Power from Voltage and Resistance: P = V^2 / R

The power of a load from its voltage and resistance.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • P = \frac{V^2}{R}
  • V = \sqrt{PR}
  • R = \frac{V^2}{P}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the power: power = (voltage^2) / (resistance)
  2. Put the values in (every value in its SI unit): power = (230^2) / (50)
  3. The answer: power: 1058 W
  4. The same answer in other units: 1.058 kW; 1.058e+6 mW

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Resistance; Power (leave it as it is if this is what you are finding) 1058 W; Voltage (leave it as it is if this is what you are finding) 230 V.

  1. The formula, arranged to find the resistance: resistance = (voltage^2) / (power)
  2. Put the values in (every value in its SI unit): resistance = (230^2) / (1058)
  3. The answer: resistance: 50 ohm
  4. The same answer in other units: 0.05 kohm

Common questions

What is the formula for power from voltage and resistance?

Power equals the voltage squared divided by the resistance. 230 V across 50 ohm is 1058 W.

How do I find the resistance of a heater?

Divide the voltage squared by the power rating. A 2300 W heater on 230 V has a resistance of 23 ohm.

Why does the power fall a lot when the voltage drops?

The voltage is squared, so a small drop in voltage gives a bigger drop in power.

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Further reading: Any school physics or electrical text (electrical power).

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