Power Equations
- P is the power dissipated or consumed, measured in watts (W)
- V is the voltage across the component, measured in volts (V)
- I is the current flowing through, measured in amperes (A)
- R is the resistance of the component, measured in ohms (Ω)
Power in a Circuit
Power is the rate at which electrical energy is converted into heat, light, or motion. In a simple circuit, the battery supplies energy and the resistor dissipates it as heat.
Power = Voltage × Current — The resistor converts electrical energy into heat at a rate measured in watts.
Electrical Power Calculator – Calculate Power, Voltage, Current & Resistance
Whether you are sizing a circuit breaker, selecting wire gauge, or estimating your electricity bill, understanding electrical power is essential. This calculator and guide cover everything from basic DC power formulas to AC power factor and three-phase systems.
What Is Electrical Power?
Electrical power is the rate at which energy is transferred through a circuit. The standard unit of power is the watt (W), named after the Scottish inventor James Watt. When current (I in amps) flows through a component driven by voltage (V in volts), the product of those two values gives you the power P in watts.
This relationship is fundamental to every calculation you will perform with the power calculator above. The value of P tells you how much energy per second the circuit consumes or delivers. A larger number of watts means the electric load draws more current at a given voltage — or the same current at a higher voltage.
In any real circuit, resistance (R, measured in Ω) also plays a role. Ohm’s law links voltage, current, and resistance together: V = I × R. By combining Ohm’s law with the power equation, you can derive every variable you need from just two known values.
DC Power Calculator — Formulas and Examples
Direct-current (DC) circuits are the simplest to calculate because the voltage and current remain constant over time. Batteries, solar cells, and most low-voltage electronic circuits operate on DC power.
Calculate Power from Voltage and Current (DC)
If you know the voltage V across a component and the current I through it, multiply the two to obtain the power P in watts:
Example: A 12 V battery supplies 3 A to a motor. The power consumed is P = 12 V × 3 A = 36 W. That value is all you need to size the wiring and confirm the battery can handle the load.
Calculate Power from Voltage and Resistance (DC)
When you know V and R but not the current, substitute Ohm’s law (I = V / R) into the power formula:
Example: A heating element with a resistance of 8 Ω is connected to a 24 V supply. The power it dissipates is P = 24² / 8 = 576 / 8 = 72 W. This calculation confirms the watt rating you need for safe operation. For more on how resistors behave in circuits, see our Series & Parallel Resistor Calculator.
Calculate Power from Current and Resistance (DC)
If you know the current and the resistance but not the voltage, use:
Example: A wire carrying 5 A has a resistance of 2 Ω. The power lost as heat is P = 5² × 2 = 50 W. That lost energy heats the conductor, which is why proper wire gauge selection matters in every circuit. Our Voltage Drop Calculator helps you account for these losses over long cable runs.
Finding Unknown Values in a DC Circuit
Because the four quantities — power (P), voltage (V), current (I), and resistance (R) — are all interrelated, any two known values let you derive the remaining two. Below is a quick-reference table showing how to rearrange the formulas.
| Known Values | Find P (W) | Find V (V) | Find I (A) | Find R (Ω) |
|---|---|---|---|---|
| V and I | V × I | — | — | V / I |
| V and R | V² / R | — | V / R | — |
| I and R | I² × R | I × R | — | — |
| P and V | — | — | P / V | V² / P |
| P and I | — | P / I | — | P / I² |
| P and R | — | √(P × R) | √(P / R) | — |
The square root expressions in the last row come from rearranging P = I² × R and P = V² / R. The calculator above handles all six combinations automatically — just enter any two values and it solves for the rest with step-by-step working.
AC Power Calculator — Power Factor and Phase
Alternating-current (AC) power is more complex than DC because the voltage and current waveforms can shift out of phase with each other. In AC systems you need to account for the power factor, which describes how effectively the circuit converts supplied voltage and current into real, usable power.
Understanding Power Factor in AC Circuits
The power factor (PF) is the cosine of the phase angle (φ) between the voltage and the current waveforms. A purely resistive load has a factor of 1, meaning all the supplied power does useful work. Inductive or capacitive loads cause the phase angle to increase, which reduces the real power delivered for the same V and I values. For dedicated power factor analysis, try our Power Factor Calculator.
Here, Vrms and Irms are the root-mean-square values of voltage and current. RMS values represent the effective, steady-state equivalents of the oscillating AC waveform and are the numbers your multimeter displays.
Apparent Power, Real Power, and Reactive Power
AC power analysis involves three related quantities. Apparent power (S) is measured in volt-amps (VA) and equals V × I without considering the phase angle. Real power (P) is the actual power consumed, measured in W. Reactive power (Q) represents energy that oscillates between the source and the load without doing useful work, measured in VAR.
The relationship between the three forms a right triangle known as the power triangle, where S is the hypotenuse: S² = P² + Q². This is why the power factor matters so much in industrial and commercial electrical installations. For detailed power loss analysis in components, see our Power Dissipation Calculator.
Single-Phase vs. Three-Phase AC Power
Residential circuits typically use single-phase AC power at 120 V or 240 V. The standard formula P = V × I × PF applies directly. Three-phase systems, common in commercial and industrial settings, require an additional factor:
The √3 (approximately 1.732) appears because of the 120-degree phase offset between the three voltage waveforms. VL is the line-to-line voltage and IL is the line current. For full three-phase calculations, use our Three Phase Power Calculator.
Key Power Formulas at a Glance
The table below consolidates every essential formula for converting between power, voltage, current, and resistance in both DC and AC circuits.
| Formula | Application | Notes |
|---|---|---|
| P = V × I | DC & AC (with PF) | Fundamental power equation |
| P = V² / R | DC circuit | When current is unknown |
| P = I² × R | DC circuit | When V is unknown |
| V = I × R | DC & AC | Ohm’s law |
| P = Vrms × Irms × PF | Single-phase AC | PF = cos(φ) |
| P = √3 × VL × IL × PF | Three-phase AC | VL = line voltage |
| E = P × t | Energy calculation | E in watt-hours when t is in hours |
Energy and Power Consumption
While power (P) measures the instantaneous rate of energy transfer, total energy consumed depends on how long the device operates:
For example, a 100 W light bulb running for 10 hours consumes 1,000 Wh, or 1 kWh. Utility companies bill you by the kilowatt-hour, so understanding power consumption directly impacts your electric bill.
Estimating Power Consumption for Common Devices
Knowing the watt rating and daily usage time of your appliances gives you a clear picture of where your energy goes. A microwave oven rated at 1,200 W used for 0.5 hours per day consumes 600 Wh daily. A desktop computer drawing 250 W for eight hours uses 2,000 Wh — or 2 kWh — each day.
Unit Conversions for Voltage, Current, and Resistance
Working with electrical values often means switching between unit prefixes. Here are the most common conversions.
| Quantity | Base Unit | Common Conversions |
|---|---|---|
| Power | W (watt) | 1 kW = 1,000 W | 1 MW = 1,000,000 W |
| Voltage | V (volt) | 1 kV = 1,000 V | 1 mV = 0.001 V |
| Current | A (amp) | 1 mA = 0.001 A | 1 µA = 0.000001 A |
| Resistance | Ω (ohm) | 1 kΩ = 1,000 Ω | 1 MΩ = 1,000,000 Ω |
| Energy | Wh (watt-hour) | 1 kWh = 1,000 Wh | 3,600,000 J = 1 kWh |
Getting the unit conversions right before plugging a number into any formula prevents costly mistakes. The calculator above supports mW/W/kW, mV/V/kV, mA/A/µA, and Ω/kΩ/MΩ — select the unit that matches your measurement and it handles the conversion automatically.
How This Calculator Helps You
The calculator above eliminates manual maths and reduces the chance of error. Enter any two values you know and it returns the other two instantly, with step-by-step working shown so you can follow the calculation.
Practical Scenarios
Sizing a circuit breaker: Enter the voltage of your supply and the total amp draw. The calculator returns the power in watts, which you compare against the breaker’s rating.
Selecting wire gauge: Given the current in amps and the wire’s resistance, calculate the power lost as heat along the conductor. Our Voltage Drop Calculator works alongside this for long cable runs.
Evaluating solar panels: A panel’s rated voltage and current let you compute peak power output. Accounting for the real-world power factor of the connected inverter gives a more accurate value of delivered AC power.
Checking battery life: Divide the battery’s energy capacity (in Wh) by the load’s power consumption (in W) to estimate run time. For a 50 Wh laptop battery powering a 25 W load, you get roughly two hours of operation. For runtime calculations, try our Battery Runtime Calculator.
Frequently Asked Questions
Last updated: March 2026