Ohm's law: two formulas that size almost any small circuit
Two formulas cover a surprising share of practical electronics. Resistance = voltage ÷ current, and power = voltage × current. Learn what each symbol actually refers to and you can size a resistor, pick a power rating, and work out why a component is running hot.
The method
Voltage (V, in volts) is the electrical push across a component. Current (I, in amps) is the flow through it. Resistance (R, in ohms) is how much the component opposes that flow, and power (P, in watts) is the rate it turns electrical energy into heat.
R = V ÷ IP = V × I
The one thing to be careful about: V means the voltage across the component you are asking about, not the supply voltage of the whole circuit. That distinction is the source of most wrong answers, and it is worth more than the formulas themselves.
A real example: 12 V, 2 A
A component with 12 volts across it drawing 2 amps:
- Resistance:
12 ÷ 2 = 6ohms. - Power:
12 × 2 = 24watts.
24 watts is a lot of heat for a small part. If that were a resistor, a quarter-watt component would not merely underperform — it would burn. The power figure is the one that decides what you can physically use, and it is the one people forget to check.
A real example: sizing a resistor for an LED
This is the classic case, and the classic mistake. Say a 9 V battery, an LED that drops 2 V, and a target current of 20 mA (0.02 A).
The wrong move is 9 ÷ 0.02 = 450 ohms, because 9 V is not across the resistor. The LED takes 2 V of it. What the resistor actually sees is 9 − 2 = 7 V.
- Resistance:
7 ÷ 0.02 = 350ohms. - Power in the resistor:
7 × 0.02 = 0.14watts.
So a 350-ohm resistor (or the nearest standard value above it), and 0.14 W means a common quarter-watt part is comfortable. Using 450 ohms instead would not damage anything — it would just run the LED dimmer than intended, at about 15.6 mA. The error is quiet, which is exactly why it survives.
A real example: reading a mains appliance
A 120 V appliance drawing 0.5 A: 120 ÷ 0.5 = 240 ohms, and 120 × 0.5 = 60 watts. Working backwards is just as useful — a label quoting 60 W on 120 V implies 60 ÷ 120 = 0.5 A, which is what tells you whether a circuit or an extension lead can carry it.
The other two forms
Power has three equivalent expressions, and the right one is whichever uses the two numbers you already have: P = V × I, P = I2 × R, and P = V2 ÷ R. They are the same relationship with Ohm's law substituted in, so they always agree. Checking our LED resistor with the second form: 0.022 × 350 = 0.0004 × 350 = 0.14 W — the same answer, arrived at from the current and resistance instead of the voltage.
What this doesn't cover
This is direct current and components that behave predictably. Ohm's law describes resistors well; it does not describe diodes, LEDs or transistors, whose current does not rise in proportion to voltage — which is precisely why the LED above was handled by subtracting its forward voltage rather than by giving it a resistance. Alternating current adds reactance and power factor, so the same arithmetic on an AC motor will not give you its real power draw. And a current of zero means nothing is flowing at all, so there is no resistance figure to report.
Run your own numbers
The free Ohm's Law calculator takes a voltage and a current and returns both resistance and power, entirely on your device. Give it the voltage across the part you care about.