Joule heating is the heat produced when current flows through resistance: H = I² × R × t, in joules. Heat grows with the square of the current and with resistance and time, so doubling the current makes four times the heat. In calories, H = 0.24 × I² × R × t.
Current flowing through resistance makes heat, and the heat grows with the square of the current, the resistance and the time. Kettles, space heaters, blown fuses and loose terminals that run hot all follow the same rule. Pick your country to load the usual heat unit: BTU in the United States and a few others, kilojoules elsewhere.
Result
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Formula
- H = I² × R × t (joules)
- H = 0.24 × I² × R × t (calories)
- 1 cal = 4.184 J, 1 BTU ≈ 1,055 J, 1 Wh = 3,600 J
How to use it
- Pick your country to load the heat unit.
- Enter current, resistance and time.
- Read the heat and heating power. A slightly higher contact resistance at high current is enough to make a joint run hot.
This is an estimating tool. Follow your local electrical code and have a qualified electrician confirm any real installation.
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Frequently asked questions
What is Joule’s first law?
The heat produced in a conductor equals current squared times resistance times time, measured in joules. Kettles, space heaters and fuses all rely on it.
Why does a loose connection get hot?
A loose joint touches over a smaller area, so its resistance rises. Heating power is I² × R, so in a high-current circuit even a little extra resistance at the joint makes noticeable heat, and in bad cases melts insulation or starts a fire.
How do joules, calories and BTU convert?
1 calorie is about 4.184 J, 1 BTU is about 1,055 J, and 1 Wh is 3,600 J. Heating and cooling in the United States is often rated in BTU; most other places use kilojoules or kilocalories.
Why does a fuse blow?
A fuse element is a thin metal chosen to melt easily. Above its rating the I² × R heat builds faster than it can escape, the element reaches its melting point and opens the circuit, protecting the wiring behind it.
