Three-Phase Power
Power across three phases - motor current estimates and switchboard loading.
Why this matters
Where it occurs
Industrial plants run on three-phase power. Motor nameplates, switchboards and generators all reference the three-phase formulas.
Why calculate it
Three-phase delivers power on three conductors at 120-degree spacing, which is why the square root of three appears in the math.
What decision it supports
What is this motor's expected full-load current? Is the switchboard balanced? Is the cable sized right?
What happens if it is wrong
Forgetting the root of three or the power factor gives current estimates that are 40% wrong - enough to mis-size protection dangerously.
The concept
Three-phase power is P = √3 x V x I x PF, where V and I are line voltage and line current. The √3 (about 1.732) accounts for the three phases working together.
Rearranged, the motor current estimate is I = P / (√3 x V x PF). A 15 kW motor at 460 V with a 0.85 power factor draws about 22 A.
Power factor is the fraction of the apparent power that becomes real work - ignoring it underestimates the current the conductors must carry.
Formula
Three-Phase Power
P = sqrt(3) x V x I x PF
- P = Real power (watts (W))
- V = Line voltage (volts (V))
- I = Line current (amperes (A))
- PF = Power factor (0 to 1)
Worked example
Problem: Estimate the full-load current of a 15 kW, 460 V, 0.85 PF three-phase motor.
- Rearrange: I = P / (√3 x V x PF).
- Substitute: I = 15000 / (1.732 x 460 x 0.85).
- Multiply the denominator: 1.732 x 460 x 0.85 = 677.
- Divide: I = 15000 / 677 = 22.1 A.
About 22 A - the value to compare with a clamp meter reading.
Quick solve: practice it
A 30 kW motor runs at 460 V with PF 0.9. Estimate its line current.
Quick-solve habit: calculate, then ask yourself - does this answer make sense in real units?
Games that use this mathematics
Apply the calculation inside a workplace simulation.