How to use the Three Phase Power Calculator
- 1. Choose what to findPower, line current from power, or two-wattmeter readings.
- 2. Enter voltage and pfLine voltage like 415 V and the power factor.
- 3. See P, Q, SPlus phase voltage, phase current and impedance per phase.
Three-phase power formulas
For a balanced load, P = √3 VL IL cos φ, Q = √3 VL IL sin φ and S = √3 VL IL. In star, Vph = VL/√3 and Iph = IL. In delta, Vph = VL and Iph = IL/√3. The power formula is the same for both.
Worked example: 415 V, 10 A, pf 0.8. P = 1.732 × 415 × 10 × 0.8 = 5,750 W, S = 7,188 VA and Q = 4,313 VAR. For a 7.5 kW motor with 88% efficiency and pf 0.85 on 415 V, the input is 8,523 W and IL = 8,523 / (1.732 × 415 × 0.85) = 13.95 A.
Two-wattmeter method and exam questions
Two wattmeters measure total power in a three-wire system: P = W1 + W2 and tan φ = √3 (W1 − W2)/(W1 + W2). With W1 = 3,000 W and W2 = 1,000 W, P = 4 kW, tan φ = 0.866, φ = 40.9° and pf = 0.756. At pf 0.5 one meter reads zero; below 0.5 it reads negative.
- Find the line current of a 415 V, 20 kW load at 0.9 pf.
- Find phase current and impedance for a delta load.
- Find the power factor from two wattmeter readings.
- Compare star and delta power for the same impedances (delta is three times more).
Frequently asked questions
Is the formula different for star and delta?
No. P = √3 VL IL cos φ works for both when you use line values. Only the phase voltage and phase current differ.
Why does one wattmeter read negative?
When the power factor is below 0.5, the phase angle makes one meter's reading negative. Reverse its current coil and subtract the reading.
What voltage should I use in India?
Low-voltage three-phase supply is 415 V line (about 240 V phase), at 50 Hz. Use the value given in your question.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.