Power calculator

Use the power calculator

Pick the phase mode at the top, then choose which two values you have ("I know:") — V&I, V&P, V&R, I&P, I&R, or P&R. The other two compute live, with apparent power, reactive power, HP, and BTU/hr in the detail panel.

The power formula

One formula covers DC, two cover AC — the only difference is the cos φ correction (single-phase AC) and the additional √3 factor (three-phase line-to-line). Solving for current or resistance is just rearranging the equation.

Worked example: 50 HP three-phase motor on 480 V

A 50 HP industrial motor running on a 480 V three-phase service at 0.85 power factor and 92% efficiency. Compute kW input, FLA (full-load amps), and the kVA the transformer must supply.

How to calculate power, step by step

1. Identify what you know. Pick any two of {voltage V, current I, power P, resistance R}. The other two follow from Ohm's Law and the power equation.
2. Pick the phase mode. DC for batteries and pure-resistance loads. Single-phase AC for residential mains. Three-phase AC for commercial / industrial service. The √3 factor enters only for three-phase.
3. For AC, set the power factor cos φ. Pure resistive (heaters, incandescent lamps) → cos φ = 1.0. Motors typically 0.80–0.90. Highly inductive loads (welders, fluorescent ballasts) 0.50–0.75. Power factor connects active and apparent power: P = S × cos φ.
4. Apply the formula. P = V·I (DC), P = V·I·cos φ (1-phase), P = √3·V_LL·I·cos φ (3-phase). Solve for the missing variable algebraically — or use the calculator above.
5. Convert to other units if needed. Watts → kilowatts (÷1000), HP (÷745.7), BTU/hr (×3.412). Apparent power S = V·I (1ph) or √3·V·I (3ph), in volt-amps. Reactive Q = √(S² − P²), in VAR.
6. Sanity-check against the device nameplate. Motor nameplate gives FLA (full-load amps), HP, V, PF, efficiency. Computed kW from those values should match within 5–10%; bigger discrepancy suggests wrong PF or efficiency assumption.

Reference table — typical loads

Active vs apparent vs reactive power

Variants and special cases

DC power

Pure resistive: P = V·I, no power factor. Used for battery systems, solar PV, EVs, USB. Energy in batteries: Wh = Ah × V.

Single-phase AC power

P = V·I·cos φ for active, S = V·I for apparent. Standard residential mains worldwide; cos φ depends on connected loads (mostly resistive in homes).

Three-phase AC power (balanced)

P = √3·V_LL·I·cos φ. Used for nearly all commercial and industrial service. Power flow is constant in time (smoother than single-phase ripple).

Apparent power and the kVA rating

Transformers, UPS systems, and generators are rated in kVA, not kW — they must supply the full apparent power regardless of PF. A 100 kVA transformer can deliver 100 kW only at PF = 1.0; at PF 0.7 it delivers 70 kW (but still 100 kVA worth of current).

Reactive power and the power triangle

P, Q, and S form a right triangle: S² = P² + Q², φ = arctan(Q/P). Capacitive Q is conventionally negative (current leads voltage); inductive Q is positive (current lags). The triangle is the geometric basis for power-factor correction.

Mechanical horsepower

1 HP = 745.7 W (US) or 735.5 W (metric PS). HP from torque: HP = T(lb-ft) × RPM / 5252. Motor shaft HP equals input kW × efficiency, where η is typically 0.85–0.95.

RMS vs instantaneous power

For sinusoidal AC, instantaneous power oscillates at 2× line frequency between 0 and peak. The "average power" or "RMS power" reported by all standard meters is what the equations compute. Don\'t confuse RMS power with peak power — the latter is double.

Power in capacitors and inductors

Pure capacitors and inductors store and release energy without net dissipation. Their average active power is zero; their reactive power is significant. This is why filters can be lossless but still affect circuit behaviour.

Power loss in conductors

Conductor power loss P_loss = I² × R_cable, dissipated as heat. For a 30 m run of 10 AWG Cu carrying 20 A: R ≈ 0.1 Ω, P_loss ≈ 40 W — small compared to a typical load but it adds up across long runs and motivates voltage-drop limits. See Voltage Drop Calculator.

Power quick reference — torque, horsepower, 3-phase, amps

Related concepts on this site

Frequently asked questions

How do you calculate power?

Three forms depending on the system. DC: P = V × I. Single-phase AC: P = V × I × cos φ (active power, kW). Three-phase AC: P = √3 × V_LL × I × cos φ. Example: 120 V × 10 A DC = 1200 W. Same on AC at PF 0.85: 120 × 10 × 0.85 = 1020 W active. Use the calculator above with the right phase mode for your case.

How to calculate horsepower from torque?

HP = (Torque × RPM) / 5252 with torque in lb-ft, RPM in revolutions per minute. The 5252 constant comes from 33000 ft-lb/min per HP divided by 2π. Example: 100 lb-ft of torque at 3600 RPM = 100 × 3600 / 5252 = 68.5 HP. In SI units: HP = (Nm × RPM) / 7121, or P (kW) = (Nm × RPM) / 9550. This is also the answer to "how horsepower is calculated" from a measured torque and shaft speed.

How to calculate torque from horsepower?

Inverse of the above: Torque (lb-ft) = HP × 5252 / RPM. Example: a 50 HP motor at 1800 RPM produces 50 × 5252 / 1800 = 146 lb-ft of torque. Two motors of equal HP can have very different torque depending on RPM — a slow-turning motor produces more torque, which is why high-torque applications use gear reducers to trade RPM for torque.

How to measure DC power?

Two instruments: a DC voltmeter across the load (measures V) and a DC ammeter in series (measures I). DC power P = V × I, no power factor. For accurate reading at high power, use a Hall-effect or shunt-resistor current sensor; for very low power, use a four-wire (Kelvin) connection to eliminate lead resistance. Multimeters with simultaneous V/I display make this routine — or use a dedicated DC power meter that integrates over time to also report energy (Wh).

What is the difference between active, apparent, and reactive power?

Active power (P, watts) is the real work being done — heat, light, mechanical output. Reactive power (Q, VAR) is shuffled between source and reactive components (inductors, capacitors) without doing net work. Apparent power (S, VA) is the geometric sum: S = √(P² + Q²). The relationship cos φ = P/S defines power factor. Utilities bill on active power (kWh) but penalise low PF because reactive current still loads the conductors.

How is power related to energy?

Power is the rate of energy use; energy is power × time. Units: 1 watt-hour (Wh) = 3600 joules of energy. kWh = kW × hours. A 1.5 kW heater run for 4 hours uses 6 kWh of energy. Utility billing is in kWh. To estimate operating cost: kWh × electricity rate ($/kWh) = $ per period. The calculator above shows instantaneous power (W); multiply by your duty cycle (hours per day, days per year) to get energy.

What is power factor and why does it matter?

Power factor cos φ = P/S, the ratio of active to apparent power. PF = 1.0 means all current is doing useful work; PF = 0.7 means 30% of the current is "wasted" cycling reactive energy. Low PF still loads conductors and transformers, so utilities charge a PF penalty above ~0.85 demand. Industrial loads (motors) are typically 0.80–0.85 PF; capacitor banks can correct this back toward 1.0 — see Power Factor calculator.

Sources and methodology

1. Ohm, G. S. Die galvanische Kette, mathematisch bearbeitet, 1827.
2. IEEE. IEEE Std 100 — Authoritative Dictionary of IEEE Standards Terms, 7th Edition.
3. NFPA. NEC 70 — National Electrical Code, 2023. Article 100 (definitions), 430.250 (motor FLA).
4. BIPM. The International System of Units (SI), 9th Edition, 2019.
5. Steinmetz, C. P. Theory and Calculation of Alternating Current Phenomena, McGraw-Hill, 1897.