Power calculation three-phase current

🔌 Three-Phase Power Calculations

Three-phase power is the backbone of industrial energy supply. With three phase-shifted alternating currents, it enables efficient operation of electric motors and high-performance systems. Our calculators consider the √3 factor for precise three-phase calculations.

Available Calculations:

Apparent Power: S = U × I × √3

Total power in three-phase systems

Active Power: P = U × I × cos φ × √3

Effective power in three-phase motors

Reactive Power: Q = U × I × sin φ × √3

Reactive power in three-phase systems

Power Factor: cos φ = P / S

Ratio of active to apparent power

Reactive Factor: sin φ = Q / S

Ratio of reactive to apparent power

Why Three-Phase Power in Industry?

Three-phase power consists of three alternating currents shifted by 120°. This enables constant power output and efficient energy transmission. The √3 factor (approx. 1.732) is characteristic of all three-phase calculations. Typical applications include electric motors, industrial plants, and high-voltage transmission with 400V voltage.

Three-Phase Apparent Power
S = U × I × √3

Calculate the apparent power, voltage or current.

S = U × I × √3

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase motor has a rated current of 129.9 Ampere. What apparent power results from these values?
S = U × I × √3
S = 400 V × 129.9 A × √3
S = 90 kVA

Units of Measurement:
Apparent Power S = Kilovolt-Ampere [kVA]
Voltage U = Volt [V]
Current I = Ampere [A]
√3 or 1.73 = unitless

Three-Phase Active Power
P = U × I × cos φ × √3

Calculate the active power, voltage, current or power factor.

P = U × I × cos φ × √3

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase standard motor has a rated current of 25.18 Ampere and a cos φ of 0.86. What electrical power results from these values?
P = U × I × cos φ × √3
P = 400 V × 25.18 A × 0.86 × √3
P = 15.003 kW or 15 kW

Units of Measurement:
Active Power P = Kilowatt [kW]
Voltage U = Volt [V]
Current I = Ampere [A]
cos φ = unitless
√3 or 1.73 = unitless

Three-Phase Reactive Power
Q = U × I × sin φ × √3

Calculate the reactive power, voltage, current or sin φ.

Q = U × I × sin φ × √3

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase standard motor has a rated current of 34.516 Ampere and a sin φ of 0.92. What reactive power results from these values?
Q = U × I × sin φ × √3
Q = 400 V × 34.516 A × 0.92 × √3
Q = 22 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Voltage U = Volt [V]
Current I = Ampere [A]
sin φ = unitless
√3 or 1.73 = unitless

Three-Phase Power Factor
cos φ = P / S

Calculate cos φ, active power or apparent power.

cos φ = P / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 4.0 kW three-phase motor (or 400V electric motor) has a cos phi of 0.85. What apparent power results from these values?
cos φ = P / S
S = P / cos φ
S = 4.0 kW / 0.85
S = 4.706 kVA

Units of Measurement:
Active Power P = Kilowatt [kW]
Apparent Power S = Kilovolt-Ampere [kVA]
cos φ = unitless

Three-Phase Reactive Factor
sin φ = Q / S

Calculate sin φ, reactive power or apparent power.

sin φ = Q / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A three-phase motor with apparent power of 15 kVA has a sin phi of 0.33. What reactive power results from these values?
sin φ = Q / S
Q = S × sin φ
Q = 15 kVA × 0.33
Q = 4.95 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Apparent Power S = Kilovolt-Ampere [kVA]
sin φ = unitless

Formulas for three-phase current

  • Active power: P = U × I × cos φ × √3
  • Apparent power: S = U × I × √3
  • Reactive power: Q = U × I × sin φ × √3
  • Active power factor: cos φ = P / S
  • Reactive power factor: sin φ = Q / S

U is the voltage in volts, I is the current in amperes. The factor √3 (around 1.732) is characteristic for all three-phase calculations because three-phase current consists of three alternating currents that are 120° out of phase.

Apparent power, active power and reactive power

The apparent power is made up of active power and reactive power. Unlike these two, it is independent of the phase shift φ. For the same apparent power, the greater the angle between 0 and 90°, the greater the reactive power.

Calculation example of apparent power

A 400V three-phase motor has a rated current of 129.9A.

S = U × I × √3
S = 400V × 129.9A × √3
S = 90 kVA