Electrical calculator

Power Factor Calculator

Calculate power factor from real power, voltage, and current for single-phase and three-phase (line-line or line-neutral) circuits. Try it free.

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Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance

Input interpretation: Enter values to calculate.
Result: —
Assurance: Engineering
Declared partition coverage: PASS · 4/4 declared partitions (1phi, 3phi-ll, 3phi-ln, invalid-domain) · Matrix
Known limitations: P_kW in; S/Q out in kVA/kvar
Core CVP does not include live graph, viewport, or pointer interaction.
Model: Power factor λ, apparent power S (kVA), and reactive power Q (kVAR) from V, I, and P; UI also estimates phase angle and correction capacitance from optional f.
Scope: Sinusoidal RMS voltage and current magnitudes.
Verification: Engine tested · Source checked · v1.5.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions: Calculation 1.5.1 · CVP protocol 1.0.0-proposed
CVP identity: 8/8 property · digest 3a01980707da
Legacy regression: 26/26 tests · Production surface contract 4/4
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 8/8 CVP boundary · 8/8 invalid · 8/8 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources: IEC 60050 — International Electrotechnical Vocabulary — Apparent power (IEV 131-11-41)
IEC 60050 — International Electrotechnical Vocabulary — Reactive power (IEV 131-11-44)
IEC 60050 — International Electrotechnical Vocabulary — Power factor (IEV 131-11-46)
IEEE Std 1459-2025 — Power factor as P/S; apparent, active, and reactive power (S² = P² + Q²)
BIPM SI Brochure (9th edition, version 4.01) — SI units related to electrical power
Sources
Evidence: 10 legacy golden · 8 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 8/8 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Power factorPF = P ÷ S = cos φ

Apparent power (1φ)S(kVA) = V × I ÷ 1000

Apparent power (3φ L-L)S(kVA) = √3 × VL-L × I ÷ 1000

Reactive powerQ = √(S² − P²)

Correction capacitorC = 1000 × Q ÷ (2π f V²) [F]

iP in kW, S in kVA, Q in kVAR. Three-phase L-N mode uses S = 3×VL-N×I/1000 and C = 1000×Q/(3×2πf V²). Capacitor estimate fully cancels Q toward unity PF — not a substitute for engineered bank sizing with harmonics and utility rules.

How to use

Choose single-phase or three-phase

For three-phase, pick line-to-line or line-to-neutral voltage basis.

Enter V, I, real power (kW), and frequency

Use RMS volts and amps. Frequency is only for the capacitor estimate (typically 50 or 60 Hz).

Read PF, S, Q, angle, and C

PF is also shown as a percent. Capacitance is listed in µF and F.

Example calculations

Common configurations with formula and result.

Single-phase load

230 V · 10 A · 1.8 kW

S = 230×10/1000 · PF = 1.8/S

S = 2.3 kVA · PF ≈ 0.783

Unity PF check

230 V · 10 A · 2.3 kW

P = S

PF = 1.000 · Q = 0

Three-phase L-L

400 V · 50 A · 30 kW

S = √3×400×50/1000

S ≈ 34.64 kVA · PF ≈ 0.866

Office-style PF

50 kW · 60 kVA (from meter)

PF = 50/60

PF ≈ 0.833 · Q ≈ 33.2 kVAR

Typical power factor by load (illustrative)

Common values at a glance.

Load type	Typical PF	Notes
Resistive heater / incandescent	≈ 1.00	Unity
Motor (full load)	0.80–0.90	Lagging
Motor (light load)	0.40–0.60	Often needs correction
Fluorescent (magnetic ballast)	0.50–0.70	Lagging
LED (quality driver)	0.90–0.99	Varies
Welding equipment	0.50–0.70	Lagging
Office building (aggregate)	0.80–0.90	Often corrected

i Many utilities target PF ≥ 0.90–0.95 to avoid penalties. Values vary by equipment and loading.

Power Factor calculator specification

Version 1.5.1 · Engine tested

Calculation status

Engine tested 26/26 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.5.1

Review policy · Evidence

Definition: Power factor (PF) is the ratio of real power P to apparent power S in an AC circuit: PF = P / S = cos φ. It is dimensionless (0 to 1). This calculator finds PF, S (kVA), Q (kVAR), phase angle, and an idealized correction capacitor from voltage, current, real power, and frequency.
What it calculates: Power factor λ, apparent power S (kVA), and reactive power Q (kVAR) from V, I, and P; UI also estimates phase angle and correction capacitance from optional f.
Inputs: Voltage V (V RMS), must be > 0
Current I (A RMS), ≥ 0
Real power P (kW), ≥ 0
Phase mode: single, three-ll, or three-ln
Optional frequency f (Hz) for UI capacitor estimate only
Outputs: Power factor pf (0–1)
Apparent power S (kVA)
Reactive power Q (kVAR)
UI only: phase angle φ and correction C
Formula: PF=P/S; S from V·I (×√3 or ×3); Q=√(S²−P²); UI C=1000·Q/(2πfV²)
Assumptions: Sinusoidal RMS voltage and current magnitudes.
Balanced three-phase when 3φ L-L or L-N modes are selected.
Correction capacitor estimate (UI) fully offsets computed Q toward unity PF (idealized).
Units: V, A, kW → PF, kVA, kVAR
Boundary conditions: V ≤ 0 → VOLTAGE_MUST_BE_POSITIVE
Missing V/I/P_kW → MISSING_REQUIRED_INPUT
Negative I or P_kW → VALUE_MUST_BE_NON_NEGATIVE
Unknown mode → INVALID_MODE
When P > S, PF capped at 1 and Q = 0 (soft clamp)
I = 0 and P = 0 → S = 0, pf = 0 (valid)
Example: 230 V, 10 A, 1.8 kW, 1φ → PF ≈ 0.783, S = 2.3 kVA
Validation cases: 13 published on this page · 26/26 tests · Production surface contract 4/4 · View evidence
230 V, 10 A, 1.8 kW, 1φ → PF ≈ 0.783, S = 2.3 kVA
230 V, 10 A, 2.3 kW, 1φ → PF = 1, Q = 0
400 V, 50 A, 30 kW, 3φ L-L → S ≈ 34.64 kVA, PF ≈ 0.866
230 V, 10 A, 1.15 kW, 1φ (P = S/2) → PF = 0.5
230 V, 10 A, 2.5 kW, 1φ (P > S) → PF capped at 1; Q = 0
230 V, 10 A, 1.8 kW, 50 Hz, 1φ → C → non-zero µF correction capacitor (UI only)
230 V, 20 A, 3.6 kW, 1φ (2× I and P) → S = 4.6 kVA, PF ≈ 0.783 (same PF)
400 V, 25 A, 15 kW, 3φ L-L (half current vs 50 A case) → S ≈ 17.32 kVA, PF ≈ 0.866
0 V, 10 A, 1.8 kW, 1φ → error VOLTAGE_MUST_BE_POSITIVE
mode=dc → error INVALID_MODE
230 V, 10 A, −1 kW → error VALUE_MUST_BE_NON_NEGATIVE
230 V, 10 A, 0 kW, 1φ → PF = 0, S = 2.3 kVA
230 V, 0 A, 0 kW, 1φ → S = 0, PF = 0
Sources: IEC 60050 — International Electrotechnical Vocabulary — Apparent power (IEV 131-11-41) · accessed 2026-09-05
Supports: S = U × I definition of apparent power; unit volt-ampere (VA / kVA)
IEC 60050 — International Electrotechnical Vocabulary — Reactive power (IEV 131-11-44) · accessed 2026-09-05
Supports: Q = S sin φ under sinusoidal conditions; unit var / kVAR
IEC 60050 — International Electrotechnical Vocabulary — Power factor (IEV 131-11-46) · accessed 2026-09-05
Supports: λ = |P| / S; PF displayed as P/S (sinusoidal displacement factor cos φ when applicable)
IEEE Std 1459-2025 — Power factor as P/S; apparent, active, and reactive power (S² = P² + Q²) · 2025-05-16 · errata checked · accessed 2026-09-05
Supports: PF = P/S; Q = √(S² − P²); capacitor sizing from Q and f
BIPM SI Brochure (9th edition, version 4.01) — SI units related to electrical power · 2026-06 · DOI · accessed 2026-09-05
Supports: V, A, W relationships underlying kVA/kVAR scaling
Calculation version: 1.5.1

Background

Interpretation and common distinctions.

Calculate power factor, apparent power, reactive power, phase angle, and an idealized correction capacitor from voltage, current, real power, and frequency.

Default example: 230 V · 10 A · 1.8 kW (single-phase) → PF ≈ 0.783, S = 2.3 kVA.

Supported and not supported

Supported

Single-phase AC: S = V·I/1000
Balanced three-phase L-L: S = √3·VL-L·I/1000
Balanced three-phase L-N: S = 3·VL-N·I/1000
API result { S, pf, Q } via electrical.power_factor
UI-only correction capacitor estimate from optional frequency

Not supported

DC systems (PF is an AC concept)
Unbalanced three-phase or harmonic-rich loads
Engineered capacitor bank design / utility interconnection rules
Displacement vs distortion power factor separation

Agent / API notes

Capability id: electrical.power_factor · tool id: power-factor · pin calculation_version: 1.5.1.

Stable error codes include VOLTAGE_MUST_BE_POSITIVE, MISSING_REQUIRED_INPUT, VALUE_MUST_BE_NON_NEGATIVE, INVALID_NUMBER, and INVALID_MODE.

Real, reactive, and apparent power

Symbol	Name	Unit	Role
P	Real / true / active power	W, kW	Does useful work; dissipated in resistance
Q	Reactive power	VAR, kVAR	Oscillates with inductance/capacitance; net energy ≈ 0 over a cycle
S	Apparent power	VA, kVA	Product of RMS V and I (with √3 for 3φ L-L); capacity the supply must support

Power factor:

PF = P/S = cosφ

A PF of 0.75 means about 75% of the apparent power is real work; the rest is reactive.

The power triangle

S² = P² + Q² Q = √(S^(2) − P^2) φ = cos⁻¹(PF)

Legs: P and Q
Hypotenuse: S
Angle φ between P and S is the impedance phase angle

Formulas used by this calculator

Single-phase

S(kVA) = (V × I)/1000 PF = (P(kW))/(S(kVA))

Three-phase (line-to-line)

S(kVA) = (√3 × V(L−L) × I)/1000

Three-phase (line-to-neutral)

S(kVA) = (3 × V(L−N) × I)/1000

Correction capacitance (to cancel Q)

C(F) = (1000 × Q(kVAR))/(2π f V²)

(For L-N mode the denominator uses 3 × 2π f V².) Result is also shown in µF.

Resistance, reactance, and impedance (related idea)

Analogous to the power triangle:

Z² = R² + X² P = I²R Q = I²X S = I²Z

Perfect resistors: X ≈ 0, PF → 1. Inductors/capacitors: large X, lower PF.

Why correction matters

Lower PF → higher current for the same real power → more I²R losses and tighter transformer/cable capacity.
Utilities often require PF above about 0.90–0.95.
Adding capacitance near inductive loads can cancel lagging VAR (do not over-correct into a leading PF without design review).

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Frequently asked questions

Key distinctions behind the calculation.

What is power factor?

Power factor is real power divided by apparent power: PF = P / S = cos φ. A PF of 0.87 means about 87% of the apparent power does real work; the rest is reactive.

What are P, Q, and S?

P (watts/kW) is real/true power that does work. Q (VAR/kVAR) is reactive power from inductors and capacitors. S (VA/kVA) is apparent power: the vector combination of P and Q, with S² = P² + Q².

How do I calculate power factor from V, I, and P?

Single-phase: S(kVA) = V×I/1000, then PF = P(kW)/S. Three-phase line-to-line: S = √3×VL-L×I/1000. Reactive power Q = √(S² − P²).

What is a good power factor?

Unity (1.0) is ideal. Many facilities aim for 0.95 or higher. Below about 0.85–0.90, utilities often apply penalties and wiring/transformer capacity is used less efficiently.

Does power factor apply to DC?

In steady DC, voltage and current are in phase and PF is effectively 1. Power factor is an AC concept tied to phase shift and reactive power.

How does capacitor correction work in this tool?

The calculator estimates C to cancel the computed Q at your voltage and frequency (toward unity PF). Real designs may target a specific PF (e.g. 0.95), include steps/banks, and must consider harmonics — verify with an engineer.

What voltage do I enter for three-phase?

Use the line-to-line tab with VL-L, or the line-to-neutral tab with VL-N. Mixing them with the wrong formula skews S and PF.

Does PF have a unit?

No. It is dimensionless (or shown as a percent).

What if voltage is missing or zero?

The calculator and API reject the request with VOLTAGE_MUST_BE_POSITIVE. Zero volts is not treated as a valid S = 0 / PF = 0 shortcut.

What if real power exceeds apparent power?

PF is capped at 1 and Q is set to 0 (soft clamp). Check that V, I, and P are consistent and use matching units (kW vs W).