Electrical Power Calculator

Calculate electrical power using P = VI = I²R = V²/R. Find any variable given two others.

⚡ Electricity📐 P = VI💡 Power
Voltage (V)
Current (I) A
⚠️ Enter valid numbers.

What Is Electrical Power?

Electrical power (P) is the rate of energy transfer in an electric circuit, measured in watts (W = J/s). Three equivalent formulas relate power to voltage, current, and resistance: P = VI = I²R = V²/R. These are all derived from Ohm's Law (V = IR) — any one can be computed from any two of V, I, and R.

The P = I²R form is particularly important for understanding energy loss in resistors (Joule heating). It shows that power loss scales with the square of current — doubling current quadruples power dissipated as heat. This is why power transmission uses high voltage (low current) to minimize I²R losses over long distances.

Power determines component selection in circuits. A resistor rated at ¼ W in a circuit dissipating 1 W will overheat and fail. Engineers calculate P = I²R for each component and select components with adequate power ratings (typically 2× the calculated value as a safety margin).

Electrical power units: 1 W = 1 J/s. Household: kW (kilowatts). Power plants: MW to GW. The kilowatt-hour (kWh) is the energy unit: 1 kWh = 3.6 MJ. A 1 kW heater running for 2 hours consumes 2 kWh.

Formula Reference Table

Solve ForFormulaNotes
PowerP = V·I = I²R = V²/RWatts (W)
From voltage and currentP = V·IDirect calculation
From current and resistanceP = I²·RJoule heating formula
From voltage and resistanceP = V²/RCommon for fixed-V circuits
Energy over timeE = P·tJoules = Watts × seconds
Efficiencyη = P_out/P_in × 100%Percentage

3 Worked Examples

Example 1
Incandescent vs LED

120 V, 60 W bulb: I = P/V = 60/120 = 0.5 A; R = V/I = 240 Ω. LED equivalent (8 W): I = 0.067 A, R = 1,800 Ω.

  • Bulb: P = VI = 120 × 0.5 = 60 W (≈3 W visible, 57 W heat)
  • LED: P = 8 W (≈6 W visible, 2 W heat)
  • LED is 7.5× more power-efficient for same light output
✓ LED uses 87% less power for equivalent light
Example 2
Electric Kettle — Resistance

2,500 W kettle on 240 V mains. Find current and element resistance.

  • I = P/V = 2500/240 = 10.4 A
  • R = V/I = 240/10.4 = 23.1 Ω
  • Or R = V²/P = 57,600/2,500 = 23.0 Ω ✓
✓ I = 10.4 A; R = 23 Ω heating element
Example 3
Resistor Power Rating

100 Ω resistor in circuit with 20 V across it. Power dissipated?

  • P = V²/R = 400/100 = 4 W
  • Standard 100 Ω resistors: 1/4 W, 1/2 W, 1 W, 2 W
  • Must use ≥ 5 W rated resistor (safety margin 2×: ≥ 8 W)
✓ P = 4 W; use ≥ 5 W resistor

Real-World Applications

⚡
Power Plants
Power plant output is measured in MW (megawatts) or GW. A 1 GW nuclear plant generates P = 1×10⁹ W continuously. At $0.05/kWh wholesale: revenue = 10⁹/1000 × 0.05 = $50,000 per hour.
💡
Appliance Ratings
All electrical appliances are rated in watts or VA. The nameplate shows rated power at rated voltage. Exceeding rated current (P = I²R) can cause overheating, fire, or component failure.
🔋
Battery Systems
Battery power ratings: P = V × I_discharge. A 12 V, 100 Ah battery: energy = 12 × 100 = 1,200 Wh = 1.2 kWh. Discharge rate (C-rate): 1C = full discharge in 1 hour = P_max = 1,200 W.
🏭
Industrial Motors
Motor nameplate: power factor × rated voltage × rated current = apparent power (kVA). True power = kVA × PF. Motor efficiency = P_mechanical/P_electrical. Premium motors achieve 95%+ efficiency.
🌡️
Thermal Management
Electronics generate heat P = I²R. Thermal resistance θ (°C/W) determines temperature rise: ΔT = P × θ. A 5 W device with θ = 20°C/W rises 100°C above ambient — requiring heat sinks to reduce effective θ.

Common Mistakes to Avoid

⚠️
P = IV not P = V²/I

The three power formulas use multiplication, not division for the I²R and V²/R forms. P = I²R (multiply); P = V²/R (divide by R). Double-check: larger R → more power dissipated per amp (I²R), but less power for same voltage (V²/R — dividing by larger R).

⚠️
Peak vs RMS for AC power

AC average power uses RMS values: P = V_rms × I_rms × cos(φ). For a purely resistive load (φ=0): P = V_rms × I_rms. V_rms = V_peak/√2 for sine wave. Using peak values gives P that is 2× too high.

⚠️
Confusing power and energy

Power (W) is rate; energy (J or kWh) is total. A 1000 W device consumes 1 kWh if run for 1 hour — or 0.5 kWh if run for 30 min.

⚠️
Ignoring power factor for AC loads

For inductive/capacitive loads: P_true = V×I×cos(φ). The apparent power S = VI (VA); power factor PF = P/S. Motors and fluorescent lights have PF < 1.

⚠️
Wrong resistor power rating

Always use a resistor rated for more than calculated P. Minimum factor of 1.5–2×. P_calculated = 1 W → minimum resistor rating = 2 W. The standard series is 1/8, 1/4, 1/2, 1, 2, 5, 10, 25 W.

Frequently Asked Questions

Why are there three power formulas? ▾
All three are equivalent via Ohm's Law (V = IR). P = VI (use when V and I known); P = I²R (use when I and R known — common for loss calculations); P = V²/R (use when V and R known — common for fixed-voltage circuits). They all give the same result.
What is reactive power? ▾
In AC circuits with inductors or capacitors: P_true = VI cos(φ) (real power, does work). Q = VI sin(φ) (reactive power, stored/returned, VAR). S = VI (apparent power, VA). PF = P/S = cos(φ). Reactive power is transmitted but not consumed; it reduces power line efficiency.
What determines transformer efficiency? ▾
Transformers have core losses (hysteresis + eddy current, ∝ frequency and B²) and copper losses (I²R in windings). Efficiency η = P_out/(P_out + P_core + P_copper). Modern distribution transformers achieve 98–99.5% efficiency.
How does power dissipation relate to heat? ▾
All electrical power not converted to mechanical work or light becomes heat (Joule heating). P_heat = I²R. Temperature rise: ΔT = P_heat × thermal resistance (°C/W). Adequate heatsinking maintains safe junction temperatures in power electronics.
What is a watt-hour? ▾
1 Wh = 1 W × 1 hour = 3,600 J. 1 kWh = 3.6 MJ. This is the utility billing unit. A 100 W bulb running 10 hours = 1 kWh. US average home: ~900 kWh/month. Electric vehicle: ~15–25 kWh/100 km.
What is maximum power transfer? ▾
Maximum power transfers from source (internal resistance r) to load (R_L) when R_L = r. P_max = EMF²/(4r). For maximum efficiency (not maximum power), use R_L >> r. Power electronics deliberately mismatch impedances for efficiency; RF antennas are matched for maximum signal.
How do smart meters measure power? ▾
Smart meters sample voltage and current at high rate (thousands of samples/second), multiply instantaneous V × I, and integrate over time for energy. They capture true power including harmonics and power factor — much more accurate than simple current-only electromechanical meters.
What is standby power? ▾
Electronics in standby still draw 0.5–10 W each. With 50 devices at 5 W average: 250 W × 8,760 hr/year = 2,190 kWh/year. Many countries now mandate standby power < 0.5 W per device. Smart power strips and EcoDesign regulations address this 'vampire power' problem.

Related Physics Calculators

🔌 Ohm's Law ⚡ Electrical Energy 🔌 Series Resistors ⚡ Efficiency 🔋 Capacitance

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