Ohm's law: volts, amps, ohms and watts

What is Ohm's law?

Voltage equals current times resistance: V = I × R. Push 12 volts across a 4 ohm resistor and 12 ÷ 4 = 3 amps flow. Knowing any two of the three gives the third.

How do I calculate power from voltage and current?

Multiply them: P = V × I. A load drawing 10 amps at 120 volts uses 1,200 watts, and its resistance is 120 ÷ 10 = 12 ohms. With the resistance instead, P = I² × R or P = V² ÷ R.

How do I find the resistance of a heater from its watts?

Divide the voltage squared by the watts: R = V² ÷ P. A 1,500 W heater on 120 V has 14,400 ÷ 1,500 = 9.6 ohms of resistance and draws 1,500 ÷ 120 = 12.5 amps.

Does Ohm's law work for AC?

For resistive loads such as heaters and incandescent lamps, yes. Motors, transformers and electronics have a power factor below 1, so watts are less than volts × amps — use the watts to amps calculator with the power factor for them.

How do I work with milliamps and kilohms?

Convert to amps and ohms first: 1 mA = 0.001 A and 1 kΩ = 1,000 Ω. A 5 V supply across a 220 Ω resistor drives 5 ÷ 220 = 0.0227 A, or 22.7 mA — a common sum for sizing an LED resistor.

What size resistor power rating do I need?

Work out the power it will dissipate, P = V² ÷ R, and pick a rating comfortably above it. A 100 ohm resistor across 12 volts passes 120 milliamps and dissipates 1.44 watts, so a ¼ watt part would overheat and a 2 watt part is the safer choice.

Why doesn't an LED or a diode follow Ohm's law?

Because their resistance is not constant: the current rises very steeply once the voltage passes a threshold. Ohm's law is useful around them, though, for the resistor in series: the resistor's voltage is the supply voltage minus the LED's forward voltage, and V = I × R then gives the current. The LED resistor calculator does this.

What happens to a heater's power if the voltage drops?

The resistance stays about the same, so power falls with the square of the voltage. The 28.8 ohm heater in the example below, which uses 2,000 watts at 240 volts, would use 500 watts at 120 volts: half the voltage, a quarter of the power.

The formulas and what you can find

Ohm's law is V = I × R, with V in volts, I in amps and R in ohms. Combined with P = V × I for power in watts it gives ten working formulas for finding one unknown from two knowns: I = V ÷ R, R = V ÷ I, P = I² × R, P = V² ÷ R, V = √(P × R), I = √(P ÷ R), R = V² ÷ P, R = P ÷ I², I = P ÷ V, and V = P ÷ I. Enter any two of the four quantities and the calculator returns the other two. The relation applies to the part of the circuit across which you measure V, with I the current through that same part.

Worked example: an electric heater

A heater labeled 2,000 W on a 240 V circuit. With power and voltage known, the current is I = P ÷ V = 2,000 ÷ 240 = 8.33 A, and the resistance is R = V ÷ I = 240 ÷ 8.33 = 28.8 Ω (the same as V² ÷ P = 57,600 ÷ 2,000 = 28.8 Ω). For a 220 ohm resistor rated ½ watt, the largest voltage it can take is V = √(P × R) = √(0.5 × 220) = 10.5 V, at which it passes 47.7 mA. A 150 ohm resistor carrying 20 mA drops V = I × R = 3 V.

Where Ohm's law stops

Resistance is not a fixed property of every part. The resistance of an object depends on temperature, and in most metals it rises as the material warms, so a lamp or heating element has a different resistance when hot than when cold. Semiconductor devices such as diodes and LEDs are not ohmic at all. For AC circuits the law holds with RMS values for resistive loads, but coils, capacitors and motors need impedance and the power factor.

Common mistakes

Unit prefixes cause most wrong answers: convert milliamps to amps and kilohms to ohms before multiplying. Another is using the power formula with the wrong pair, such as V² ÷ R with a current. A third is applying the supply voltage to one resistor in a series circuit: V = I × R refers to the voltage across that resistor only, and the voltages across the parts add up to the supply voltage. Finally, a rating label such as 2,000 W describes the device at its rated voltage, not at any voltage.

Sources: OpenStax, University Physics Volume 2, chapter 9 “Current and Resistance” (resistance as the ratio of voltage to current, temperature dependence of resistance). Related: LED resistor calculator, watts to amps calculator, series and parallel calculator, voltage divider calculator.