What is the formula to convert kW to kVA?

kVA = kW divided by the power factor (PF). For example, 8 kW at a power factor of 0.8 gives 8 ÷ 0.8 = 10 kVA. The power factor is always between 0 and 1 and represents the fraction of apparent power that does real work.

What is the difference between kW and kVA?

kW (kilowatts) measures real power — the energy that actually does work, such as spinning a motor or generating heat. kVA (kilovolt-amperes) measures apparent power — the total power drawn from the supply, including both the working component and the reactive component that oscillates back and forth without doing net work. The ratio of kW to kVA is the power factor.

Why do I need to know kVA if I already know kW?

Generators, UPS units, transformers and circuit breakers are all rated in kVA, not kW. If you size equipment on kW alone without accounting for power factor, you will undersize the apparent-power capacity and risk overloading the supply or tripping protection devices. kVA is the figure you need when specifying supply infrastructure.

What is a typical power factor for an electric motor?

At full load most induction motors run at 0.85 to 0.92. At partial load the power factor drops — a motor running at 50 percent load might only reach 0.70 to 0.75. Variable-frequency drives and power-factor correction capacitors can raise the effective PF back toward 0.95 or higher.

How do I calculate kVA for a three-phase system?

For three-phase systems the apparent power formula is S (kVA) = (square root of 3) times V times I divided by 1000, where V is the line-to-line voltage and I is the line current. The kW to kVA relationship stays the same: kVA = kW divided by PF, regardless of whether the system is single-phase or three-phase.

What is reactive power (kVAR) and why does it matter?

Reactive power (Q, measured in kVAR) is the power that magnetises inductive loads like motors and transformers. It flows back and forth on the circuit without doing useful work, but it still flows through cables and switchgear and causes heating and voltage drop. The power triangle links all three: S (kVA) squared equals P (kW) squared plus Q (kVAR) squared. Reducing kVAR with capacitor banks lowers the kVA demand and can cut utility demand charges.

kW to kVA Calculator

The kW to kVA calculator converts real power (kilowatts) into apparent power (kilovolt-amperes) using the power factor — the single most important number when sizing generators, UPS systems, transformers, switchgear and cables. Every electrical installation has a power triangle connecting three quantities: real power P (kW), apparent power S (kVA) and reactive power Q (kVAR). Get the triangle wrong and you under-rate equipment, overload circuits or pay unnecessary demand charges on your electricity bill.

This tool computes all three sides of that triangle from a single kW and power-factor entry. It also derives the phase angle, an estimate of the current your load draws at standard voltage, and a full reference table so you can compare kVA across a range of power factors without re-entering values.

How it works

The fundamental formula is:

kVA = kW ÷ PF

where PF is the power factor — a dimensionless number from 0 to 1. At PF = 1.0 (a purely resistive load such as an electric heater), kVA equals kW exactly: all apparent power is real power. As inductance increases and PF falls toward 0.8 or lower, the kVA figure climbs above kW, meaning the supply must deliver more current than the useful work alone would require.

From the primary result the tool then calculates:

Reactive power Q — using the power-triangle identity Q = sqrt(S² - P²), expressed in kVAR.
Phase angle θ — arccos(PF), the angle between the voltage and current phasors, in degrees.
Estimated current — rearranging S = V × I (single-phase) or S = √3 × V × I (three-phase) to give I = S × 1000 ÷ V (single) or I = S × 1000 ÷ (√3 × V) (three-phase), using 230 V and 400 V as reference voltages respectively.

The voltage/current panel also runs the calculation in reverse: enter measured volts and amps and the tool derives kVA directly, then applies the power factor to give kW as well.

Worked example

A 15 kW motor runs at a power factor of 0.85:

Apparent power: 15 ÷ 0.85 = 17.65 kVA
Reactive power: sqrt(17.65² - 15²) = 9.29 kVAR
Phase angle: arccos(0.85) = 31.79°
Current at 400 V (3-phase): 17.65 × 1000 ÷ (√3 × 400) = 25.49 A

If you specified a generator purely on kW you would look for a 15 kW set, but you actually need one rated for at least 17.65 kVA — otherwise the reactive current overloads the alternator windings even though the real-power demand appears within limits.

Formula note

The power triangle obeys Pythagoras in the phasor domain:

S² = P² + Q² PF = P ÷ S = cos(θ) Q = S × sin(θ)

For three-phase circuits the apparent power from line voltage and current is:

S (kVA) = √3 × V_L × I_L ÷ 1000

where V_L is the line-to-line (phase-to-phase) voltage and I_L is the line current. The √3 factor (approximately 1.7321) accounts for the 120° separation between phases. The kW-to-kVA formula itself (kVA = kW ÷ PF) is the same for both single- and three-phase systems.

All arithmetic runs locally in your browser — no values are uploaded or stored.