# Joule's law calculator

Created by Luis Hoyos
Last updated: Sep 14, 2022

Welcome to Joule's law calculator, a tool created to calculate the heat generated by a current-carrying cable. Apart from calculating heat generation, you can use this tool to compute any of the other variables of the joule heating equation.

## What is Joule heating?

Joule heating refers to the phenomenon of heat generation when an electric current passes through a conductor. This heat generation comes from the electrical energy of the charged particles (electrons, usually) that make up the current. The charged particles collide with the body of the conductor, losing part of its electrical energy, which converts into thermal energy (heat).

Joule's first law, or Joule's law, is the mathematical formulation of the joule heating phenomenon. This mathematical formulation lets us know how much energy per unit time (power) is converted into heat if we know the electric current and voltage drop through the conductor.

## Joule heating equation

The most general version of the joule heating formula is:

P = I × V

, where:

• P — Power of heat generated, calculated in watts (W);
• I — Current, in amperes (A); and
• V — Voltage drop through the conductor, in volts (V).

The previous equation can be expressed in terms of other variables. We know that power equals the heat generated per unit of time (P = Q/t). Additionally, if the conductor behaves according to Ohm's law (it's a perfect resistor that entirely converts the power into heat), we can express voltage according to that law (V = I × R).

Applying the previous equations to the original joule heating formula, we obtain the version used by this Joule's law calculator:

Q = I² × R × t

, where:

• R — Resistance, in ohms (Ω);
• t — Current flow time, in seconds (s); and
• Q — Heat generated, calculated in joules (J).

For example, let's use Joule's law to calculate the heat generated during 5 minutes in a water heater working at 20 A with a 10 Ω resistor.

Applying the joule heating equation requires the time to be in seconds. Using a time converter, we know that t = 5 min = 300 s. Applying that and the rest of the variables in the formula:

Q = I² × R × t = (20 A)² × 10 Ω × 300 s
Q = 1200000 J

Was it easy? Using our Joule's law calculator is easier.

Luis Hoyos
Current (I)
A
Resistance (R)
Ω
Time (t)
sec
Heat (Q)
J
If you need to calculate Joule's law in terms of power and voltage, use our resistor wattage calculator.
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