How it works
Ohm's Law describes the relationship between three fundamental electrical quantities: voltage (V), current (I), and resistance (R). The law states that voltage equals current times resistance, no matter which direction you need to work in.
V = I × R
I = V ÷ R
R = V ÷ I
Those three lines are one equation, not three. Start from V = I × R, divide both sides by R and you have I = V ÷ R; divide instead by I and you have R = V ÷ I. Whichever quantity you are missing ends up alone on the left.
What the law is actually saying is that current is what flows, voltage is what pushes it, and resistance is what holds it back. Push harder and more flows; resist harder and less does. The water analogy is imperfect but it earns its keep here: voltage is the pressure, current is the flow rate, and resistance is how narrow the pipe is. Everything the equation predicts follows from that picture.
This calculator also derives power (P = V × I) once you know both voltage and current. Power is always shown in the result panel, whether you entered it directly or the calculator solved for one of the three circuit values.
Power is the quantity that usually matters in practice, because it is what turns into heat. It is worth noting that power is not proportional to current. Substituting V = I × R gives P = I² × R, so doubling the current quadruples the heat. That is why an undersized wire fails suddenly rather than gradually.
Worked example
A circuit with current of 2 amps through a 5-ohm resistor.
- Use the formula V = I × R.
- Substitute: V = 2 × 5.
- That gives 10 volts.
- Power: P = 10 × 2 = 20 watts.
The voltage is 10 V and the power is 20 W.
- Use I = V ÷ R.
- Substitute: I = 12 ÷ 220.
- That gives 0.0545 amps, which is usually written 54.5 mA.
- Power: P = 12 × 0.0545 = 0.65 watts.
The current is 54.5 mA and the resistor dissipates 0.65 W.
The most common real use of Ohm's Law: sizing a series resistor for an LED. A 9 V battery, an LED that drops 2 V and wants 20 mA.
- The resistor does not see all 9 V. The LED takes 2 V, leaving 9 − 2 = 7 V.
- Put the current in amps: 20 mA = 0.02 A.
- Use R = V ÷ I: 7 ÷ 0.02.
- That gives 350 ohms.
- Check the heat: P = I² × R = 0.02² × 350 = 0.14 W.
Use 350 Ω, and at 0.14 W a quarter-watt resistor is fine while an eighth-watt one is not.
Milliamps, kilohms, and the factor-of-1000 mistake
Ohm's Law only works in base units: volts, amps, ohms. Real components are labelled in milliamps and kilohms, and putting those numbers straight into the formula is how most wrong answers happen. They come out wrong by a factor of exactly 1,000, which is large enough to notice but not always large enough to look absurd.
| Written as | Means | In base units |
|---|---|---|
| 1 mA | milliamp | 0.001 A |
| 20 mA | milliamps | 0.02 A |
| 1 mV | millivolt | 0.001 V |
| 1 kΩ | kilohm | 1,000 Ω |
| 4.7 kΩ | kilohms | 4,700 Ω |
| 1 MΩ | megohm | 1,000,000 Ω |
A quick sanity check: at ordinary electronics voltages, currents through resistors in the hundreds or thousands of ohms land in milliamps. If your answer comes out in whole amps, you have probably left a resistance in kilohms.
Three ways to write power
Power has three equivalent forms, and which one you reach for depends on which two quantities you happen to know. They always agree.
P = V × I
P = I² × R
P = V² ÷ R
Checking the 12 V and 220 Ω example all three ways: V × I gives 12 × 0.0545 = 0.65 W; I²R gives 0.0545² × 220 = 0.65 W; and V²/R gives 144 ÷ 220 = 0.65 W. Same answer, three routes.
The middle form is the one worth internalising, because it is where the squared term lives. Heat rises with the square of current, so a modest increase in current is a large increase in temperature, which is why component ratings and wire gauges have hard limits rather than gentle ones.
Common questions
What is Ohm's Law?
It's the relationship V = I × R between voltage, current and resistance in a simple circuit: voltage equals current times resistance. Any one of the three can be found if you know the other two.
How is power calculated from these values?
Power in watts is P = V × I, voltage times current. It's shown automatically here as a derived value once voltage and current are both known, whether you entered them directly or the calculator solved for one.
Does this work for AC circuits?
This is the basic DC form of Ohm's Law. AC circuits with reactance (capacitors, inductors) use impedance instead of plain resistance, which this calculator doesn't model.
My answer is out by a factor of 1000. What did I do?
Almost certainly entered milliamps as amps, or kilohms as ohms. The formula needs base units: 20 mA is 0.02 A, and 4.7 kΩ is 4,700 Ω. That single slip is the most common source of wrong answers here.
Why does an LED need a resistor, and how do I size it?
An LED barely resists current on its own, so without a resistor it draws whatever the supply will give and destroys itself. Size the resistor on the voltage it sees, not the supply voltage: subtract the LED's forward voltage first. A 9 V supply with a 2 V LED at 20 mA needs (9 − 2) ÷ 0.02 = 350 Ω.
What wattage resistor do I need?
Work out P = I² × R and pick a rating comfortably above it. The 350 Ω resistor above dissipates 0.14 W, so a quarter-watt part is fine and an eighth-watt one is not. Resistors run hot near their rating, so leaving headroom is normal practice rather than caution.