Ohm's law calculator

Ohm's law is the one equation the whole trade stands on. Voltage equals current times resistance:

V = I × R

Bolt on the power equation, P = V × I, and between the two of them you can find any of the four values, volts, amps, ohms or watts, from any two you already know. Shuffle the algebra around and you get 12 rearrangements. Here's every one, so you never have to derive it on the back of a chocolate wrapper again:

If you learned this as the Ohm's law wheel, the circle with P, V, I and R in the middle and all 12 formulas round the rim, this table is the same thing flattened out into rows you can actually scan. Same twelve formulas, same maths, less squinting at a pie chart.

The Ohm's law triangle

If you only remember one thing from college, make it the triangle. V sits on top, I and R sit side by side underneath. Cover the value you want and the triangle hands you the formula: cover V and you're left with I × R, cover I and you get V over R, cover R and you get V over I. That's it. Three formulas for the price of one memory trick, and the same trick works for the power triangle with P on top of I and V.

A worked example: the 3 kW immersion

Take the classic, a 3 kW immersion heater on a 230 V supply. Current first: I = P / V, so 3000 / 230 = 13.04 A. Now resistance: R = V² / P, so 230 × 230 / 3000 = 17.6 Ω. Two lines of arithmetic and you know the element should draw about 13 A and read roughly 17.6 ohms across its terminals. If you'd rather skip the arithmetic entirely, the watts to amps calculator and kW to amps calculator do the current conversion in one box.

What common loads should read on a resistance test

This is where Ohm's law earns real money. Every resistive load has a resistance you can predict before the probes come out: R = V² / P at 230 V. Dead test the load, compare against the prediction, and a fault announces itself. Here's the arithmetic already done for the usual suspects:

Three honest caveats. A cold element reads a touch under the calculated figure, because resistance rises with temperature. Showers often run more than one element switched in stages, so what you measure depends on which elements are in circuit. And filament lamps are the extreme case, their cold resistance is a fraction of the working figure, so don't condemn a lamp on a low ohms reading.

Sanity-check an element in four steps

1. Get the rated power off the data plate: 3 kW immersion, 8.5 kW shower, whatever it says.
2. Work out the expected resistance, R = V² / P, or just type the power and 230 V into the calculator above.
3. Safely isolate, disconnect the element, and measure across its terminals on a low-ohms or continuity range.
4. Compare. In the right ballpark, slightly under when cold, is healthy. Open circuit means the element has failed, near zero means it's shorted, and any reading to earth means it's scrap.

Where you'll actually use it on site

This isn't exam trivia. Ohm's law earns its keep every single day:

• Estimating what resistance an element or load should read before you put the meter on it, so a dead short or open circuit jumps out instantly.
• Sanity-checking test readings. If the numbers on the tester don't square with V = I × R, question the reading before you question the installation.
• Working out the current a plate rating really pulls, so you can size the circuit properly instead of guessing.

One caveat worth tattooing somewhere visible: resistance rises with temperature. A cold immersion element reads lower on your meter than its working resistance, so don't panic when the measured figure comes in under the calculated one. And remember that every R1+R2 reading and every Zs figure you've ever recorded is Ohm's law wearing a hi-vis. The loop impedance limits in BS 7671 exist purely so enough fault current flows to trip the protective device fast, which is exactly what the maximum Zs calculator checks for you.