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3-Phase Power Calc (Formula + Solved)

Quick answer

The three-phase power formula with worked solutions: P = root3 x VL x IL x cos phi applied to motors, heaters, and transformers, step by step.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How Does the 3-Phase Power Calc Work?

P = √3 × VL × IL × cos φ = 3 × VP × IP × cos φ

This calculator is the formula workshop: it shows both equivalent forms - line quantities (root3 x VL x IL) and phase quantities (3 x VP x IP) - and walks the arithmetic. Example: a delta heater drawing 10 A per line at 400 V with unity PF: P = 1.732 x 400 x 10 = 6.93 kW; each of the three elements dissipates 2.31 kW. Reverse direction: a 30 kW motor at 400 V, PF 0.86, draws I = 30000/(1.732 x 400 x 0.86) = 50.4 A per line. Apparent power sizes the hardware: that 30 kW motor at PF 0.86 needs a 34.9 kVA transformer and 50.4 A breaker, while improving PF to 0.95 drops both to 31.6 kVA and 45.6 A - correction pays twice.

  1. 1

    Pick what you know

    Power, current, or voltage set.

  2. 2

    Enter the values

    Line or phase quantities.

  3. 3

    Read the worked solution

    Each step of the formula shown.

Use Cases

Working motor and heater sizing problems for exams

Cross-checking instrument readings against theory

Converting between line and phase quantities in star/delta

Common Mistakes

  • Mixing line voltage with phase current in one formula

  • Double-counting root3 when starting from phase values

  • Forgetting unity PF does not apply to motors - only to resistive heaters

FAQs

When do I use 3 x VP x IP instead of root3 x VL x IL?

They are the same answer via different measurements. In star, VL = root3 VP and IP = IL, so 3 x VP x IP = root3 x VL x IL. Use whichever pair your meters actually read.

How do I find line current from power?

Rearrange: I = P/(root3 x VL x cos phi). A 22 kW motor at 400 V and PF 0.85 draws 22000/(1.732 x 400 x 0.85) = 37.3 A. Add efficiency for input current: divide again by 0.92 to get 40.6 A.

Does a 230/400 V system change the math?

No - 230 V is simply 400/root3, the phase voltage of a star-connected 400 V system. Plug in 400 V as VL and the formulas hold; using 230 with the root3 formula double-counts the root3.

Why is my measured power lower than the nameplate?

Motors rarely run at full load: a 30 kW machine driving a 60 percent load draws about 19.5 kW. Nameplate ratings are capability, not consumption - measure or log before billing estimates.

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