Ohm's Law and Electrical Power, Explained
The Ohm's law formula V = I × R explained: how to calculate voltage, current, resistance and power, with worked examples, units, series and parallel circuits.
By Udit Agarwal · Updated October 18, 2026
Ohm's law states that the voltage across a resistor equals the current through it multiplied by its resistance: V = I × R. Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω), so 12 volts across a 4 Ω resistor drives 12 ÷ 4 = 3 amps. Add the power formula P = V × I, and any two of voltage, current, resistance and power give you the other two. That 12 V, 4 Ω circuit turns 36 watts into heat.
Georg Simon Ohm published the relationship in 1827. Voltage is the electrical pressure that pushes charge around a circuit, current is the rate at which charge flows (the symbol I comes from the French intensité du courant), and resistance is how strongly a component opposes the flow. One volt drives one amp through one ohm.
Rearranging V = I × R gives three forms:
| To find | Formula | Example |
|---|---|---|
| Voltage | V = I × R | 0.5 A through 24 Ω: 0.5 × 24 = 12 V |
| Current | I = V ÷ R | 12 V across 4 Ω: 12 ÷ 4 = 3 A |
| Resistance | R = V ÷ I | 9 V driving 0.03 A: 9 ÷ 0.03 = 300 Ω |
In the Ohm's law triangle, a common memory aid, V sits on top of I and R. Cover the quantity you want: side by side means multiply, and one above the other means divide.
Power, in watts (W), is the rate at which a component uses energy, and it equals voltage times current: P = V × I, often taught as Watt's law. Substituting Ohm's law gives two more forms, P = I² × R and P = V² ÷ R. Rearranged, they make the twelve formulas of the Ohm's law wheel:
| Quantity | Formulas |
|---|---|
| Voltage (V) | I × R, P ÷ I, √(P × R) |
| Current (I) | V ÷ R, P ÷ V, √(P ÷ R) |
| Resistance (R) | V ÷ I, V² ÷ P, P ÷ I² |
| Power (P) | V × I, I² × R, V² ÷ R |
A 2,000 W heater on 230 V draws 2,000 ÷ 230 = 8.7 A, and its element has a working resistance of 230² ÷ 2,000 = 26.45 Ω. A 1,500 W space heater on 120 V draws 12.5 A, most of what a standard 15 A household circuit can carry, so two of them on one circuit trip the breaker.
Energy is power multiplied by time: running that heater for 3 hours uses 2 kW × 3 h = 6 kWh. The Electricity Cost Calculator turns wattage and hours of use into a running cost.
The formulas only work in base units: volts, amps, ohms and watts. Electronics values usually carry an SI prefix:
| Prefix | Symbol | Multiply by | Example |
|---|---|---|---|
| micro | µ | 0.000001 | 50 µA = 0.00005 A |
| milli | m | 0.001 | 20 mA = 0.02 A |
| kilo | k | 1,000 | 4.7 kΩ = 4,700 Ω |
| mega | M | 1,000,000 | 1 MΩ = 1,000,000 Ω |
On schematics the prefix often replaces the decimal point: 4k7 is 4.7 kΩ and 2R2 is 2.2 Ω. The classic slip is entering 20 for 20 mA, which puts the answer out by a factor of 1,000. Volts, milliamps, kilohms and milliwatts also form a consistent set, so 9 V across 4.7 kΩ draws 9 ÷ 4.7 = 1.91 mA and dissipates 9 × 1.91 = 17.2 mW.
An LED needs a series resistor to limit its current. The resistor takes whatever voltage the LED does not, so R = (supply voltage − LED forward voltage) ÷ LED current.
A red LED typically has a forward voltage of about 2 V, and 20 mA is a common rating for a standard 5 mm LED; check the datasheet for yours. On a 5 V supply the resistor sees 5 − 2 = 3 V, so R = 3 ÷ 0.02 = 150 Ω. It dissipates 0.02² × 150 = 0.06 W, well within a common 0.25 W resistor. A 150 Ω resistor is marked brown, green, brown, which the Resistor Color Code Calculator decodes.
When the result falls between standard values, round up, which lowers the current slightly. A white LED of about 3.2 V on a 9 V battery needs (9 − 3.2) ÷ 0.02 = 290 Ω. The next value up in the common E12 series is 330 Ω, which gives 5.8 ÷ 330 = 17.6 mA.
In series, the same current flows through each resistor and the resistances add, so 100 Ω and 220 Ω make 320 Ω. On 9 V the current is 9 ÷ 320 = 28.1 mA, and the voltage splits in proportion to resistance: 2.81 V across the 100 Ω resistor and 6.19 V across the 220 Ω one. That split is how a voltage divider works.
In parallel, each resistor gets the same voltage and the current divides. The total is 1 ÷ (1/R1 + 1/R2 + …), which for two resistors is (R1 × R2) ÷ (R1 + R2), so the same pair makes 22,000 ÷ 320 = 68.75 Ω. A parallel total is always smaller than the smallest resistor, and two equal resistors give half the value of one.
Wires have resistance too. A cable run of 0.1 Ω carrying 10 A loses 10 × 0.1 = 1 V, under half a percent of 230 V but 8.3% of 12 V. The Voltage Drop Calculator works this out from the wire gauge, length and current, and the Wire Gauge Converter lists the resistance of each gauge.
Ohm's law holds for ohmic components, such as metal wires and resistors at a steady temperature, whose resistance does not change with voltage. Many parts behave differently:
For mains AC, use RMS values: the 230 V or 120 V on a label is RMS, and the peak is √2 times higher, about 325 V or 170 V. The formulas then hold for resistive loads such as heaters and kettles. For motors and many electronic power supplies, V × I gives apparent power in volt-amperes, and real power in watts is that figure times the power factor, a number between 0 and 1.
Current through the body does the harm, and Ohm's law shows how voltage drives it. OSHA's safety training uses about 100,000 Ω for dry skin and 1,000 Ω for wet skin. At 120 V that is about 1 mA through dry skin, barely perceptible, but 120 mA through wet skin, enough to cause ventricular fibrillation. Protective devices act at this scale: under the IEC 60364 wiring standard, an RCD for personal protection is rated at no more than 30 mA, and a US Class A GFCI trips at 4 to 6 mA under UL 943.
Under IEC 61140, extra-low voltage means at most 50 V AC or 120 V ripple-free DC. Batteries, USB and most hobby electronics sit well below that, and household mains sits far above it. Switch a circuit off at the breaker and prove it dead with a tester before touching mains wiring, and leave fixed wiring to a qualified electrician where local rules require one. Check any calculated value with a multimeter, since real components have tolerances and drift with temperature.
The Ohm's Law Calculator has four fields: Voltage (V), Current (A), Resistance (Ω) and Power (W). Fill in any two and leave the others empty. It solves the missing pair as you type, labels them "(computed)" and lists all four values, with a button that copies the set. For the LED above, enter 3 in Voltage and 0.02 in Current to get 150 Ω and 0.06 W.
It assumes ideal, purely resistive parts, so it suits resistors, heaters and wires but not an LED. Everything is calculated in your browser, and nothing you type is uploaded.
What is Ohm's law in simple terms? The current through a resistor is proportional to the voltage across it: more voltage means more current, and more resistance means less. As a formula it is V = I × R, with V in volts, I in amps and R in ohms.
How do you calculate resistance from voltage and current? Divide the voltage by the current: R = V ÷ I. A part drawing 0.03 A from 9 V has a resistance of 9 ÷ 0.03 = 300 Ω. Convert milliamps to amps first, or the answer comes out a thousand times too small.
How do you convert watts to amps? Divide the power by the voltage: I = P ÷ V. A 60 W load on 12 V draws 5 A. Motors and electronics draw more than P ÷ V because of their power factor.
Does Ohm's law work for AC? Yes, for resistive loads, using RMS voltage and current, which is what mains ratings quote. Circuits with capacitors or inductors use impedance in place of resistance.
Why doesn't Ohm's law work for an LED? An LED is a diode, and once the voltage passes its forward voltage the current rises steeply instead of in proportion. Apply Ohm's law to the series resistor instead: R = (supply voltage − forward voltage) ÷ current.
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