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Electrical calculator

Electric Power Calculator

Calculate electrical power in watts from voltage and current for DC, single-phase AC, or balanced three-phase AC, from current and resistance, or from energy over time.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 26/26 tests · Production surface contract 1/1 · v1.3.0
Input interpretation
Enter values to calculate.
Result
—
Model
Real power (W) from V×I×PF (1φ/3φ), from I²R, or average power from energy and time.
Scope
Three-phase path uses balanced line-to-line RMS voltage.
Verification
Engine tested · 26/26 tests · Production surface contract 1/1 · Source checked · v1.3.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
14 golden · 7 boundary · 5 property · Production surface contract 1/1 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.3.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T13:56:15.885Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

DC / resistiveP = V × I
AC 1φP = V × I × PF
AC 3φ (L-L)P = √3 × V × I × PF
With resistanceP = I²R
EnergyP = E / Δt
iEnter line-to-line voltage for three-phase. Blank PF defaults to 1; PF = 0 is valid (P = 0). This tool computes real power in watts; apparent power (VA) is V×I without PF — see Amps to VA. Resistance tab is I + R only.

How to use

1

Choose a method

V×I (with phase/PF), I²R for resistive heating, or energy÷time for average power.

2

Enter the known values

For AC V×I, set PF and single/three phase. DC: PF = 1, single phase.

3

Read power in watts

Divide by 1000 for kW. Energy cost needs kWh = (W × hours) / 1000.

Example calculations

Common configurations with formula and result.

ϟ

DC / resistive

120 V · 10 A · PF 1

P = V × I
1,200 W (1.2 kW)
ϟ

Phone charger

5 V · 2 A

P = V × I
10 W
ϟ

I²R heating

0.5 A · 10 Ω

P = I²R
2.5 W
ϟ

I²R heating (same identity as V²/R)

2 A · 6 Ω (equivalent to 12 V across 6 Ω via Ohm’s law)

P = I²R
24 W
ϟ

3φ motor

400 V · 20 A · PF 0.9

P = √3 × V × I × PF
12,471 W
ϟ

Average power

3600 J in 3600 s

P = E/Δt
1 W

Typical power factor (illustrative)

Common values at a glance.

DeviceTypical PF
Incandescent / resistive heater1.00
Electric oven (resistive)1.00
Fluorescent lamp0.93
Induction motor (full load)0.85
Induction motor (half load)0.73
Inductive oven / many motors0.85
i Illustrative only; not used by the calculator engine. Prefer nameplate or measured values for design.

Electric Power calculator specification

Version 1.3.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Electrical power is the rate of energy transfer in a circuit, measured in watts (W). For DC, P = V × I. For AC, real power is P = V × I × PF (× √3 for three-phase line-to-line). The resistance tab computes P = I²R. Average power is P = E / Δt.
What it calculates
Real power (W) from V×I×PF (1φ/3φ), from I²R, or average power from energy and time.
Inputs
  • Voltage V and current I (+ PF, phase), or
  • Resistance R and current I, or
  • Energy E (J) and time Δt (s)
Outputs
  • Power in watts
Formula
P=V·I·PF (1φ); P=√3·V·I·PF (3φ L-L); P=I²R; P=E/Δt
Assumptions
  • Three-phase path uses balanced line-to-line RMS voltage.
  • PF on the V×I path is total power factor λ = |P|/S in [0, 1]; blank PF defaults to 1.
  • I²R path assumes resistive power dissipation (I + R inputs). V²/R is the Ohm’s-law identity, not a third tab.
  • Energy path is average power P = E/Δt with Δt > 0.
Units
  • V, A, PF, Ω, J, s → W
Boundary conditions
  • V×I path: zero V or I → 0 W
  • Blank / omitted PF defaults to 1; PF = 0 is valid and yields P = 0
  • PF < 0 or PF > 1 → INVALID_POWER_FACTOR
  • I²R path: zero R or I → 0 W; negative R → VALUE_MUST_BE_NON_NEGATIVE
  • Energy path: Δt ≤ 0 → INVALID_TIME_INTERVAL (not a soft 0 W)
  • Zero energy with Δt > 0 → 0 W
  • Non-finite inputs → INVALID_NUMBER
Example
230 V × 10 A × 1 (1φ) = 2300 W
Validation cases

19 published on this page · 26/26 tests · Production surface contract 1/1 · View evidence

  • 230 V, 10 A, PF 1, 1φ → 2300 W
  • 120 V, 10 A, PF 1, 1φ → 1200 W
  • 5 V, 2 A, PF 1, 1φ → 10 W
  • 0.5 A, 10 Ω (I²R) → 2.5 W
  • 400 V, 20 A, PF 0.9, 3φ → ≈12470.766 W
  • 3600 J, 3600 s → 1 W
  • 460 V, 10 A, PF 1 (2× V) → 4600 W (linear in V)
  • 230 V, 10 A, PF 0.5 → 1150 W (linear in PF)
  • 1 A, 10 Ω (2× I on I²R) → 10 W (quadratic in I)
  • 0 V, 10 A, PF 1 → 0 W
  • 230 V, 0 A, PF 1 → 0 W
  • 230 V, 10 A, PF 0 → 0 W
  • 230 V, 10 A, PF −0.1 → INVALID_POWER_FACTOR
  • 230 V, 10 A, PF 1.1 → INVALID_POWER_FACTOR
  • 3600 J, 0 s → INVALID_TIME_INTERVAL
  • 0 J, 0 s → INVALID_TIME_INTERVAL
  • 0 J, 3600 s → 0 W
  • 10 Ω, 0 A (I²R) → 0 W
  • R = −1 Ω, 1 A (I²R) → VALUE_MUST_BE_NON_NEGATIVE
Sources
  • Watt’s law / power identity — Real power P = V × I × PF (1φ); P = √3 × V × I × PF (3φ L-L)
    Supports: P from V×I path with phase and PF
  • Joule heating / Ohm’s law forms — P = I²R = V²/R for resistive dissipation
    Supports: P from I²R mode
  • Energy–power relation — Average power P = E / Δt (J/s → W)
    Supports: P from energy mode
  • IEC 60050 — International Electrotechnical Vocabulary — Active power (IEV 131-11-42) · accessed 2026-09-05
    Supports: P is active power; unit watt (W). V×I path computes P, not apparent power S.
  • IEC 60050 — International Electrotechnical Vocabulary — Power factor (IEV 131-11-46) · accessed 2026-09-05
    Supports: λ = |P| / S; AC V×I path multiplies by λ
  • IEEE Std 1459-2025 — Power factor and real vs apparent power · 2025-05-16 · errata checked · accessed 2026-09-05
    Supports: PF on AC V×I path; power triangle context
  • BIPM SI Brochure (9th edition, version 4.01) — SI units for watt, volt, ampere, and joule · 2026-06 · DOI · accessed 2026-09-05
    Supports: W = J/s; DC P = V·I; P = I²R = V²/R for ohmic dissipation
  • NIST Guide to the SI (SP 811) — Watt as joule per second
    Supports: W = J/s; SI relationships for V, A, Ω, W
Calculation version
1.3.0

Background

Interpretation and common distinctions.

What is electrical power?

Electrical power is how fast electrical energy is transferred or converted — measured in watts (W).

  • 1 W = 1 J/s
  • For a simple resistive case, 1 W = 1 V · A

Think of current as “how much charge flows” and voltage as “how much energy each unit of charge carries.” Their product (with power factor on AC) is power.

Power formulas

DC and resistive loads

P = V × I = I² R = (V²)/R

AC single-phase (real power)

P = V × I × PF

where V and I are RMS values. Power factor is PF=|P|/S. For sinusoidal voltage and current this reduces to |cosφ|; with harmonic or nonlinear loads, true PF also includes distortion.

AC three-phase (line-to-line)

P = √3 × V(L−L) × I × PF

Average power from energy

P = E/(Δ t)

with E in joules and Δ t in seconds. Utility energy:

kWh = (P(W) × tₕ)/1000

Power triangle (AC)

Symbol Name Unit
P Real power W
Q Reactive power VAR
S Apparent power VA

S² = P² + Q², PF = |P/S|

P = V I cosφ, Q = V I sinφ

These identities are the conventional (sinusoidal steady-state) power triangle. For single-phase they use RMS V and I; three-phase magnitudes also involve √3 with line quantities. With harmonics, true PF is not simply |cosφ|.

What is power factor?

In AC, voltage and current can be out of phase. That reduces real power for the same V and I.

  • PF = 1 — fully in sync (heaters, incandescent lamps)
  • PF < 1 — motors, fluorescent lights, many electronics
  • PF → 0 — very little real power is transferred for the same RMS voltage and current; this can result from phase displacement and/or waveform distortion.

Typical values (illustrative only; not used by the calculator engine):

Device PF
Resistive heater / oven 1.00
Fluorescent lamp ≈ 0.93
Induction motor, full load ≈ 0.85
Induction motor, half load ≈ 0.73

Energy and electricity cost

E(kWh) = (P(W) × tₕₒᵤᵣₛ)/1000

Cost = E(kWh) × price per kWh

Example: 1500 W heater × 8 h × 0.12/kWh → 1.5 × 8 × 0.12 =1.44/day.

Use the energy cost calculator for bill-style estimates. Common appliance wattages vary widely (LED lamps a few watts; HVAC and dryers kilowatts) — check the nameplate.

Units quick reference

Unit Meaning
W / kW Power (1 kW = 1000 W)
Wh / kWh Energy
VA / kVA Apparent power
VAR Reactive power
hp ≈ 746 W (mechanical) or ≈ 736 W (metric)

Other calculators in this family: Amps to kW Calculator, Amps to VA Calculator, Amps to Volts Calculator, Energy Consumption Calculator, Energy Cost Calculator, eV to Volts Calculator, kVA to Amps Calculator, kVA to kW Calculator . Explore all Power & Energy.

→ Amps to kW Calculator Convert amps and volts to real power in kW for DC, AC single-phase, and balanced AC three-phase line-to-line. Runs locally in your browser. Free online tool — no sign-up. › → Amps to VA Calculator Convert amps and volts to apparent power in VA or kVA for single-phase and three-phase circuits. Also convert VA back to amps. Fast and free. › → Amps to Volts Calculator Solve voltage from current and resistance or power using Ohm’s law and P = V × I. Supports resistive DC and RMS AC estimates with clear formulas. › → Energy Consumption Calculator Estimate energy use in kWh from device watts and hours of operation. Useful for appliance and load planning. Runs locally in your browser. Try it free. › → Energy Cost Calculator Estimate electricity usage cost from watts/hours or kWh and your unit rate. Supports custom billing periods; standing charges and taxes are excluded. Runs locally in your browser. › → eV to Volts Calculator Relate electronvolt energy to electric potential difference through ΔE = qΔV. eV and volts measure different physical quantities. Runs locally in your browser. › → kVA to Amps Calculator Convert kVA and voltage to line current for single-phase and three-phase systems. Uses √3 for three-phase line-to-line volts. Runs locally in your browser. › → kVA to kW Calculator Convert apparent power (kVA) to real power (kW) with power factor. States when PF is required and when loads are assumed balanced. Try it free. ›
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Frequently asked questions

Key distinctions behind the calculation.

What is electrical power?

It is the rate of energy transfer in a circuit, in watts (W). One watt equals one joule per second. In circuit terms, 1 W = 1 V·A for a resistive DC case.

How do you calculate electrical power?

DC: P = V × I. AC single-phase: P = V × I × PF. AC three-phase (line-to-line): P = √3 × V × I × PF. Resistive heating on this page: P = I²R. The Ohm’s-law identity P = V²/R is on the Ohm’s Law calculator.

What is power factor?

Power factor is PF = |P| / S. For sinusoidal voltage and current, PF reduces to |cos φ|. With harmonic or nonlinear loads (rectifiers, SMPS, LED drivers), true power factor also includes distortion and is not simply cos φ.

What is the power triangle?

In sinusoidal steady state, real power P (W), reactive power Q (VAR), and apparent power S (VA) form the conventional power triangle S² = P² + Q², and PF = |P/S|. That identity is the conventional (displacement) triangle — not a complete model of distorted waveforms.

P = VI vs P = I²R vs P = V²/R — which to use?

All are consistent for resistive circuits via Ohm’s law. This calculator’s resistance tab is I + R (P = I²R). For V + R (P = V²/R) use the Ohm’s Law calculator.

How is power related to energy and cost?

Energy E = P × t. In joules and seconds, P = E/Δt. Utility billing uses kWh: kWh = (W × hours) / 1000, then cost = kWh × rate.

Is “RMS watts” a real unit?

Power is in watts. People often multiply RMS voltage by RMS current; that product is power for a resistive load, but “watts RMS” is informal shorthand, not a separate SI unit.