Three Phase Power Calculator
This three phase power calculator needs voltage, current and power factor: at 400 V, 16 A and a power factor of 0.9 the real power is about 9.98 kW. It also works backwards from power to current.
Example: What do you want to calculate: Power from voltage and current · Line-to-line voltage 400 V · Current per line 16 A · Power factor cos φ 0.9 · Load connection: Star (wye) → Result: P = 9.98 kW · S = 11.09 kVA · Q = 4.83 kvar. Source: Wikipedia – Drehstrom (power, star and delta connection). Updated: .
How it is calculated
Real power in a three-phase system is P = √3 · U · I · cos φ with the voltage U between two lines, the current I per line and the power factor cos φ. Apparent power is S = √3 · U · I, reactive power Q = √(S² − P²).
How it is calculated
At 400 V and 16 A the apparent power is √3 · 400 · 16 = 11.09 kVA. With cos φ = 0.9 that is 9.98 kW real power and 4.83 kvar reactive power. In the “current from power” direction, I = P / (√3 · U · cos φ · η): a motor with 11 kW shaft power, η = 90 % and cos φ = 0.9 draws about 19.6 A at 400 V.
Star and delta
In a star connection each phase winding sees U/√3 (231 V at 400 V) and carries the full line current. In a delta connection each winding sees the full voltage and carries I/√3. The total power follows the same formula in both cases.
- With cos φ = 1 (heating elements, cookers) real power equals apparent power.
- Motors have a power factor of about 0.8 to 0.9; efficiency must be considered as well.
- For fusing, the current counts, not the real power alone.
Frequently asked questions
How do you calculate three-phase power?
P = √3 · U · I · cos φ. At 400 V, 16 A and cos φ = 1 that is about 11.1 kW; with cos φ = 0.9 about 9.98 kW.
How many amps does an 11 kW three-phase motor draw?
At 400 V, cos φ = 0.9 and 90 % efficiency about 19.6 A. Ignoring efficiency and with cos φ = 1 it would be 15.9 A.
What is the difference between star and delta?
In star each phase sees U/√3 and carries the line current; in delta it sees U and carries I/√3. The power across all three phases is the same when the phase values are matched.
Sources and legal basis
- Wikipedia – Drehstrom (power, star and delta connection)
- Wikipedia – Three-phase electric power
- Wikipedia – Wirkleistung, Blindleistung und Scheinleistung (active, reactive and apparent power)
As of: · Editorial policy
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