Power and heat

Every resistor that has current flowing through it turns some electrical energy into heat. Usually it is so little that you never notice. But if a resistor is too small for the job, it gets hot, changes value, discolours, and eventually burns. This page explains how to calculate that heat and how to choose a resistor that stays cool. It uses Ohm's law, so read that page first if you haven't.

Power

The rate at which a part uses energy is called power, measured in watts (W). Small amounts are given in milliwatts (mW), and 1,000 mW is 1 W. In a resistor all of that power becomes heat.

The basic formula is P = V × I: the voltage across the part multiplied by the current through it. Combined with Ohm's law it gives two more versions, which are handy when you know the resistance instead of the voltage or the current:

• P = V × I when you know voltage and current
• P = I × I × R when you know current and resistance
• P = V × V ÷ R when you know voltage and resistance

All three give the same answer for the same circuit. Use whichever matches the values you have. As with Ohm's law, convert milliamps to amps and kilohms to ohms first.

Power ratings

Every resistor has a power rating, the most power it can turn into heat without damage. The common small resistors used in hobby circuits are rated 1/4 W (0.25 W). There are also 1/8 W, 1/2 W, 1 W and 2 W versions, and the higher the rating, the physically bigger the resistor, because a bigger body gets rid of heat more easily.

The usual rule is to choose a rating at least twice the power you calculated. A resistor running at its full rating is very hot to touch and wears out faster, and real values are never exactly what you calculated. The tool above shows each common size against your power, and marks which ones keep that margin.

Examples

A 450 Ω resistor with 20 mA through it: P = 0.02 × 0.02 × 450 = 0.18 W, or 180 mW. Twice that is 0.36 W, so a 1/4 W resistor would be too close to its limit and a 1/2 W resistor is the right choice.

A 1 kΩ resistor across 5 V: P = 5 × 5 ÷ 1,000 = 0.025 W, only 25 mW. Any common resistor is fine here.

12 V across a 10 Ω resistor: P = 12 × 12 ÷ 10 = 14.4 W. No small resistor can take that. It would smoke within seconds. In a case like this the right answer is usually to change the circuit, not to buy a huge resistor.

Heat in other parts

Resistors are not the only parts that warm up. LEDs, transistors and chips have their own limits, given in their datasheets. The datasheet is the document the manufacturer publishes for each part, with its limits and typical values, and it is always the final word on what a part can take.

Batteries and wires heat up too when the current is large, which is why the short circuit from the first page is dangerous: a few amps through thin wire turns into a lot of heat very quickly.