Maps for Math

The Ohm’s law wheel: every way to connect V, I, R, and P

Voltage, current, resistance, and power are tied together by two laws: V = IR and P = VI. Rearranging them gives twelve formulas, arranged here as a wheel. Whichever two quantities you know, one formula on the wheel gives each of the other two, which is why electricians and hobbyists keep this chart handy.

V5 VV = I·RV = P/IV = √(P·R)I22.7 mAI = V/Rstep 1I = P/VI = √(P/R)R220 ΩR = V/IR = V²/PR = P/I²P114 mWP = V·Istep 2P = I²·RP = V²/R
= 22.7 mA · from I = V / R
= 114 mW · from P = V × I

Point at or tab to a formula to see what it uses and where it comes from.

Show the work

  1. Step 1: CurrentI = \frac{V}{R} = \frac{(5\,\mathrm{V})}{(220\,\Omega)} = 0.02273\,\mathrm{A}
  2. Step 2: PowerP = VI = (5\,\mathrm{V})\cdot(0.02273\,\mathrm{A}) = 0.1136\,\mathrm{W}

How the formulas connect

Every formula on the wheel comes from just two facts. Ohm’s law, V=IRV = IR, says the push (voltage) equals the flow (current) times how hard the part resists. Power, P=VIP = VI, says the energy used each second is push times flow. Substitute one into the other and you get the rest: P=I2RP = I^2R and P=V2/RP = V^2/R, and each of those rearranged for every letter.

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See it in action

Questions people ask

What is the Ohm’s law wheel?

A chart of the 12 formulas that connect voltage (V), current (I), resistance (R), and power (P). Each quarter of the wheel holds the three ways to calculate one of them.

How many values do I need to know?

Any two. From any pair, the other two can be calculated.

What if I enter three values that don’t agree?

The solver checks them. If, say, V, I, and R don’t satisfy V = IR, it shows #CONFLICT! and explains which value is off. Release one value and it will be calculated instead.

Family FAM-001 · rev 1 · 12 formulas · updated 2026-09-25