# Three-phase power calculator

The three-phase power calculator calculates the apparent, active and reactive power for three-phase AC systems

## 3-phase power calculator parameters

• Voltage (V): Enter the phase-to-phase ($$V_{LL}$$) voltage for a 3-phase AC supply in volts.
• Current (I): Enter the the current in Amperes (A).
• Power factor (cosΦ). Enter the power factor of the load. Its between 0 and 1.

## How to calculate 3-phase power?

### The 3-phase power formula for active power is:

$$P_{kW}=\dfrac{\sqrt{3} \cdot V_{LL} \cdot I \cdot \cos \phi } { 1000 }$$

Where,

• $$V_{LL}$$ is the 3-phase line voltage,
• $$I$$ is the current, and
• $$\cos \phi$$ is the power factor between 0 and 1.

### The 3-phase power formula for apparent power is:

$$S_{kVA}=\dfrac{ \sqrt{3} \cdot V_{LL} \cdot I}{ 1000 }$$

Where,

• $$V_{LL}$$ is the 3-phase line voltage, and
• $$I$$ is the current.

### The 3-phase power formula for reactive power is:

$$Q_{kvar}=\dfrac{\sqrt{3} \cdot V_{LL} \cdot I \cdot \sin{\phi}}{ 1000 }$$

Where,

• $$\sin{\phi} = \sqrt{ 1 -(\cos{\phi)}^2}$$, and
• $$\cos \phi$$ is the power factor between 0 and 1.

Alternative 3-phase power formula for reactive power is:

$$Q_{kvar}=\sqrt{ S_{kVA}^2 – P_{kW}^2 }$$

Where,

• $$S_{kVA}$$ is the 3-phase apparent power, and
• $$P_{kW}$$ is the 3-phase active power.