Electric Power Calculator | P=VI, V²/R & I²R
Calculate electric power from any two of voltage, current, and resistance. Includes energy consumption in kWh and electricity cost estimation with preset appliances.
Leave blank to skip energy/cost calculation. Average US rate ≈ $0.13/kWh.
Press Enter to calculate · Esc to reset
What Is the Electric Power Calculator | P=VI, V²/R & I²R?
Electric power is the rate at which electrical energy is transferred, either generated by a source or consumed by a load. Measured in watts (W), it is the product of voltage and current: P = VI. This relationship emerges directly from the definition of voltage (energy per unit charge) and current (charge per unit time), so P = (J/C) × (C/s) = J/s = W.
Ohm's law (V = IR) connects voltage, current, and resistance in a resistive circuit. Substituting into P = VI gives the other two power formulas: P = (IR) × I = I²R and P = V × (V/R) = V²/R. All three formulas are mathematically equivalent, the choice of which to use depends on which two quantities are known.
Energy is power multiplied by time. Electricity billing uses kilowatt-hours (kWh): run a 1000 W appliance for one hour and you consume 1 kWh. The global average electricity rate is roughly $0.10–0.20/kWh, though it varies widely by country and time-of-use tariff. The energy calculation in this tool lets you estimate both session cost and monthly cost for any device.
In AC circuits with reactive components (inductors, capacitors), the situation is more nuanced: apparent power (VA) ≠ real power (W). The ratio is called the power factor (PF). This calculator computes real power, which applies exactly to DC circuits and to resistive AC loads (heaters, incandescent bulbs) where the power factor is 1.
Formula
| Symbol | Name | Description |
|---|---|---|
| P | Power | Rate of energy transfer or consumption; watts [W] or kilowatts [kW] |
| V | Voltage | Electrical potential difference driving current through the circuit; volts [V] |
| I | Current | Rate of charge flow; amperes [A] |
| R | Resistance | Opposition to current flow; ohms [Ω]; from Ohm's law R = V/I |
| E | Energy | Power × time; kilowatt-hours [kWh] for electricity billing |
| t | Time | Duration of operation; hours [h] |
| rate | Electricity rate | Cost per unit of energy; dollars per kilowatt-hour [$/kWh] |
| kWh | Kilowatt-hour | Standard billing unit; 1 kWh = 1 kW used for 1 hour = 3.6 MJ |
How to Use
- 1Choose a formula mode: Select "P = V×I", "P = V²/R", or "P = I²R" depending on which two quantities you know. The mode tabs switch the input labels automatically.
- 2Load a preset (optional): Click a preset (Kettle, LED Bulb, Laptop, Hair Dryer, Motor Coil, EV Charger) to populate typical real-world values and see a result immediately.
- 3Enter your known values: Type values for both required inputs. Voltage in volts, current in amps, resistance in ohms. Fractional values are supported (e.g. 0.065 A for a 65 mA LED).
- 4Add time and rate (optional): Enter a run time in hours and your electricity rate in $/kWh to calculate energy consumption and cost. Leave blank to skip this section.
- 5Press Calculate or Enter: Click the "Calculate Power" button or press Enter from any input field. The result appears with a power badge, derived V/I/R values, and energy/cost if entered.
- 6Read the results: The primary result shows power in the most readable unit (mW, W, kW, MW). Derived values appear in the grid below. Expand "Calculation steps" to see how each value was obtained.
- 7Copy or reset: Click "Copy results" to copy all values to the clipboard. Click Reset or press Esc to clear the form. Your last inputs are saved to browser storage and restored on the next visit.
Example Calculation
Example 1: Kettle, V×I mode
A 230 V kettle draws 10.4 A. Find the power, resistance, and cost per boil (3 min = 0.05 h at $0.15/kWh).
Example 2: LED bulb, V²/R mode
A 230 V circuit feeds a 5,290 Ω load (typical 10 W LED equivalent). Confirm the wattage.
Example 3: Motor winding, I²R mode
A motor coil carries 5 A through a winding with 8 Ω resistance. How much power is dissipated as heat?
Understanding Electric Power | P=VI, V²/R & I²R
Power vs Energy, The Key Distinction
Power and energy are related but distinct quantities. Power (watts) measures how fast energy flows at any instant, it's a rate. Energy (joules or kWh) is the total amount of energy that has flowed over a period of time. Your electricity bill charges for energy consumed, not for power level. A 2 kW kettle running for 6 minutes uses the same energy as a 200 W laptop running for 60 minutes (both = 0.2 kWh).
Ohm's Law and the Power Triangle
The three power formulas all follow from two fundamental relationships: P = VI (power equals voltage times current) and V = IR (Ohm's law). Together they form what engineers call the "power triangle", knowing any two of V, I, R fully determines the third and all three power values. This is why this calculator only asks for two inputs: the third is always derivable.
AC vs DC Power
- ›DC circuits: P = VI always holds exactly. Resistance is constant. Examples: batteries, solar panels, LED drivers.
- ›Resistive AC loads: P = V_rms × I_rms still gives the correct real power, and the power factor is 1. Examples: electric heaters, incandescent bulbs, toasters.
- ›Reactive AC loads: inductors (motors) and capacitors cause current to lag or lead voltage. Apparent power (VA) > real power (W). Power factor PF = P / (V_rms × I_rms). Examples: induction motors, fluorescent ballasts, switch-mode power supplies.
- ›This calculator computes real power and applies correctly to DC and to any resistive load. For reactive loads, multiply the result by your load's power factor to get actual real power.
Electricity Rates and Cost Context
Electricity costs vary significantly by region and by time-of-use tariff. The calculator defaults suggest $0.13/kWh (the approximate US residential average as reported by the U.S. Energy Information Administration), but you should enter your actual rate from your electricity bill for accurate results. Commercial rates, peak-hour surcharges, and tiered pricing can push the effective rate to $0.25–0.50/kWh in some markets.
Common Appliance Power Levels
| Appliance | Typical Power | Monthly kWh* | Monthly Cost* |
|---|---|---|---|
| LED bulb | 8–12 W | 1.5 | $0.20 |
| Laptop | 45–65 W | 9.8 | $1.27 |
| Desktop PC | 100–300 W | 36 | $4.68 |
| Refrigerator | 100–200 W | 60 | $7.80 |
| Washing machine | 500–1500 W | 60 | $7.80 |
| Electric kettle | 1500–3000 W | 5 | $0.65 |
| Air conditioner | 1000–3500 W | 210 | $27.30 |
| Level 2 EV charger | 6400–9600 W | 288 | $37.44 |
* Based on typical usage hours and $0.13/kWh. Actual costs vary.
Joule Heating and Safety
When current flows through a resistive conductor, power is dissipated as heat: P = I²R. This is called Joule heating (or ohmic heating). It is the basis of electric heaters, toasters, and incandescent bulbs, but it is also the root cause of overloaded wire fires. Every wire has a current rating (ampacity) determined by how much heat it can safely shed to the surrounding environment. Exceeding the ampacity raises the wire temperature, which can melt insulation and start fires. Circuit breakers and fuses protect against this by interrupting the circuit when current exceeds a safe threshold.
Efficiency and Power Factor
Real-world devices are not 100% efficient. A motor rated at 1 kW output may consume 1.25 kW of electrical input (80% efficient). The "lost" 250 W is dissipated as heat in the windings (I²R losses), friction, and magnetic hysteresis. Energy labels on appliances show the annual energy consumption assuming standard usage patterns, which is a more practical guide than nameplate power ratings alone.
Frequently Asked Questions
What is the difference between watts and kilowatt-hours?
Watts (W) measure power, how fast energy is being used at any instant. Kilowatt-hours (kWh) measure energy, the total amount of energy used over time.
- • A 100 W bulb uses 100 joules every second.
- • Run it for 10 hours and it consumes 1 kWh (= 100 W × 10 h ÷ 1000).
- • Your electricity bill charges for kWh, not watts, because you pay for energy used, not for how powerful the device is.
Quick formula: kWh = Watts × Hours ÷ 1000
Which formula should I use, P=VI, P=V²/R, or P=I²R?
The choice depends on which two values you already know:
- • Know voltage and current? Use P = V × I, the most common case (appliance rated in volts and amps).
- • Know voltage and resistance? Use P = V² / R, useful for resistor heat dissipation calculations in circuits.
- • Know current and resistance? Use P = I² × R, common for calculating wire losses and heating element wattage.
All three formulas give the same result for the same circuit, they are mathematically identical once you apply Ohm's law.
What is Ohm's law and how does it relate to power?
Ohm's law states: V = I × R, voltage equals current times resistance. It applies to any linear (ohmic) conductor at constant temperature.
Combined with P = VI, substituting Ohm's law gives all three power formulas:
- • Replace V with IR: P = (IR) × I = I²R
- • Replace I with V/R: P = V × (V/R) = V²/R
This means knowing any two of V, I, R is always enough to calculate all three, and therefore power, for a resistive circuit.
How do I calculate my monthly electricity bill for an appliance?
Use this formula: Monthly cost = P(kW) × hours/day × 30 × rate ($/kWh)
Step by step:
- Find the appliance wattage (usually on a label or nameplate).
- Convert to kW: divide by 1000. A 1500 W dryer = 1.5 kW.
- Estimate daily hours of use. A dryer used once daily for 45 min = 0.75 h/day.
- Multiply: 1.5 kW × 0.75 h × 30 days = 33.75 kWh/month.
- Find your rate from your electricity bill (look for $/kWh or cents/kWh).
- Cost = 33.75 kWh × $0.15 = $5.06/month.
The calculator handles all of this once you enter power, time, and rate.
Does this calculator work for AC circuits?
It depends on the type of load:
- • Resistive AC loads (heaters, incandescent bulbs, toasters): Yes, P = V_rms × I_rms gives the correct real power, and power factor = 1.
- • Reactive loads (motors, fluorescent ballasts, most switching power supplies): The calculator gives apparent power (VA). Real power = VA × power factor. A motor with a 0.85 power factor consuming 10 A at 230 V has apparent power = 2300 VA but real power = 1955 W.
- • For DC circuits, all three formulas are always exact.
When in doubt, use the P = VI formula with RMS values and be aware that reactive loads may have a power factor less than 1.
What causes a circuit breaker to trip?
A circuit breaker trips when current through the circuit exceeds a safe threshold, typically 15 A, 20 A, or 30 A for residential circuits.
- • Overload: too many appliances running simultaneously draw more current than the wire can safely carry. Example: three 1500 W appliances on a 15 A / 120 V circuit draw 37.5 A total, well above the 15 A limit.
- • Short circuit: a direct connection between live and neutral/earth creates near-zero resistance. Even at low voltage, current surges to dangerous levels instantly.
- • Ground fault: current finds an unintended path to earth, often through a person. GFCI outlets detect as little as 5 mA of leakage and trip in milliseconds.
Use P = VI to check whether your planned appliances fit within the circuit limit: sum the watts, divide by the circuit voltage to get total amps, and keep below 80% of the breaker rating.
What is power factor and why does it matter?
Power factor (PF) is the ratio of real power (watts) to apparent power (volt-amperes):
PF = Real Power (W) / Apparent Power (VA)
- • PF = 1 for purely resistive loads: all the current flowing does useful work.
- • PF < 1 for inductive or capacitive loads: some current oscillates back and forth without doing net work, but still heats the wires.
- • A motor with PF = 0.8 drawing 10 A at 230 V has apparent power = 2300 VA but delivers only 1840 W of real power.
- • Utilities care because they must supply the full apparent power even though they can only bill for real power. Large industrial customers pay a power factor penalty if PF drops below a threshold.
For household purposes, power factor mainly matters for motors and larger HVAC equipment. LED drivers and modern switch-mode supplies usually have PF ≥ 0.9.
Does this calculator save my inputs?
Yes, all inputs are automatically saved to your browser's localStorage as you type:
- • Formula mode (V×I, V²/R, or I²R), both primary values, run time, and electricity rate are persisted.
- • Everything stays in your browser, nothing is transmitted to any server.
- • When you return to the page, your last inputs are restored automatically.
- • Click Reset (or press Esc) to clear the form and delete the saved data.