Electrical power is the rate at which electrical energy is converted into another form — heat, light, motion or stored energy. The basic relationship is P = V × I (Watt's Law). Combined with Ohm's Law it also gives P = I²R and P = V²/R. For AC circuits the useful (real) power is reduced by the power factor, and three-phase systems add a factor of √3. This calculator handles all three cases and returns real power (W/kW), apparent power (VA/kVA) and reactive power (VAR/kVAR).
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Wikipedia: Electric Power, AC power & power factor, and NEC (NFPA 70) load rules.
Electrical safety notice. Mains voltage can kill on contact. Use these calculations for design and estimation only; live-circuit work must follow your local code (NEC, IEC 60364, BS 7671, AS/NZS 3000) and be performed by a licensed electrician. See our disclaimer.
What is electrical power?
Electrical power is the rate of doing electrical work — one watt is one joule of energy transferred per second. In any circuit, instantaneous power is the product of voltage and current. For a steady DC circuit or a purely resistive load, that reduces to the simple product below.
Where P is power in watts (W), V is voltage in volts (V), and I is current in amperes (A). Substituting Ohm's Law (V = I × R) gives the two most useful derived forms for resistive loads:
DC, single-phase and three-phase power formulas
The formula you use depends on the supply. The key differences are the power factor (AC only) and the √3 factor for balanced three-phase systems.
| Supply | Real power P (W) | Apparent power S (VA) | Current from power |
|---|---|---|---|
| DC / resistive | P = V × I | S = P | I = P / V |
| Single-phase AC | P = V × I × PF | S = V × I | I = P / (V × PF) |
| Three-phase AC | P = √3 × VLL × I × PF | S = √3 × VLL × I | I = P / (√3 × VLL × PF) |
Real power (watts) does useful work. Apparent power (volt-amps) is what the supply, cables and transformers must actually carry. Reactive power (VAR) is the part that flows back and forth with the magnetic and electric fields of motors and capacitors and does no net work: Q = √(S² − P²).
Worked example 1 — power and current of a single-phase heater
Scenario: A 2400 W resistive water heater runs on a 240 V single-phase supply. What current does it draw, and what is the heating element's resistance?
Step 1 — current from power. A heater is resistive, so power factor = 1:
Step 2 — element resistance from Ohm's / Watt's Law:
At 10 A continuous, the NEC's 80% continuous-load rule means this heater needs at least a 10 / 0.8 = 12.5 A circuit, so a 15 A or 16 A breaker with appropriately sized cable is the practical minimum. Size the conductor with our cable-sizing calculator.
Worked example 2 — three-phase motor real, apparent and reactive power
Scenario: A three-phase induction motor draws 30 A from a 415 V (line-to-line) supply at a power factor of 0.85. Find the real, apparent and reactive power.
The motor does 18.3 kW of useful work but the supply must carry 21.6 kVA. Correcting the power factor toward 1.0 with capacitors reduces the apparent power and the current — see the power-factor correction calculator. To convert this load into a full-load current for cable and breaker sizing, see the 3-phase power calculator.
kW vs kWh — power vs energy (the most common confusion)
This is the single most misunderstood point in electrical billing. Power (kW) is how fast you use energy at any instant. Energy (kWh) is power multiplied by how long it runs — and energy is what you pay for.
Examples: a 2 kW heater for 3 hours uses 2 × 3 = 6 kWh. A 10 W LED bulb left on for 24 hours uses 0.01 × 24 = 0.24 kWh. At an electricity price of $0.30/kWh, that heater session costs 6 × 0.30 = $1.80. The calculator above gives you the kW; multiply by your run-time and tariff for the cost.
Common mistakes when calculating electrical power
- Confusing watts (W) and volt-amps (VA). They are equal only at power factor 1.0. A 0.8-PF load draws 25% more VA than its watt rating, and cables/transformers are sized on VA, not W.
- Forgetting the √3 in three-phase. Three-phase power is √3 (1.732) × line voltage × line current × PF — not simply V × I. Omitting √3 underestimates power by 42%.
- Using phase voltage instead of line voltage. The three-phase formula above uses line-to-line voltage (e.g. 415 V), not phase voltage (240 V). Mixing them up gives a √3 error.
- Mixing kW and kWh. kW is a rate; kWh is an amount of energy. Your bill is in kWh.
- Ignoring power factor on motors and electronics. Inductive motors and switch-mode supplies have PF well below 1, so the current is higher than W / V would suggest.
Reference: power, current and typical circuits
Quick estimates assuming the load is at rated power and nominal voltage. Real currents vary ±10–15% with supply voltage; motors draw 6–8× rated current at startup.
| Load | Power | Supply | Current | Typical circuit |
|---|---|---|---|---|
| LED lighting circuit | 200 W | 230 V, 1φ | 0.87 A | 6 A |
| Refrigerator | 150 W | 120 V, 1φ | 1.25 A | 15 A shared |
| Microwave | 1100 W | 120 V, 1φ | 9.2 A | 20 A |
| Water heater | 2400 W | 240 V, 1φ | 10 A | 16 A |
| EV charger (Level 2) | 7.2 kW | 240 V, 1φ | 30 A | 40 A |
| Small 3-phase motor | 18.3 kW | 415 V, 3φ, PF 0.85 | 30 A | 40 A + starter |
Where electrical power calculations are used
- Cable & breaker sizing — converting an appliance or motor's power rating into the current the circuit must carry.
- Energy cost estimation — power × run-time × tariff to predict the bill.
- Generator & inverter selection — matching kVA capacity to the connected real and apparent load.
- Solar & battery design — balancing PV output, inverter rating and load power.
- Power-factor correction — reducing apparent power and current to avoid utility penalties.
- Heater & element design — choosing resistance for a target wattage at a given voltage.
Sources & further reading
- Wikipedia — Electric Power (definitions of instantaneous, real, reactive and apparent power).
- Wikipedia — AC Power & Power Factor (power triangle, VA, VAR, cosφ).
- NFPA — National Electrical Code (NEC, NFPA 70) (continuous-load and circuit rules).
- IEC 60364 — Low-voltage electrical installations (international wiring standard).
Frequently Asked Questions
Multiply voltage by current: P = V × I. For a resistor you can also use P = I² × R or P = V² ÷ R. For single-phase AC, P = V × I × power factor; for three-phase AC, P = √3 × V(line-to-line) × I × power factor.
Real power P in watts equals voltage times current: P = V × I. Combined with Ohm's Law (V = I × R) this gives the derived forms P = I² × R and P = V² ÷ R.
Watts measure real power that does useful work. Volt-amps (VA) measure apparent power, the product of RMS voltage and current. They are equal only at power factor 1.0; otherwise VA = W ÷ PF, so a 0.8-PF load draws 25% more VA than its watt rating. Cables and transformers are sized on VA.
P = √3 × V(line-to-line) × I(line) × power factor. For a 415 V, 30 A motor at PF 0.85: P = 1.732 × 415 × 30 × 0.85 ≈ 18.3 kW, with apparent power √3 × 415 × 30 ≈ 21.6 kVA.
A kilowatt (kW) is power — the rate of energy use. A kilowatt-hour (kWh) is energy — power × time. A 2 kW heater running 3 hours uses 6 kWh, which is what the electricity bill charges for.
Rearrange P = V × I. DC or resistive: I = P ÷ V. Single-phase AC: I = P ÷ (V × PF). Three-phase AC: I = P ÷ (√3 × V × PF).
Power factor is real power (W) ÷ apparent power (VA), equal to cosφ for sinusoidal AC. A low power factor means more current for the same useful power — larger cables and switchgear, and possible utility penalties below about 0.9.
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