What the Single-Phase Power Calculator does
This calculator works out the missing sides of a single-phase power triangle. Give it any workable pair - voltage and current, a power and the power factor, or kW and kVA - and it returns real power in watts, apparent power in volt-amperes, reactive power in volt-amperes reactive, the current, the phase angle and the formula it used.
The distinction matters because a cable, a breaker and a supply agreement all care about different sides of that triangle. A 5 kVA load at 0.6 power factor delivers only 3 kW of useful work, but the cable still has to carry the full 21.7 A that 5 kVA implies at 230 V. Everything here is arithmetic done in your browser; nothing is sent anywhere.
How to use it
- Enter the two things you know and clear the fields you do not. The calculator establishes apparent power first and works the rest from it.
- Set the power factor honestly. Resistive loads - heaters, kettles, filament lamps - are 1.0. Small motors run between about 0.75 and 0.9 at full load and much worse lightly loaded. Switch-mode supplies and LED drivers vary enormously, so measure rather than assume.
- Read the three powers together. The kVA figure sizes the cable and the protective device; the kW figure is what the meter bills; the kVAr figure is what a capacitor bank would remove.
- Add the hours the load runs to see daily and annual energy, which is the figure to compare against an electricity bill.
- Use copy, CSV or JSON to take the numbers into a schedule, or the share link to send someone the same inputs - the link carries the configuration only, never any other data.
Reading the results
Real power (kW) is the average rate at which energy is actually converted into work or heat. It is what a domestic meter registers.
Apparent power (kVA) is simply volts times amps. It is the figure that sizes conductors, switchgear and transformers, because those components are limited by current and voltage, not by how usefully the current is being spent.
Reactive power (kVAr) is energy that flows out to the load's magnetic or electric fields and back again each cycle. It does no work, but it occupies capacity in every cable and transformer on the way.
The phase angle is the arccosine of the power factor: 0.8 is 36.87 degrees, 0.95 is 18.19 degrees, and unity is zero. A larger angle means more of the current is doing nothing useful.
Worked example: a 230 V load drawing 10 A at 0.8 power factor
Apparent power is simply 230 x 10 = 2300 VA, or 2.3 kVA. That is what the cable and the breaker see, whatever the load is doing with it.
Real power is 2300 x 0.8 = 1840 W. Reactive power is the third side of the triangle: the square root of 2300 squared minus 1840 squared, which is 1380 VAr. Those three numbers - 1840, 1380 and 2300 - are a 3-4-5 triangle scaled by 460, which is why a power factor of 0.8 turns up so often in worked examples.
The phase angle is arccos(0.8) = 36.87 degrees, so the current peaks about 2 milliseconds after the voltage on a 50 Hz supply.
If that load runs eight hours a day it uses 1.84 x 8 = 14.72 kWh a day, or about 5,373 kWh a year. A domestic meter charges for that. A commercial supply with a kVA demand charge would bill against the 2.3 kVA instead, and correcting the power factor to 0.95 would cut the current from 10 A to 8.42 A and the apparent power to 1.94 kVA without changing the 1840 W of useful work at all.
Formulas and scoring rules
- Apparent power
S = V x IIn volt-amperes. The product of the rms voltage and the rms current, regardless of phase.- Real power
P = V x I x cos(phi) = S x pfIn watts. cos(phi) is the power factor.- Reactive power
Q = sqrt(S^2 - P^2) = S x sin(phi)In volt-amperes reactive. Positive for an inductive (lagging) load.- Current from power
I = P / (V x pf) = S / VThe route used when you give a power rather than a current.- Phase angle
phi = arccos(pf)Reported in degrees. A leading power factor gives the same magnitude with the opposite sign.- Energy
kWh = kW x hoursReal power only; reactive power carries no energy over a whole cycle.
Why power factor is not efficiency
The two are often confused. Efficiency is output divided by input and tells you how much energy is wasted. Power factor is real power divided by apparent power and tells you how much of the current is in phase with the voltage. A perfectly efficient motor can still have a poor power factor, and a badly designed heater can have a power factor of exactly 1 while wasting everything it takes.
Poor power factor costs money in two ways: the extra current heats the cables that carry it, which is a real I-squared-R loss, and many commercial tariffs charge for peak kVA or impose a penalty below an agreed power factor. Neither shows up as extra kWh on the load itself.
Where a single-phase figure stops being enough
This calculator assumes one live conductor and one neutral, a sinusoidal supply and a load that draws a sinusoidal current. Two of those assumptions fail more often than people expect.
Non-linear loads - rectifiers, variable-speed drives, cheap LED drivers - draw current in short spikes rather than a sine wave. Their displacement power factor may be near unity while their true power factor is 0.6, because of harmonic current that this arithmetic cannot see. If the load is electronic and the figures matter, a true-rms power analyser is the only honest instrument for the job.
For a three-phase load, go to the three-phase calculator instead: the root-three relationship between line and phase quantities changes every result.
Limitations: what the result does not prove
- It assumes a sinusoidal voltage and current. With a non-linear load the real power factor includes a distortion component that only a measurement can give you.
- It says nothing about whether the cable, the breaker or the supply can carry the current it calculates. Size those with the cable and breaker calculators, and have the design checked by a qualified person.
- Power factor values you type in are assumptions unless you measured them. A nameplate figure is quoted at full rated load and is worse at part load.
- Reactive power is shown as a magnitude. The calculator does not know whether your load is lagging (inductive, the usual case) or leading (capacitive), and the correction needed is opposite in each case.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- IEC 60364-5-52 - Selection and erection of wiring systems - checked 19 Sep 2026
- NFPA 70 - National Electrical Code - checked 19 Sep 2026
- IEC 60027-1 - Letter symbols for electrical technology
Frequently asked questions
How do I convert kW to amps on a single-phase supply?
Divide the power in watts by the voltage multiplied by the power factor: I = P / (V x pf). A 3 kW heater at 230 V and unity power factor draws 13.04 A; a 3 kW motor at 0.8 power factor draws 16.30 A from the same supply, because the extra current is reactive.
What is the difference between kW, kVA and kVAr?
kW is the power doing work, kVA is volts times amps as the cable experiences it, and kVAr is the reactive power swapped back and forth with the supply. They form a right-angled triangle: kVA squared equals kW squared plus kVAr squared, and the power factor is the ratio of kW to kVA.
What power factor should I use if I do not know it?
Use 1.0 for purely resistive loads such as heaters and filament lamps. For a small induction motor at full load, 0.8 to 0.85 is a reasonable assumption and the nameplate usually states it. For electronic loads, do not assume - a switch-mode supply without power-factor correction can be anywhere between 0.5 and 0.99.
Why does my meter reading not match the kVA figure?
A domestic energy meter records real energy in kWh, which follows the kW figure. The kVA figure is larger whenever the power factor is below one, but that extra apparent power is not energy and is not billed on a simple domestic tariff. Commercial tariffs often do charge for peak kVA or for a power factor below an agreed threshold.
Can the power factor be greater than one?
No. Real power can never exceed apparent power, so the ratio cannot exceed one. If you enter a kW figure larger than the kVA figure the calculator refuses it, because one of the two numbers must be wrong rather than the arithmetic.
Does a capacitor reduce my electricity bill?
It reduces the current and therefore the I-squared-R losses in your own cables, and it can remove a kVA demand charge or a low-power-factor penalty on a commercial tariff. It does not reduce the real power the load consumes, so on a simple kWh-only tariff the saving is small - mostly the cable losses you were paying for anyway.
What does the phase angle tell me in practice?
It is the time lag between the voltage and the current waveforms, expressed as an angle. At 50 Hz, one full cycle is 360 degrees in 20 milliseconds, so a 36.87 degree lag is about 2.05 milliseconds. It is the quantity an oscilloscope or a phase-angle meter reads directly, which makes it a useful cross-check on a power factor you have assumed.
Is this calculation safe to use for a real installation?
Use it to understand and to check, not to certify. The arithmetic is standard and correct, but a real circuit design also needs current-carrying capacity, derating, voltage drop, protective device coordination, earthing and local regulations, and all of it must be verified by a qualified engineer against the applicable standard.
Last reviewed by the A2Z.Tools team against the sources listed above.
