What this calculator does
Every resistor turns some electrical energy into heat as current passes through it, and the power dissipated formula tells you how much. It comes straight out of Ohm's law: once you know any two of current, voltage and resistance, the third is fixed, and so is the rate at which that resistor is converting electricity into heat.
The three versions of the formula, P = I²R, P = VI and P = V²/R, all describe the same physical quantity from a different starting pair of values. Picking the version that matches what you actually measured avoids an extra step of working out the missing quantity first.
The formula
Choose which two values you know. If it is current and resistance, power is current squared times resistance. If it is voltage and current, power is simply their product. If it is voltage and resistance, power is voltage squared divided by resistance. All three give the same answer for the same underlying circuit, since Ohm's law (V = IR) links the three quantities together.
| Term | Meaning |
|---|---|
| P | Power dissipated, in watts, the rate at which electrical energy converts to heat. |
| I | Current flowing through the resistor, in amps. |
| V | Voltage across the resistor, in volts. |
| R | Resistance, in ohms. |
The inputs explained
| Field | What to enter |
|---|---|
| Values you know | Pick the two quantities you actually have; the third is not needed for that calculation. |
| Current (I) (A) | Current through the resistor, used when you know current and resistance, or voltage and current. |
| Voltage (V) (V) | Voltage across the resistor, used when you know voltage and current, or voltage and resistance. |
| Resistance (R) (Ω) | Resistance value, used when you know current and resistance, or voltage and resistance. |
When to use it
Sizing a resistor's power rating
Resistors are rated for how much heat they can safely dissipate. Working out the expected power dissipation from the circuit's current and resistance tells you whether a 0.25 W resistor will survive, or whether a larger, higher-rated part is needed.
Checking a heating element
Heaters, kettle elements and similar resistive loads are rated by the power they dissipate at their working voltage. Given the element's resistance and the supply voltage, P = V²/R gives the wattage directly.
Estimating running cost
Once the power dissipated is known, multiplying by the hours run and the electricity price converts a circuit's heat loss into an actual cost, rather than leaving it as an abstract wattage.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How power dissipated changes with current, at a fixed resistance
The same 6 Ω resistor, carrying a range of currents.
How power dissipated changes with voltage, at a fixed resistance
The same 100 Ω load, across a range of supply voltages.
Questions
Why are there three different formulas for the same thing?
They all follow from Ohm's law, V = IR. Substituting that relationship into P = VI gives P = I²R or P = V²/R depending on which variable you eliminate, so all three describe the same power for a resistor obeying Ohm's law.
Does this work for any electrical component, not just resistors?
It applies exactly to components that behave as pure resistances. Components with reactance, such as capacitors, inductors or motors, dissipate real power differently and need the power factor accounted for, which this calculator does not cover.
What happens to the dissipated power physically?
It leaves the circuit as heat. That is why resistors carry a power rating in watts: exceeding it means the component generates heat faster than it can shed it, and it overheats or fails.
Is power dissipated the same as power consumed?
For a simple resistive load, yes, all the electrical power delivered to it is dissipated as heat. For more complex loads that also do mechanical work or store energy, dissipation is only part of the total power consumed.
For the underlying relationship between voltage, current and resistance, see the Ohm's law calculator. For the electrical work and running cost that power dissipation feeds into, see the work, power and efficiency calculator.