Ohm's law and the power formula
Ohm's law links the three basic quantities of a circuit: the voltage V across a part, the current I through it and its resistance R. In the form taught in physics courses it reads V = I × R. The power P that the part turns into heat or work is the voltage times the current, P = V × I. Put one into the other and you get the two other power formulas, P = I² × R and P = V² ÷ R.
That makes four quantities and two equations, so any two values fix the other two. The calculator above takes the two fields you typed in last as the inputs, picks the matching formulas and fills in the rest.
The units: volt, ampere, ohm and watt
Volts, amps, ohms and watts are all SI units; amps is the everyday name for amperes. The ampere is one of the seven SI base units. The other three are derived units with special names, and the NIST guide to the SI defines them through each other:
| Quantity | Unit | Symbol | In other SI units |
|---|---|---|---|
| Electric current | ampere | A | base unit |
| Potential difference (voltage) | volt | V | W/A |
| Electric resistance | ohm | Ω | V/A |
| Power | watt | W | J/s |
Real circuits span many orders of magnitude, so values carry SI prefixes. The prefix symbol attaches directly to the unit symbol, as in mA or kΩ. These are the ones the calculator offers:
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| micro | µ | 10−6 | 50 µA = 0.00005 A |
| milli | m | 10−3 | 20 mA = 0.02 A |
| kilo | k | 103 | 4.7 kΩ = 4,700 Ω |
| mega | M | 106 | 1 MΩ = 1,000,000 Ω |
All twelve formulas
The formula wheel in the tool collects every rearrangement. Find the quantity you want in the middle, then use the formula in its quarter of the ring that needs only the values you have.
| You want | From V and I | From V and R | From V and P | From I and R | From I and P | From R and P |
|---|---|---|---|---|---|---|
| V | given | given | given | I × R | P ÷ I | √(P × R) |
| I | given | V ÷ R | P ÷ V | given | given | √(P ÷ R) |
| R | V ÷ I | given | V² ÷ P | given | P ÷ I² | given |
| P | V × I | V² ÷ R | given | I² × R | given | given |
Worked example: 12 V across 220 Ω
A 220 Ω resistor sits across a 12 V supply. The current is I = V ÷ R = 12 ÷ 220 = 54.55 mA. The power the resistor turns into heat is P = V² ÷ R = 144 ÷ 220 = 654.5 mW. You get the same number from P = V × I or P = I² × R. Check it against the power rating in the resistor's datasheet. Double the voltage to 24 V and the power grows four times, to 2.618 W, because voltage enters the power formula squared.
Resistors in series and in parallel
Resistors in a chain, one after the other, carry the same current, and their resistances add: R = R1 + R2 + R3 + …. Resistors side by side share the same voltage, and their reciprocals add: 1/R = 1/R1 + 1/R2 + 1/R3 + …. For 220 Ω, 330 Ω and 470 Ω that gives 1.02 kΩ in series and 103.1 Ω in parallel. The parallel result is always below the smallest single resistor, because each extra path lets more current through. For two equal resistors in parallel it is exactly half of one.
To read the value of a resistor from its color bands, use the resistor color code calculator. To work out what an appliance costs to run from its watts, use the electricity cost calculator.
When Ohm's law does not apply
Ohm's law describes ohmic devices, where the current is proportional to the voltage. A resistor at a steady temperature behaves that way. Many parts do not. A diode is the classic counterexample: with the voltage one way round it passes almost no current, the other way round it starts to conduct at about 0.7 V. Resistance also changes with temperature, so a part that heats up drifts away from its cold value. The power formula P = V × I holds for any device, ohmic or not.
How to use the Ohm's law calculator
- 1Type the two values you know, for example the voltage and the resistance, and pick a prefix like mA or kΩ next to each field if you need one.
- 2Read the other two values in the result, with the formula and your numbers below them. The highlighted part of the formula wheel shows which formulas were used.
- 3To combine resistors, type their values in the series and parallel box and press Use as resistance. Copy result or Copy link keeps your numbers.
Sources
- NIST Special Publication 811, Chapter 4: ampere as a base unit; volt (W/A), ohm (V/A) and watt (J/s) as derived units; SI prefixes
- NIST: Metric (SI) prefixes: factors and symbols from pico to giga
- OpenStax University Physics Volume 2, 9.4 Ohm's Law: V = IR, ohmic and nonohmic devices, the diode
- OpenStax University Physics Volume 2, 9.5 Electrical Energy and Power: P = IV = I²R = V²/R
- OpenStax University Physics Volume 2, 10.2 Resistors in Series and Parallel: equivalent resistance formulas
Frequently asked questions
What is Ohm’s law?
Ohm’s law says that the current through a conductor is proportional to the voltage across it: V = I × R. V is the voltage in volts, I the current in amperes and R the resistance in ohms. Rearranged, I = V ÷ R and R = V ÷ I. Together with P = V × I for power, any two of the four values give you the other two.
How do I calculate current from voltage and resistance?
Divide the voltage by the resistance: I = V ÷ R. With 12 V across 220 Ω, I = 12 ÷ 220 = 54.55 mA. Keep the units in base form before you divide, or let the calculator handle the prefixes: 220 Ω is 0.22 kΩ, and 12 V ÷ 0.22 kΩ gives milliamperes.
How do I calculate watts from volts and amps?
Multiply them: P = V × I. A device that draws 500 mA at 120 V uses 120 × 0.5 = 60 W. If you know the resistance instead of the current, use P = V² ÷ R or P = I² × R.
What do mA, kΩ and µA mean?
They are SI prefixes in front of the unit. m (milli) is one thousandth, µ (micro) one millionth, k (kilo) a thousand and M (mega) a million. So 20 mA is 0.02 A, 4.7 kΩ is 4,700 Ω and 1 MΩ is 1,000,000 Ω. Pick the prefix next to each field, or type the plain number and keep the prefix at the base unit.
How do I find the resistance from watts and volts?
Use R = V² ÷ P. A device that draws 60 W at 120 V behaves like 120² ÷ 60 = 240 Ω while it runs. For a lamp or a heater this is the hot resistance at that operating point; measured cold with a meter, it can be different, because resistance changes with temperature.
Does Ohm’s law work for every component?
No. It holds for ohmic devices, where the current is proportional to the voltage, such as a resistor at a steady temperature. A diode is the textbook nonohmic example: it lets almost no current through in one direction and conducts in the other once the voltage passes about 0.7 V. P = V × I still gives the power for any device.
How do I add resistors in series and in parallel?
In series, add the values: 220 + 330 + 470 = 1.02 kΩ. In parallel, add the reciprocals and take the reciprocal of the sum: 1 ÷ (1/220 + 1/330 + 1/470) = 103.1 Ω. The parallel total is always smaller than the smallest resistor. The series and parallel box under the calculator does both for any list of values.