Single phase power calculator
Single phase power calculator
Active, apparent and reactive power on one phase, and the angle between voltage and current that separates them.
How this is calculated
Apparent power S = V x I. Active power P = S x cos φ, which is the part that does work. Reactive power Q = S x sin φ, and √(P² + Q²) returns S — the three are a right triangle, not three separate measurements.
- A resistive heater draws current in step with the voltage, so cos φ is 1 and every watt is active. Windings and capacitor-start loads shift it, and the shifted part still occupies the cable and the transformer even though it does no work.
- This is the sinusoidal, steady-state reading. With a non-linear load — a drive, a switched-mode supply, an LED driver — the current is not a sine wave and power factor splits into displacement and distortion; a true-power meter is the only way to read it.
Volts times amps is not watts unless the load is a heater. The three powers — working, apparent and idle — are the sides of one triangle, and the power factor is the angle between them.
What the reactive part actually costs
Reactive power does no work and does not appear on a domestic unit bill, but it occupies the transformer, the cable and the alternator exactly as if it did. That is why an industrial connection is charged on maximum kVA rather than kW, and why a poor power factor is a bill item rather than a physics curiosity.
The angle line is the same information as the power factor in a form that makes the triangle visible. At 0.92 the current is 23.07° behind the voltage, and the cosine of that is the fraction of the apparent power doing work.
Worked through
A single-phase load at 230 V drawing 4.5 A has an apparent power of 1,035 VA. At a power factor of 0.92, 952.2 W of that is doing work and 405.6 VAR is circulating.
The check is the triangle: √(952.2² + 405.6²) = 1,035, back to V × I exactly. If a set of three power figures does not close like that, one of them was measured against a different definition.
Questions readers ask
Is the voltage line-to-neutral or line-to-line?
On a single-phase supply the two are the same thing — one live and one neutral, 230 V in a house. The line-to-line figure of 415 V belongs to a three-phase system and would give a wrong answer here by a factor of √3.
What power factor should I type for a motor?
The one on the plate at full load, and nothing at all for part load — a motor’s power factor falls sharply as it is lightly loaded, and a nameplate figure used at a quarter load overstates it badly. The plate describes the machine at its rating, not at any other point.
Does this work for a non-linear load?
No. A switched-mode supply, a drive or an LED driver draws current in spikes rather than a sine, so the true power is not V × I × cos φ of the fundamental. A meter that measures watts directly is the only honest reading, and displacement power factor and distortion are then separate quantities.
Why is apparent power in VA and not watts?
Because it is the product of the two things the supply has to deliver — pressure and flow — without any claim about how much of it becomes work. Equipment rated in VA, kVA or HP is rated on what it must carry, which is why a generator and a transformer both avoid the watt.
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