Motor Full-Load Current (Three Phase)

Calculates a three-phase motor's rated full-load current from its power, line voltage, power factor, and efficiency.

Written by the Vorzep Team

Electric MachinesMotor Sizing

Motor Full-Load Current Calculator Three‑Phase

I = P / (√3 · V · cos θ · η)

I = full‑load current (A) · P = power (W) · V = line voltage (V) · cos θ = power factor · η = efficiency

⟹ Solve ⟷ I, P, V, cos θ, η

Current (I)

Power (P)

Voltage (V)

Power Factor (cos θ)

—

Efficiency (η)

—

Please fix the errors above.

Solve for: Current (I) Power (P) Voltage (V) Power Factor (cos θ) Efficiency (η)

Presets:

Full-Load Current —

—

I: — P: — V: — PF: — η: —

✓ Copied!

Current Gauge —

Low (< 10 A) Medium (10–100 A) High (> 100 A)

I = P / (√3 · V · cos θ · η) · All values must be positive. Power factor and efficiency are between 0 and 1.

Variables

Symbol	Quantity	Unit
I	Full-load current	A
P	Output power (mechanical)	W
V	Line-to-line voltage	V
cos θ	Power factor	dimensionless
η	Motor efficiency	dimensionless (0 to 1)

What it means

For a three‑phase motor, the full‑load current is given by I = P / (√3 × V × cosθ × η), where P is the output power (W), V is the line‑to‑line voltage, cosθ is the power factor, and η is the efficiency. The √3 factor accounts for the three‑phase configuration. This current is used for selecting overload relays, contactors, and cable sizing. Example: A 5kW, 400V, three‑phase motor with power factor 0.85 and efficiency 90% draws I = 5000 / (1.732 × 400 × 0.85 × 0.9) = 5000 / (529.9) ≈ 9.43A. This is typical for a motor of this rating.

Worked example

Three‑Phase Motor FLC – Practical Example

Real‑World

Scenario: A 15 HP (11.19 kW) three‑phase motor runs at 400 V, efficiency 90%, pf 0.86. Find the full‑load current.

Parameter	Value
P	11,190 W
V_L	400 V
cos θ	0.86
η	0.90
Formula	`I = P / (√3 × V_L × cos θ × η)`

1√3 × 400 × 0.86 × 0.90 = 1.732 × 400 × 0.774 = 536.4

2I = 11190 / 536.4 ≈ 20.86 A

Final Design I ≈ 20.9 A ✓ Full‑load current

Why: Three‑phase motor current is less than single‑phase for the same power due to √3 factor – important for cable and protection sizing.

Common mistakes

Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.

Applications

Motor full‑load current (three phase): I = P/(√3×V×cosθ×η) calculates the line current for three‑phase motors. This is widely used for industrial motor installations. Engineers use it to size feeders, breakers, and starters. This formula is essential for three‑phase motor protection and control.

Three‑phase motor circuit design and protection
Motor starter and contactor sizing
Cable sizing for industrial motors
Power factor and efficiency analysis
Educational understanding of three‑phase motor currents