Ohm's Law Calculator

The four quantities and the two formulas

Ohm's law ties three things together: voltage, current and resistance. Voltage (V) is the push, measured in volts. Current (I) is the flow, measured in amperes. Resistance (R) is the opposition, measured in ohms. The law says the current through a resistor equals the voltage across it divided by its resistance, which rearranges to V = I x R.

Power (P) is the fourth quantity, measured in watts. It is the rate at which energy turns into heat or work, and it comes from the same three values: P = V x I. Substitute V = I x R and you get P = I^2 x R. Substitute I = V / R and you get P = V^2 / R. All four forms describe the same circuit, and the one you use depends on which values you already know.

The units are SI units, and the definitions behind them come from the NIST definitions of the SI base units. One volt drives one ampere through one ohm, and that combination dissipates one watt. That single sentence covers most of what this page does.

Worked example: a 12 V LED strip

A 12 V strip draws 0.5 A. That is the pair of numbers the calculator wants: voltage and current. The other two values follow directly.

Resistance: R = V / I = 12 / 0.5 = 24 ohms. Power: P = V x I = 12 x 0.5 = 6 W. The strip turns 6 W of electrical energy into light and heat, and the heat part is why the backing tape matters on a long run.

All three power formulas give the same 6 W, which is a useful check when you are learning the algebra. If one of them disagrees, you divided when you should have multiplied.

For a power supply, 6 W at 12 V means a 1 A adapter runs at half load, which is comfortable. A 0.5 A adapter would run at its limit and heat up, so buy the supply for the power, not for the exact current on the label.

Worked example: sizing a resistor for one LED

A red LED needs about 2 V across it and about 20 mA through it. Suppose the supply is 5 V. The resistor has to absorb the difference, so the voltage across the resistor is 5 - 2 = 3 V.

Current is 20 mA, which is 0.02 A. Resistors work in amps, not milliamps, and mixing those units is the most common mistake in this calculation. R = V / I = 3 / 0.02 = 150 ohms. A 150 ohm resistor is a standard value, so no rounding is needed.

Now check the heat. P = V x I = 3 x 0.02 = 0.06 W. The smallest common resistor is rated 0.25 W, which is more than four times what the part will dissipate, so a 1/4 W resistor is fine. A 1/8 W part would also work at 0.06 W, but it leaves less margin if the supply voltage drifts up.

The same arithmetic explains why LEDs need a resistor at all. A diode does not follow Ohm's law: its current climbs steeply once the voltage passes its forward drop, so a small voltage change causes a large current change. The resistor turns the supply difference into a current the LED can survive.

The power formulas, and where the heat goes

Every watt that a component dissipates becomes heat. That is fine for a heater and a problem for everything else. The two power formulas tell you which value to attack when something runs hot.

P = I^2 x R says the heat in a wire grows with the square of the current. Double the current and the loss quadruples. That is why long runs use thicker wire rather than a bigger fuse: the resistance of the run is what turns current into heat.

A worked case: 15 A through 100 ft of 12 AWG copper (50 ft out and 50 ft back). The resistance of that run is 0.193 ohms, so P = I^2 x R = 225 x 0.193 = 43.4 W. Forty three watts spread along a cable inside a wall is the reason codes limit how much current a given wire size may carry.

P = V^2 / R is the form to use when the voltage is fixed, as it is on a wall circuit. A 1,500 W space heater on 120 V has an effective resistance of 120^2 / 1500 = 9.6 ohms, which is why it draws 12.5 A.

Voltage drop along a wire run

Wires are resistors, just small ones. The resistance is quoted per 1,000 ft at 75 degrees C in the National Electrical Code, Chapter 9, Table 8. To get the drop, multiply the round trip length by the resistance per foot and then by the current.

Read the 12 AWG row: 1.93 ohms per 1,000 ft means 0.193 ohms for 100 ft of conductor, because the current has to travel out and back. At 15 A the drop is 15 x 0.193 = 2.9 V, which is 2.4 percent of 120 V.

The usual design target, from the informational notes in the code, is no more than 3 percent on a branch circuit and 5 percent from the service to the last outlet. A 14 AWG circuit at 50 ft already sits at 3.8 percent, which is why 12 AWG is the common choice for a 20 A kitchen circuit.

Household circuits and the 80 percent rule

A 15 A breaker on a 120 V circuit carries 15 x 120 = 1,800 W in theory. The code does not let you use all of it for a load that runs for three hours or more. Continuous loads are limited to 80 percent of the breaker rating, so the practical ceiling is 15 x 0.8 = 12 A, or 12 x 120 = 1,440 W.

The heater is the one to watch. At 12.5 A it exceeds the 12 A continuous limit for a 15 A circuit all by itself, before anything else is plugged in. That is why a space heater on a bedroom circuit with a computer and a lamp is a common cause of tripped breakers.

The resistance column is a teaching aid, not a measurement. Motors, chargers and LED drivers are not plain resistors, so their current does not scale linearly with voltage. Use the watts and amps columns for load planning and treat the ohms column as the equivalent value at that operating point.

When Ohm's law does not hold

The law applies to resistors that keep a steady resistance. Several common parts do not.

Diodes and LEDs. Current rises sharply once the forward voltage is reached, so a tiny voltage change produces a large current change. A series resistor or a current driver is what makes the math usable.

Motors. A motor draws several times its running current at startup, because a stopped motor has almost no back voltage. A 10 A running load can pull far more for a second, which is why motor circuits get their own sizing rules.

Incandescent bulbs. The filament is cold at switch-on, so its resistance is low and the inrush current is high. A 60 W bulb on 120 V runs at 240 ohms hot, but reads much lower on a multimeter when cold.

AC circuits. The formula still works if you use RMS values, which is what a multimeter reports for AC. With motors and transformers the current and voltage peak at different moments, so watts are lower than volts times amps; that gap is the power factor.

For everything else, a resistor, a heating element, a length of wire, the law holds well enough that the four formulas above are all you need. The OpenStax treatment of Ohm's law covers the same ground with lab examples, and OSHA's electrical safety pages explain why the current matters more than the voltage when a person becomes part of the circuit.