Electrical & Mechanical Engineering

Power Formula

Learn common power formulas including P = VI, single-phase and three-phase AC power, and mechanical P = Tω, with worked examples and a live electrical power calculator.

Governing equation

DC electrical power: P = V × I

Power is the rate at which energy is transferred or work is done. The correct equation depends on whether the system is electrical, mechanical or another energy domain.

For single-phase AC real power, P = V I cosφ. For balanced three-phase AC, P = √3 V I cosφ. Rotational mechanical power can be written P = Tω.

Live calculator

DC electrical power calculator

Uses P = V × I for DC or purely resistive conditions.

Voltage

Current

Result

960W

0.96 kW

Formula variables and units

Symbol	Meaning	Typical SI unit
P	Power	W
V	Voltage	V
I	Current	A
cosφ	Power factor for AC real power	dimensionless
T, ω	Torque and angular speed for rotating mechanical power	N·m, rad/s

How to calculate it

1Identify the physical system and required power type.
2For DC, multiply voltage by current.
3For AC real power, include power factor and the correct phase relationship.
4For rotating mechanical systems, use torque multiplied by angular speed.
5Keep units consistent and distinguish W, kW, VA and kVA.

Common mistakes

Using P = VI for AC real power without considering power factor where required.
Forgetting the √3 factor for balanced three-phase line quantities.
Confusing real power kW with apparent power kVA.
Mixing RPM directly with rad/s in P = Tω.

Worked examples

DC electrical example

Given: V = 48 V, I = 20 A

Working: P = 48 × 20

Power = 960 W = 0.96 kW.

Three-phase example

Given: VLL = 415 V, I = 100 A, PF = 0.9

Working: P = √3 × 415 × 100 × 0.9

Real power ≈ 64.7 kW.

Go deeper

Use the dedicated OneCalcApp tool

The quick calculator above demonstrates the governing equation. Open the related engineering tool for broader inputs, outputs and calculation context where available.

Engineering Calculators