Ohm's law in one page
Four quantities describe almost every DC circuit: voltage (V, the push), current (I, the flow), resistance (R, what opposes the flow) and power (P, the energy converted per second). Ohm's law relates the first three — V = I × R — and the power equation adds the fourth, P = V × I. Know any two and the other two follow, which is why this calculator asks for a pair rather than filling in a form.
The twelve rearrangements
| Find | From voltage and current | Using resistance |
|---|---|---|
| Voltage V | — | V = I × R = √(P × R) |
| Current I | I = P ÷ V | I = V ÷ R = √(P ÷ R) |
| Resistance R | R = V ÷ I | R = V² ÷ P = P ÷ I² |
| Power P | P = V × I | P = I² × R = V² ÷ R |
Worked examples
- 12 V across a 24 Ω resistor: I = 12 ÷ 24 = 0.5 A, and P = 12 × 0.5 = 6 W — a resistor that needs a 10 W rating, not a quarter-watt part.
- A 5 V supply driving 20 mA into an LED: R = 5 ÷ 0.02 = 250 Ω, P = 5 × 0.02 = 0.1 W, so a 1/4 W resistor is fine.
- A 2 kW kettle on 230 V: I = 2000 ÷ 230 = 8.7 A, R = 230² ÷ 2000 = 26.5 Ω.
Units, and the milliamps trap
Ohm's law only works if you keep the units consistent: volts with amps and ohms, or millivolts with milliamps and ohms. The most common arithmetic error in electronics is dividing volts by milliamps and reporting the answer as ohms — it is out by a factor of a thousand. The unit selectors here handle that conversion for you; when you work by hand, convert to base units first.
AC is not DC: RMS, peak and average
A mains socket rated at 230 V does not sit at 230 V — it swings between about +325 V and −325 V, 50 times a second. The 230 V figure is the RMS value (root mean square), chosen because it delivers the same heating power as 230 V DC. For a sine wave:
- peak = RMS × √2 (230 V RMS → 325 V peak), and peak-to-peak = 2 × peak (650 V).
- RMS = peak ÷ √2, and the rectified average is 0.637 × peak.
- Use RMS for power, heating and resistor ratings; use peak-to-peak when choosing insulation, capacitor and transistor voltage ratings. A "400 V" capacitor on a 230 V mains circuit is marginal, because the peak is 325 V and transients go higher.
Ohm's law still applies at every instant to a resistive load, so P = V² ÷ R works with RMS volts directly — no extra factors. It does not work with peak volts unless you divide by two afterwards, which is exactly the kind of slip that makes a resistor run hot.
Frequently asked questions
What is Ohm’s law in one sentence?
Voltage equals current multiplied by resistance (V = I × R). Rearranged: I = V ÷ R and R = V ÷ I. Add the power equation P = V × I and you can solve for any one quantity from any two of the others.
How do I calculate power from voltage and resistance?
P = V² ÷ R. For 12 V across 24 Ω: 144 ÷ 24 = 6 W. The same result comes from P = I² × R once you know I = 0.5 A, and both forms are useful — use V² ÷ R when you know the supply, I² × R when you know the current.
What size resistor do I need for an LED?
Subtract the LED forward voltage from the supply and divide by the desired current: (5 − 2) ÷ 0.02 = 150 Ω for 20 mA from a 5 V supply. Then check the power: P = I² × R = 0.02² × 150 = 0.06 W, so a standard quarter-watt resistor is fine.
What is the difference between RMS and peak voltage?
RMS is the value that produces the same heating as DC, while peak is the highest instantaneous value. For a sine wave, peak = RMS × √2: a 230 V RMS mains supply peaks at 325 V, and its peak-to-peak swing is 650 V. Use RMS for power and peak-to-peak for voltage ratings.
Why do I get the wrong answer when I use milliamps?
Because the units no longer match. Dividing 5 V by 20 mA gives 0.25, which is 0.25 volts per milliamp — equal to 250 Ω, not 0.25 Ω. Convert milliamps to amps first (20 mA = 0.02 A) or work entirely in millivolts, milliamps and ohms.
Does Ohm’s law work for AC circuits?
Yes, for resistive loads, using RMS values: a 230 V RMS heater element of 26.5 Ω draws 8.7 A RMS and dissipates 2 kW. With motors, transformers and capacitors, impedance and phase shift replace plain resistance, and the arithmetic needs complex numbers rather than this simple relation.