Ohm's Law Chart with Wheel and Calculator

How to use the wheel and the triangle

• Decide which quantity you need, then look in its quadrant on the wheel. It lists three formulas. Choose the one that uses the two values you already know.
• The V-I-R triangle is the short version for the first law: put V on top and I and R side by side underneath. Cover the one you want. Side by side means multiply (V = I × R), top over bottom means divide (I = V ÷ R, R = V ÷ I). The P-I-V triangle works the same way for power.
• The calculator above does this for you: type any two values with their prefixes and it returns the other two and highlights the formulas it used on the wheel.

Worked example 1: a 12 V lamp

A 12 V battery is connected to a 6 Ω lamp. The current is I = V ÷ R = 12 ÷ 6 = 2 A. The power is P = V × I = 12 × 2 = 24 W. Check with the other power forms: I² × R = 2² × 6 = 24 W and V² ÷ R = 12² ÷ 6 = 24 W. Three formulas, one answer, which is a quick way to catch an arithmetic slip.

Worked example 2: a resistor for an LED

A 5 V supply drives an LED that drops 2 V and should carry 20 mA. The resistor sees the remaining 3 V, so R = V ÷ I = 3 V ÷ 20 mA = 150 Ω. It dissipates P = V × I = 3 V × 20 mA = 60 mW, so a small quarter-watt resistor is plenty. Ohm's law is applied to the resistor only: an LED is a non-linear part, so its voltage drop stays near its forward voltage instead of rising in proportion to current.

Worked example 3: a 1500 W heater

A heater is rated 1500 W at 120 V. Its current is I = P ÷ V = 1500 ÷ 120 = 12.5 A, and its resistance when hot is R = V² ÷ P = 14 400 ÷ 1500 = 9.6 Ω. Many regions limit a continuous load to 80 percent of the breaker rating, which is 12 A on a 15 A breaker, so 12.5 A is over that limit. Check your local electrical code and have a qualified electrician size the circuit. Prefixes matter too: a 10 kΩ pull-up resistor at 5 V passes only 500 µA, or 2.5 mW of power.

Where Ohm’s law applies and where it does not

The formulas on this page are for DC circuits and ideal resistors, and also for AC through a pure resistance when V and I are RMS values. With coils and capacitors the opposition to AC current is the impedance Z, and power also depends on the phase angle through the power factor, so P = V × I × cos φ. Non-linear parts such as diodes, LEDs and transistors do not have a constant resistance, and a cold lamp filament has far lower resistance than a hot one, so V = I × R with one fixed R does not describe them. Use the formulas for the resistors in the circuit and treat other parts with their datasheets.

Units and prefixes

Real circuits use small and large values: millivolts, milliamps, kilo-ohms, megohms and kilowatts. Convert to base units (volts, amperes, ohms, watts) before using the formulas, or pick the prefixes in the calculator and let it convert. Quick reference: 1 mA = 0.001 A, 1 µA = 0.000001 A, 1 kΩ = 1000 Ω and 1 MΩ = 1 000 000 Ω. A useful shortcut: kΩ with mA gives volts, and kΩ with V gives mA. When working on mains wiring, never measure live circuits yourself: leave it to a qualified electrician.