delivers no useful power at all, merely sloshing energy back and forth between the supply and the load.
Power factor is the fraction that does useful work. A power factor of 1 means everything drawn is converted; 0.5 means the supply and cabling carry twice the current needed for the actual work being done.
The formula
Apparent power is voltage times current. Real power is that multiplied by the cosine of the phase angle, and reactive power by its sine. The power factor is the cosine of the phase angle, equivalently real power divided by apparent power.
| Term | Meaning |
|---|---|
| Real power (P) | The power actually doing work, in watts. This is what the meter bills for in a domestic supply. |
| Reactive power (Q) | Power exchanged with the supply without doing work, in volt-amperes reactive. |
| Apparent power (S) | The product of RMS voltage and current, in volt-amperes. What the cabling must be rated for. |
| Power factor | The cosine of the phase angle: the fraction of apparent power that is real. |
The inputs explained
| Field | What to enter |
|---|---|
| RMS voltage (V) | RMS voltage, which is the figure a normal meter reads. |
| RMS current (A) | RMS current in amps. |
| Phase angle (V leads I) (°) | The phase angle in degrees by which voltage leads current. Zero for a purely resistive load; positive for an inductive one such as a motor. |
When to use it
Sizing cable and protection
Cabling and breakers must handle the apparent power, which can be substantially more than the real power being used.
Understanding an industrial tariff
Commercial supplies are often charged on apparent power or penalised for poor power factor, which makes correction worth money.
Assessing a motor load
Motors are inductive and typically run at a lagging power factor, especially when lightly loaded.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much power is wasted as the phase angle grows?
The same voltage and current at a range of phase angles.
| Phase angle | Real power | Power factor |
|---|---|---|
| 0° | 1,150.00 W | 1.000 (lagging) |
| 30° | 995.93 W | 0.866 (lagging) |
| 45° | 813.17 W | 0.707 (lagging) |
| 60° | 575.00 W | 0.500 (lagging) |
Questions
Why does a poor power factor matter if I am only billed for real power?
Because the extra current still flows through the cables, transformers and switchgear, causing heating and losses. Domestic customers are usually billed on real power alone, but commercial ones are frequently charged on apparent power or penalised directly.
What causes a poor power factor?
Inductive loads, mainly: motors, transformers and older fluorescent ballasts. Lightly loaded motors are particularly bad, which is why oversizing a motor hurts more than it helps.
How is power factor corrected?
Usually by adding capacitance to offset the inductance, bringing voltage and current back into phase. Correction capacitors on industrial switchboards exist for exactly this purpose.
What does lagging mean?
That the current lags behind the voltage, which is the signature of an inductive load. A capacitive load does the opposite and gives a leading power factor.
For DC power and resistance relationships, see the Ohm's law calculator. For the impedance behind the phase angle, see the impedance calculator.