Horsepower Calculator — AC Three Phase Power Supply

This is the three-phase companion to the single-phase motor calculator, tying together horsepower, voltage, current, efficiency, and power factor for a balanced three-phase AC supply. Enter any four and it returns the fifth — most often the line current, for wire and breaker sizing.

The formula — and the √3

HP = √3 · E · I · EFF · PF / 745.7. The one thing that changes from single phase is the factor of √3 (about 1.732): in a balanced three-phase system the real power is √3 × line-to-line voltage × line current × power factor. Multiply by efficiency for the shaft power, then divide by 745.7 watts per horsepower (metric divides by 1000 for kW). Be sure to use the line-to-line voltage (e.g. 460 V) and the line current, and enter efficiency and power factor as decimals between 0 and 1.

Solve in any direction

• Current — the amps a known three-phase motor will draw, for conductor and overload sizing (confirm against the NEC full-load current tables).
• Horsepower — the shaft power implied by measured voltage and current.
• Efficiency or power factor — backed out from the other four; a solved value above 1.0 signals inconsistent inputs.

Working with a single-phase supply instead? Use the single-phase horsepower calculator. For the pump side, see pump power and motor sizing.

Worked example

A 460 V three-phase motor drawing 10 A at 0.90 efficiency and 0.85 power factor delivers HP = √3 · 460 · 10 · 0.90 · 0.85 / 745.7 ≈ 8.17 hp (6.10 kW). It draws about 7967 VA of apparent power and 6772 W of real power, of which 6095 W reaches the shaft.