Ohm's Law Calculator

Ohm's law in one line, and the three that follow from it

Ohm's law says voltage equals current times resistance: V = I × R. Pair it with the power equation P = V × I and you have four quantities linked by two equations, which means any two known values pin down the other two. That is the whole trick behind this calculator. You type two numbers, it picks the algebra that fits, and it prints the formulas it used so the result is checkable rather than magic.

The units are volts (V) for electrical pressure, amps (A) for the rate of charge flow, ohms (Ω) for opposition to that flow, and watts (W) for the rate energy is converted to heat, light or motion. Keep them consistent: 20 milliamps is 0.02 A, and 4.7 kilohms is 4700 Ω. Mixing milliamps with plain amps is the single most common source of answers that are off by a factor of a thousand.

Worked example: 12 volts across a 2 amp load

Enter 12 in the voltage box and 2 in the current box. Resistance is V ÷ I = 12 ÷ 2 = 6 Ω. Power is V × I = 12 × 2 = 24 W. Now check the same circuit from another direction: if you had instead entered 12 V and 6 Ω, the tool returns I = V ÷ R = 2 A and P = V² ÷ R = 144 ÷ 6 = 24 W. Enter 24 W and 6 Ω and you get V = √(P × R) = √144 = 12 V and I = √(P ÷ R) = √4 = 2 A. Every route lands on the same circuit, which is a useful sanity check whenever a result looks surprising.

The formula wheel, unrolled

Printed versions of this table are usually drawn as a wheel with V, I, R and P in the middle and three formulas in each quadrant. The wheel is a memory aid, not extra physics — every entry is one of those two equations rearranged.

Practical example: a series resistor for an LED

An LED is not a resistor, so you never apply Ohm's law to the LED itself. You apply it to the resistor in series with it. Say you want a red LED with a 2 V forward drop running at 20 mA from a 5 V supply. The resistor has to absorb 5 − 2 = 3 V at 0.02 A. Enter 3 volts and 0.02 amps: R = 150 Ω and P = 0.06 W. The nearest standard values are 150 Ω or, to be safe, 180 Ω, and a common quarter-watt resistor dissipates 0.06 W without warming up. Do the same sum for a blue LED with a 3.2 V drop and the resistor becomes (5 − 3.2) ÷ 0.02 = 90 Ω.

Practical example: will that appliance trip the breaker?

A 1500 W space heater on a US 120 V circuit draws I = P ÷ V = 1500 ÷ 120 = 12.5 A. On a 15 A branch circuit the rule of thumb is to stay under 80 percent continuous load, which is 12 A — so that heater alone is already at the limit and nothing else should share the circuit. Run the same heater on a UK 230 V supply and it draws only 6.5 A, which is why the same wattage feels less demanding on 230 V wiring. Enter 1500 watts with 120 volts, then with 230 volts, and compare.

Where the simple law stops working

Ohm's law describes ohmic materials, where resistance stays constant as voltage changes. Plenty of real components are not ohmic. Diodes and LEDs have an exponential curve, incandescent filaments increase resistance sharply when hot (a 60 W bulb measures a fraction of its running resistance when cold), thermistors are designed to change with temperature, and semiconductors do their own thing entirely. For these, a single resistance value only describes one operating point.

Alternating current adds a second caveat. With a purely resistive AC load — a kettle, a toaster, a filament lamp — you can use RMS volts and amps in these formulas directly. Add motors, transformers or switch-mode supplies and current no longer stays in step with voltage. Resistance becomes impedance (Z), apparent power in volt-amps is no longer the same as real power in watts, and the ratio between them is the power factor. In that case V = I × Z still holds in magnitude, but P = V × I × PF is what your electricity meter records.

Finally, a safety note. Calculations are a design tool, not a substitute for competence around mains electricity. Working circuits at 120 V or 230 V can kill, and conductor sizing, breaker ratings and insulation are governed by wiring regulations rather than by arithmetic alone. Use this calculator freely for low-voltage electronics, battery projects, car wiring and homework, and hand mains work to a qualified electrician.