Resistors are bought by their resistance and destroyed by their power rating. The strip of resistors in a starter kit is almost always 1/4 watt — 250 milliwatts — and nothing on the part tells you when you are near that limit. It just gets hot, discolours, and eventually goes open circuit.
The rating is easy to check before you build, and the arithmetic is one line.
The formula, and the number you are missing
Power in a resistor is:
P = I x V = I^2 x R = V^2 / RAll three are the same statement. Which one you use depends on what you already know.
The catch is that you usually know R and the supply voltage, but the formula needs the current or the voltage across that particular resistor — and in any circuit with more than one component, those are not the supply values. That is the step where estimates go wrong, and it is the step a simulator does for you.
A worked example: the cost of a stiff divider
A voltage divider is a good demonstration because it has an obvious knob. All three circuits below split 12 V in half and put exactly 6 V at the midpoint. The only difference is the resistor values.
| divider | current | power in each resistor |
|---|---|---|
| 10 kΩ / 10 kΩ | 0.600 mA | 3.6 mW |
| 1 kΩ / 1 kΩ | 6.000 mA | 36 mW |
| 100 Ω / 100 Ω | 60.00 mA | 360 mW |
Every one of them outputs 6.0000 V. Electrically, at the midpoint, they are indistinguishable.
But the last one dissipates 360 mW in each resistor, and a standard 1/4 W resistor is rated for 250 mW. Build that divider out of the resistors in your kit and you have two parts running at 144% of rating, continuously, getting genuinely hot.
Notice the shape of it: dropping the resistors by 10x multiplies the power by 10x, and going from 10 kΩ to 100 Ω — a factor of 100 — multiplies it by 100. Power scales with current squared, and current scales inversely with resistance, so halving your resistors doubles the heat.
This is the trade-off behind the previous article: a stiffer divider resists loading better, and you pay for that stiffness in continuous current. Both effects pull in opposite directions, which is why divider values are a choice rather than a formula.
Do not design at 100% of the rating
A 1/4 W resistor will survive 250 mW in the sense that it does not immediately fail, but its rating assumes free air at a moderate ambient temperature. Inside an enclosure, next to other warm parts, in a hot room, it has less margin than the datasheet number suggests.
The common engineering practice is to derate — design for roughly half the rated power. For a 1/4 W part, treat 125 mW as your working ceiling. That leaves headroom for ambient temperature, tolerance in your supply, and the resistor sitting next to something else that is warm.
By that standard, the middle divider above (36 mW) is comfortable, and the 100 Ω one needs a 1 W part rather than a bigger safety margin on a small one.
The cases that actually catch people
- Dropping voltage with a series resistor. Any time a resistor is doing real work rather than sensing, it is turning the difference into heat. The bigger the voltage you drop, the more heat.
- Current-limiting on a supply rail. A resistor sized for a comfortable current at 5 V can be four times as hot at 12 V, because the power goes with voltage squared.
- Pull-down resistors on a high-voltage rail. Small resistance, full supply across it, running continuously.
- A divider left permanently connected. It draws its current 24 hours a day, which matters for battery life as much as for heat.
How to check yours
You need the actual current in your actual circuit, so the reliable method is to solve the circuit rather than estimate.
In CircuPilot you can describe the circuit in plain English — "a 12 V source with two 100 ohm resistors in series" — and it builds the schematic and runs real ngspice. Run the operating point, read the node voltages, and the power in any resistor is the voltage across it times the current through it. Every figure in the table above came out of that, not out of a calculator.
V1 in 0 12
R1 in mid 100
R2 mid 0 100Three quick sanity checks worth running on anything you are about to build:
1. Read the current through each resistor at the operating point.
2. Multiply by the voltage across it to get the dissipation.
3. Compare against half the rating of the part you actually own.
It takes less time than finding the right resistor in the drawer, and it is the difference between a circuit that runs warm and one that quietly goes open circuit a week later.