Sizing a generator, UPS or cable starts with the real and apparent power of the load. Enter the voltage, current and power factor for a single-phase or three-phase supply to get kW, kVA and kVAR.
Choose single or three phase.
Enter voltage, current and power factor.
Read kW, kVA and kVAR.
Three phase: S = √3 × V_L × I
Real power: P = S × pf
Reactive: Q = S × √(1 − pf²)
In AC circuits, the power a load draws is described by three linked numbers. Real power in kilowatts (kW) does useful work, such as turning a motor shaft or heating water. Apparent power in kilovolt-amperes (kVA) is the product of voltage and current and is what cables, transformers and generators must carry. Reactive power in kVAR shuttles back and forth to build magnetic and electric fields. This calculator computes all three for single-phase or three-phase supplies from voltage, current and power factor.
Electricians, facility managers and small business owners need these numbers to size a diesel generator, inverter, UPS, cable or capacitor bank. In India, homes usually get single-phase supply, while shops, workshops and factories often have three-phase low-tension connections.
1. Note the supply type, voltage, current and power factor (pf, between 0 and 1).
2. Single phase: apparent power S = V × I ÷ 1000 in kVA.
3. Three phase, with line-to-line voltage: S = √3 × V × I ÷ 1000 in kVA.
4. Real power: P = S × pf in kW.
5. Reactive power: Q = S × √(1 − pf²) in kVAR.
6. Check: P² + Q² should equal S².
In a purely resistive load, voltage and current rise and fall together, and all the power is real. Motors, transformers and fluorescent ballasts have inductance, which makes the current lag the voltage by an angle φ. The current can then be split into a part in step with the voltage, which delivers real power, and a part 90° out of step, which delivers none on average. These form a right triangle: S is the hypotenuse, P = S cos φ and Q = S sin φ. The power factor is cos φ = P ÷ S.
A three-phase supply has three voltages 120° apart. In a star connection, the voltage between two lines is √3 times the voltage from a line to neutral, because it is the vector difference of two phase voltages at 120°. That is why a 415 V line-to-line supply has about 240 V from each line to neutral. Total apparent power is three times the power per phase: 3 × V_phase × I = 3 × (V_line ÷ √3) × I = √3 × V_line × I. The same result holds for a delta connection.
For the same real power, a lower power factor means more current. More current means thicker cables, bigger transformers and more heating losses in the wiring. Utilities therefore encourage consumers with large inductive loads to keep power factor high, and many commercial and industrial tariffs charge on kVAh or add penalties for low power factor, as notified by the state electricity regulator. Installing capacitors near the load supplies the reactive power locally, reducing kVA and current for the same kW.
Suresh runs a flour mill (atta chakki) in a village near Indore on a single-phase 230 V supply. The motor draws 12 A at a power factor of 0.9, and he wants to know the kW and kVA before buying a backup generator.
Apparent power: S = V × I = 230 × 12 ÷ 1000 = 2.76 kVA
Real power: P = S × pf = 2.76 × 0.9 = 2.484 kW
Reactive power: Q = S × √(1 − pf²) = 1.2031 kVAR
Answer: Real power 2.484 kW; Apparent power 2.76 kVA; Reactive power 1.2031 kVAR
Sizing a generator or inverter in kW from the load's kW rating when its capacity is limited in kVA.
Using the line-to-neutral voltage in the three-phase formula, which needs line-to-line voltage.
Assuming a power factor of 1 for motors, pumps and compressors, which are inductive.
Forgetting starting current; motors draw several times their running current for a moment at start.
Adding kVA figures of loads with very different power factors as if they were kW.
Sizing diesel generators, inverters and UPS systems for homes, shops and factories.
Selecting cable sizes and circuit breakers from load current.
Designing power factor correction capacitor banks, from the kVAR figure.
Estimating the real power drawn by pumps, motors and air conditioners.
Electrical engineering and ITI coursework on single and three-phase circuits.
What voltage should I use for 3-phase in India?
415 V line-to-line (240 V line-to-neutral) for standard low-tension supply.
Why is my electricity bill in kWh, not kVAh?
Domestic bills charge real energy; many industrial tariffs also bill kVAh or penalise low power factor.