Resistor power dissipation:
formula and worked example

Where the heat in a resistor comes from

Every resistor turns electrical energy into heat. The component does no other useful work, so its power rating is simply a statement of how much heat the body can shed to the air without overheating, drifting out of tolerance or burning.

That makes dissipation the number that decides the physical size of a resistor, and whether it needs a heat sink, spacing from neighbours or airflow. A 1 kΩ signal resistor with microamps through it is a different object from a 20 Ω resistor with half an ampere through it, even though the schematic symbols are identical.

• Current: the current through the resistor, in amperes.
• Resistance: the resistor's value, in ohms.
• Result: power in watts, which is joules per second of heat released.

The formula and its two cousins

This version is the one to use when you know the current. If you know the voltage across the resistor instead, the equivalent forms are V²÷R or V×I. They give the same answer because of Ohm's law, so pick whichever uses the quantity you have measured or designed for.

The squared current is the important part. Heat does not scale in step with current; it scales with its square, which is why a modest overload is more damaging than it looks.

Worked example: 0.5 A through 20 Ω

A 20 Ω current-sense or load resistor carries 0.5 A in a motor-driver test fixture. How much heat must it get rid of?

1. 1Square the current: 0.5 × 0.5 = 0.25 A².
2. 2Multiply by the resistance: 0.25 × 20 = 5 W.
3. 3Cross-check using voltage: 0.5 A × 20 Ω = 10 V across the resistor, and 10 V × 0.5 A = 5 W.

Five watts is far beyond any small signal resistor. It calls for a wirewound or metal-clad power resistor, mounted where air can move across it, and not buried against other parts.

Choosing the wattage rating

A resistor rated for the calculated power exactly is running at the edge, usually in an ambient far warmer than the rating assumes. The common practice is to use a part rated at least twice the calculated dissipation, and more if the enclosure is warm or the resistor sits near other heat sources.

• Small axial parts are often rated 0.25 W or 0.5 W; at those ratings the body gets noticeably hot well before its limit.
• Resistors rated for several watts are physically larger and are frequently derated when the surrounding temperature is high.
• For this 5 W case, a 10 W rated part gives the usual two-times margin.

Ratings assume free air at a stated ambient. Inside a sealed enclosure, mounted flat on a board with other warm parts, the real allowance can be a fraction of the printed figure.

How a rise in current multiplies the heat

Raising the current from 0.5 A to 0.55 A is a 10% increase, yet the dissipation goes from 5 W to 6.05 W, a 21% increase. A 20% current rise would give 44%, and doubling the current takes you to four times the power.

This is why resistors in power circuits fail during faults rather than normal running: a fault that merely doubles the current quadruples the heat, and the part cannot keep up. Fuses or current limits upstream are what keep the resistor inside its rating.

Mistakes with power dissipation

• Using milliamps in the formula without converting to amperes, which understates the power by a factor of a million.
• Sizing the resistor to the calculated power exactly, leaving no margin for warm enclosures or supply tolerance.
• Forgetting that peak and average differ: a resistor that sees short high-current pulses must be checked against pulse ratings as well as average power.
• Calculating at nominal current and ignoring a higher worst-case current at maximum supply voltage.

A checklist before choosing the part

For a part dissipating 5 W, work through the choice in a fixed order so that nothing is left to chance.

1. 1Calculate the dissipation at the highest current the circuit can see.
2. 2Double it for a first rating target, or use the maker's derating curve for the real ambient.
3. 3Check the physical size, mounting and airflow, since a hot resistor can discolour a board or scorch wiring.
4. 4Confirm the voltage rating of the resistor, which a high-value part can exceed even when its power is low.