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kVA, kW and Power Factor Calculator

Completes the AC power triangle from any two of apparent power (kVA), real power (kW), reactive power (kVAR) and power factor, reports the phase angle and, when a voltage is given, the single- or three-phase line current, plus the capacitor kVAR needed to correct the power factor to 0.95.

When to use

You need to convert a transformer, generator or UPS kVA rating to usable kW, find the power factor or reactive power of a load, size a power-factor-correction capacitor bank, or get the current for a kVA load at a voltage.

Do not use when: You have line voltage and current of a balanced three-phase load and want the full per-phase breakdown (use three-phase-power), or the load is DC or non-sinusoidal with strong harmonics (displacement and distortion power factor differ).

Formula

S² = P² + Q²; PF = P / S; φ = arccos(PF); from S and PF: P = S × PF, Q = √(S² − P²); from P and Q: S = √(P² + Q²); from P and PF: S = P / PF; from PF and Q: S = Q / √(1 − PF²); current_a = S × 1000 / voltage_v (single) or S × 1000 / (√3 × voltage_v) (three); kvar_to_reach_pf_0_95 = max(0, Q − P × tan(arccos 0.95))

Power-triangle relations for sinusoidal AC (displacement power factor). The load is assumed inductive (lagging), which is the usual case for motors and transformers; a leading (capacitive) load has the same magnitudes with the opposite sign of Q.

Inputs

Parameter	Type	Unit	Required	Description
`apparent_power_kva`	number	kVA	no	Apparent power in kilovolt-amperes (the nameplate rating of transformers and generators). Range: > 0, ≤ 10000000
`real_power_kw`	number	kW	no	Real (active) power in kilowatts, the part that does work and is billed as energy. Range: ≥ 0, ≤ 10000000
`power_factor`	number		no	cos φ between 0 and 1 (typical: motors 0.8–0.9, resistive heaters 1.0). Range: > 0, ≤ 1
`reactive_power_kvar`	number	kVAR	no	Reactive power in kilovolt-amperes reactive (magnetising power of motors and transformers). Range: ≥ 0, ≤ 10000000
`voltage_v`	number	V	no	Optional RMS supply voltage (line-to-line for three-phase); enables the current output. Range: > 0, ≤ 1000000
`phases`	enum: single \| three		default three	Supply type used for the current calculation.

Outputs

Output	Type	Unit	Description
`apparent_power_kva`	number	kVA	S = √(P² + Q²) = P / PF.
`real_power_kw`	number	kW	P = S × PF.
`reactive_power_kvar`	number	kVAR	Q = √(S² − P²).
`power_factor`	number		PF = P / S = cos φ.
`phase_angle_degrees`	number	°	φ = arccos(PF), the angle between voltage and current.
`current_a`	number	A	I = S × 1000 / V (single-phase) or S × 1000 / (√3 × V) (three-phase); only when voltage_v is given.
`kvar_to_reach_pf_0_95`	number	kVAR	Reactive compensation needed to raise the power factor to 0.95: Q − P × tan(arccos 0.95); 0 when PF is already 0.95 or higher.
`pf_correction_note`	string		Plain-language note on correcting the power factor to the common 0.95 target (lagging load assumed).
`given`	string		Which two inputs the triangle was solved from.

Example

100 kVA at PF 0.8, 400 V three-phase: {"apparent_power_kva":100,"power_factor":0.8,"voltage_v":400,"phases":"three"} → {"apparent_power_kva":100,"real_power_kw":80,"reactive_power_kvar":60,"power_factor":0.8,"phase_angle_degrees":36.87,"current_a":144.338,"kvar_to_reach_pf_0_95":33.705}

50 kW and 30 kVAR: {"real_power_kw":50,"reactive_power_kvar":30} → {"apparent_power_kva":58.31,"power_factor":0.8575,"phase_angle_degrees":30.96,"kvar_to_reach_pf_0_95":13.566}

GET https://tttkmbb.com/api/v1/calculate/kva-kw-power-factor?apparent_power_kva=100&power_factor=0.8&voltage_v=400&phases=three

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/kva-kw-power-factor (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/kva-kw-power-factor · Markdown: https://tttkmbb.com/engineering/kva-kw-power-factor.md · JSON definition: https://tttkmbb.com/engineering/kva-kw-power-factor.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="kva-kw-power-factor"
OpenAPI operationId: convert_kva_kw_power_factor
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – AC power (power triangle) (reference)
Wikipedia – Power factor (reference)

FAQ

Why is kVA larger than kW?

Real power is only the component of the apparent power in phase with the voltage; the remaining reactive power circulates between source and load without doing work but still loads conductors and transformers. kW = kVA only at power factor 1.

How much capacitor kVAR do I need for correction?

The load's reactive power minus the reactive power allowed at the target factor: Q_c = P × (tan φ₁ − tan φ₂). For 80 kW at PF 0.8 corrected to 0.95 that is 60 − 26.3 ≈ 33.7 kVAR.

Why can I not enter PF 1 with a reactive power?

At unity power factor the reactive power is zero by definition, so the pair is contradictory; give real or apparent power instead.

Related calculators

Three-Phase Power Calculator — Full per-phase breakdown for balanced three-phase loads.
Electric Power Calculator — P = V × I for DC and unity power factor.
Wire Voltage Drop Calculator — Cable drop for the resulting current.