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P = V × I
P = I² × R
P = V² / R
V = P / I
V = I × R
V = √(P × R)
I = P / V
I = V / R
I = √(P / R)
R = V / I
R = V² / P
R = P / I²
Electrical power is the rate at which electrical energy is transferred or consumed in a circuit, measured in watts (W). It is governed by three interrelated formulas: P = V × I (power equals voltage times current), P = I²R (power equals current squared times resistance), and P = V²/R (power equals voltage squared divided by resistance). These relationships, derived from Ohm's law, form the "power wheel" that allows engineers to calculate any electrical quantity when two others are known. Understanding power is essential for sizing components, estimating energy costs, preventing overheating, and designing safe electrical systems from microelectronics to industrial power distribution.
You need any two of the four electrical quantities: power (P in watts), voltage (V in volts), current (I in amps), or resistance (R in ohms). Check your circuit schematic, power supply rating, or use a multimeter to measure the known values.
If you know voltage and current, use P = V × I. If you know current and resistance, use P = I² × R. If you know voltage and resistance, use P = V² / R. Each formula gives the same result when values are consistent.
Ensure consistent units (volts, amps, ohms). For example, a 120 V circuit drawing 10 A consumes P = 120 × 10 = 1,200 W = 1.2 kW. For milliamp circuits, convert to amps first (500 mA = 0.5 A).
Cross-check your result using an alternative formula. For component selection, always add a 20-50% safety margin -- a resistor dissipating 0.5 W should be rated for at least 1 W to prevent overheating and ensure long-term reliability.
Every electrical component has a maximum power rating. Exceeding it causes overheating, premature failure, or fire. Calculating power dissipation ensures resistors, transistors, wires, and connectors operate within safe thermal limits, protecting both the circuit and surrounding equipment.
Utilities bill by kilowatt-hours (kWh). Knowing the power consumption of devices lets you estimate operating costs: a 100 W device running 10 hours daily at $0.12/kWh costs about $3.60 per month. This drives decisions on energy-efficient equipment and usage schedules.
Power budgeting is critical for designing power supplies, battery systems, and wiring. Underestimating total power leads to voltage drops, tripped breakers, or insufficient battery life. Accurate power calculations ensure reliable operation under all expected load conditions.
| Device | Typical Power (W) | Current at 120 V | Current at 240 V | Monthly Cost* |
|---|---|---|---|---|
| LED Light Bulb | 10 | 0.08 A | 0.04 A | $0.36 |
| Laptop Computer | 50 | 0.42 A | 0.21 A | $1.80 |
| Desktop Computer | 200 | 1.67 A | 0.83 A | $7.20 |
| Refrigerator | 150 | 1.25 A | 0.63 A | $5.40 |
| Microwave Oven | 1,000 | 8.33 A | 4.17 A | $6.00 |
| Electric Heater | 1,500 | 12.5 A | 6.25 A | $54.00 |
| Hair Dryer | 1,800 | 15.0 A | 7.50 A | $3.24 |
| Central AC | 3,500 | 29.2 A | 14.6 A | $126.00 |
| Electric Oven | 2,500 | 20.8 A | 10.4 A | $18.00 |
| Washing Machine | 500 | 4.17 A | 2.08 A | $1.80 |
*Estimated at $0.12/kWh with typical daily usage hours
Watts (W) measure real power -- the energy actually consumed and converted to work or heat. Volt-amps (VA) measure apparent power in AC circuits, which includes both real and reactive components. Var (volt-ampere reactive) measures reactive power stored and released by capacitors and inductors. In DC circuits and purely resistive AC loads, watts and VA are equal.
The wattage tells you total power consumption, while the amp rating tells you the current draw on the specific circuit voltage. Since household voltage varies by country (120 V in North America, 230 V in Europe), the same wattage device draws different currents. The amp rating is critical for selecting the correct wire gauge and circuit breaker size.
For balanced three-phase loads, use P = √3 × VL × IL × cos(φ), where VL is line-to-line voltage, IL is line current, and cos(φ) is the power factor. For single-phase equivalent, use P = V × I × cos(φ). The √3 factor (approximately 1.732) accounts for the phase relationship between the three conductors.
Exceeding a power rating causes excessive heat buildup. For resistors, this can lead to discoloration, value drift, open-circuit failure, or fire. For semiconductors, thermal runaway can cause permanent damage. For wiring, insulation degrades, creating shock and fire hazards. Always derate components -- use no more than 50-75% of rated power for long-term reliability.
One mechanical horsepower equals approximately 746 watts or 0.746 kW. To convert kW to HP, divide by 0.746. To convert HP to kW, multiply by 0.746. For example, a 5 HP motor consumes about 3.73 kW. Note that electric motor efficiency (typically 85-95%) means actual electrical input power is higher than the mechanical output power.
Estimate total wattage requirements for your home, office, or project to properly size generators and power supplies.
Calculate voltage, current, and resistance relationships using the fundamental V = I × R formula and its rearrangements.
Determine current flow in circuits from voltage and resistance values for proper wire and fuse sizing.