The four quantities, and the two equations that connect them
Ohm's law relates voltage, current and resistance. The power equation adds watts and links the other three to energy. Together they let you solve any circuit where two of the four values are known.
The power equation has three equivalent forms and choosing the right one saves a step. If you know volts and amps, use V × I. If you know amps and ohms, use I² × R. If you know volts and ohms, use V² ÷ R. All three give the same answer; pick the one that avoids working out an intermediate value you do not need.
A mnemonic that actually helps
Cover the quantity you want and read what remains. For Ohm's law, write V over I R — cover V and you see I × R; cover I and you see V over R; cover R and you see V over I. For power, write P over V I, which gives P = V × I, V = P ÷ I and I = P ÷ V.
The most useful practical consequence is this: power rises with the square of current. Double the current through a fixed resistance and you quadruple the heat. This is why a slightly undersized conductor or a marginally rated connector fails so much faster than the current increase would suggest.
Three worked examples
1. Choosing a resistor for an LED
A red LED with a forward voltage of 2.0 V is to run at 20 mA from a 5 V supply. The resistor must drop 5.0 − 2.0 = 3.0 V at 20 mA, so R = 3.0 ÷ 0.02 = 150 ohms. Power dissipated is 3.0 × 0.02 = 0.06 W, so a standard quarter-watt resistor is more than adequate. A 150 ohm resistor is a standard E24 value, which means it is stocked everywhere.
2. Working out the current in a heating element
A 1500 W space heater on 120 V draws 1500 ÷ 120 = 12.5 A, and its resistance is 120 ÷ 12.5 = 9.6 ohms. That current is why a 1500 W heater belongs on a 15 A circuit at most, and why running two of them on one 20 A circuit trips the breaker.
3. Checking a shunt
A 0.01 ohm shunt carries 30 A. The voltage across it is 30 × 0.01 = 0.3 V, and the power dissipated is 30² × 0.01 = 9 W. The power figure is the one that matters here: a shunt rated for 5 W would overheat and drift, so the rating must exceed 9 W with margin.
Why the resistor wattage matters as much as the resistance
Two resistors with identical resistance can have very different power ratings — commonly available in 1/8, 1/4, 1/2, 1 and 2 watt sizes, with wirewound types well above that. The calculation tells you the dissipation; the rating tells you whether the part survives it.
The usual practice is to derate: choose a resistor rated for at least twice the calculated dissipation. That keeps the body temperature in a range where the value stays stable and the component does not discolour or lift off the board. A resistor run at its rated power is hot enough to burn a finger and its resistance will drift upward as it ages.
Also check the working voltage. Even a high-wattage resistor has a maximum voltage rating, and in high-voltage circuits that limit is frequently reached before the power limit is.
The two things this calculator cannot do for you
- It cannot pick a standard value. Calculated resistances rarely match a stocked part. E24 covers 24 values per decade and E96 covers 96. The resistor colour code calculator on this site tells you the nearest standard value and how far off it is.
- It assumes the resistance is constant. Real resistors change with temperature, and many loads — lamps, motors, diodes, anything with a semiconductor junction — are strongly non-linear. A cold incandescent filament has roughly one fifteenth the resistance it has at operating temperature, which is why inrush current on a lamp is far higher than its running current.
How this calculator is verified
The relationships implemented here are the standard Ohm's law and Joule's law identities. The arithmetic is exact; what varies is the real-world behaviour of the component you choose, which is why the notes above concentrate on ratings and non-linearity rather than on the formulas.
- NIST — definitions of the SI electrical units, including the ampere, volt and ohm.
- IEEE standards — component and measurement standards referenced by electronics practice.
- IEC — the E-series preferred number system (IEC 60063) used for standard resistor values.
Formulas and worked examples last verified: 19 September 2026.