Calculate electrical power in watts using multiple formulas: P=VI, P=I²R, P=V²/R, P=E/t, or P=τω. Includes energy cost estimation, unit conversions, and power scale comparison.
The watt (W) is the SI unit of power, defined as one joule per second. In electrical engineering, power is the rate at which energy is transferred in a circuit. For DC circuits the relationship is straightforward: P = V × I (voltage times current). For AC circuits, the power factor reduces the real power delivered: P = V × I × cos(φ). Three-phase systems multiply by √3.
Power can also be computed from resistance: P = I²R (useful when current and resistance are known) or P = V²/R (when voltage and resistance are known). Mechanical power is calculated as P = τω (torque times angular velocity). All these formulas give the same quantity — the rate of energy conversion — but from different measurable inputs.
This calculator supports five power formulas, AC power factor and three-phase options, dBm conversion for RF work, and energy cost estimation. Compare your result against everyday power references (LED bulb to EV charger) and convert between watts, kilowatts, horsepower, BTU/hour, and more.
Power calculations appear in every branch of electrical, mechanical, and thermal engineering. This calculator handles five different power formulas and automatically converts to every common unit. The energy cost estimation helps with real-world planning — just enter hours and electricity rate to see what a device costs to run. Keep these notes focused on your operational context.
P = V × I × PF (single-phase) P = √3 × V × I × PF (three-phase) P = I² × R P = V² / R P = E / t (energy ÷ time) P = τ × ω (torque × angular velocity) Where PF = power factor (0–1), ω = 2π × RPM/60
Result: 1,800 W (1.8 kW, 2.41 HP)
A 120 V, 15 A resistive circuit (PF = 1) delivers P = 120 × 15 × 1 = 1,800 W. That equals 1.8 kW or 2.41 horsepower. Running for 8 hours at $0.12/kWh costs $1.73.
DC circuit power is simply P = V × I. AC circuits complicate this because voltage and current may be out of phase. Real power (watts) = V × I × cos(φ), reactive power (VAR) = V × I × sin(φ), and apparent power (VA) = V × I. The power triangle relates these: S² = P² + Q². Only real power does useful work; reactive power oscillates between source and load.
Every component has a maximum power rating. Resistors are rated in watts (¼ W, ½ W, 1 W, etc.); exceeding the rating causes overheating and failure. Wire has a current-carrying capacity (ampacity) determined by allowable temperature rise — which is fundamentally a power dissipation (I²R) issue. Circuit breakers trip at current levels chosen to keep wiring below its temperature rating.
A wattmeter measures real power by multiplying instantaneous voltage and current. Modern digital power analyzers sample both at high rates and compute true RMS power, power factor, harmonics, and efficiency. For RF, power meters use thermistors or diodes to measure average power in dBm. Kill-A-Watt devices plug inline to measure household device power consumption and accumulated energy.
Watts measure real power (energy actually consumed). Volt-amps (VA) measure apparent power (V × I regardless of phase). The ratio is the power factor: W = VA × PF. For a purely resistive load, W = VA.
Divide power by voltage: I = P/V for DC or single-phase AC with PF = 1. For AC with a power factor: I = P/(V × PF). For three-phase: I = P/(√3 × V × PF).
A kWh is an energy unit: 1 kW consumed for 1 hour = 1 kWh = 3.6 MJ. It is the billing unit for electricity. A 100 W bulb running 10 hours uses 1 kWh.
Low power factor means you draw more current than needed for the real power consumed. This increases I²R losses in wiring, requires larger conductors, and may incur utility surcharges for industrial customers.
Both are measured in watts. An electric motor converts electrical power P = VI into mechanical power P = τω minus losses. Motor efficiency is typically 80-95%, so mechanical output is less than electrical input.
dBm is a logarithmic power unit referenced to 1 milliwatt: P(dBm) = 10 × log₁₀(P(mW)). It is used in RF engineering, telecommunications, and fiber optics because it simplifies gain/loss calculations to addition/subtraction.