The four quantities, two equations
V = I × R P = V × I
From these two, every pairing follows — the twelve formulas of the classic "Ohm's law wheel":
| Known | V = | I = | R = | P = |
|---|---|---|---|---|
| V, I | — | — | V/I | V·I |
| V, R | — | V/R | — | V²/R |
| V, P | — | P/V | V²/P | — |
| I, R | I·R | — | — | I²·R |
| I, P | P/I | — | P/I² | — |
| R, P | √(P·R) | √(P/R) | — | — |
Worked example — the instrumentation classic
A 4–20 mA signal passes through a 250 Ω input resistor. At full scale (I = 0.020 A, R = 250 Ω):
- V = 0.020 × 250 = 5.0 V (and 4 mA gives 1.0 V — the origin of the 1–5 V signal standard)
- P = I²R = 0.0004 × 250 = 0.1 W — why a ¼-watt resistor suffices
Field notes
- Watch your units: the calculator works in base units — amps, not mA. 20 mA is 0.02 A. (A wrong-by-1000 answer almost always means a mA/A slip.)
- Power ratings need margin: standard practice is to size resistors at ≥ 2× the calculated dissipation.
- Ohm's law applies to DC and resistive AC. For AC circuits with inductance or capacitance, R becomes impedance Z and power splits into real and reactive parts — see our three-phase power calculator.
Frequently asked questions
What is Ohm's law?
V = I × R: the voltage across a resistance equals the current through it times the resistance. Combined with P = V × I it links all four basic electrical quantities.
How do I calculate power from voltage and resistance?
P = V² ÷ R. For example, a 250 Ω loop resistor with 5 V across it dissipates 25 ÷ 250 = 0.1 W.
How much voltage does 20 mA drop across 250 ohms?
V = 0.020 × 250 = 5.0 V — which is exactly why a 4-20 mA signal across a 250 Ω resistor becomes the familiar 1-5 V input signal.
Provided for reference and education. Verify independently before use in safety-critical work. See our disclaimer.