Ohm's Law Calculator

What links U, I, R and P

Ohm's law expresses a simple fact: in a conductor or a resistor, the current that flows is proportional to the voltage applied. U (also written V) is the voltage in volts, measured between two points of the circuit — the potential difference that pushes the charges. I is the current in amperes, the amount of charge passing each second. R is the resistance in ohms (Ω), the opposition to the flow of this current.

The same relationship can be written in three ways depending on the unknown: U = R × I for the voltage, I = U / R for the current, R = U / I for the resistance. The power P, in watts, is the energy converted into heat each second: P = U × I, and also P = R × I² or P = U² / R depending on which quantities you have available. It is this power that determines the size of the component, not the value in ohms.

A point that is often overlooked: Ohm's law describes linear elements (resistors, wires, coils in DC). An LED, a diode or a transistor do not obey it directly; instead you start from their threshold voltage, then apply Ohm's law to the resistor placed in series. To step down a voltage with two resistors, the voltage divider calculator is more suitable.

Worked example: a red LED on 12 V

Suppose you want to light a 5 mm red LED from a 12 V battery. This LED drops about 2 V at its rated current of 20 mA; the series resistor must absorb all the rest.

1. Voltage across the resistor: U = 12 − 2 = 10 V.
2. Target current, converted to amperes: I = 20 mA = 0.020 A.
3. Resistance: R = U / I = 10 / 0.020 = 500 Ω.
4. Power dissipated: P = U × I = 10 × 0.020 = 0.2 W.

500 Ω does not exist in the standard E12 series. You would pick 470 Ω (yellow-violet-brown): the current becomes 10 / 470 = 21.3 mA, perfectly acceptable. With 560 Ω you get 17.9 mA and a slightly dimmer LED. As for the package, 0.2 W in a 1/4 W (0.25 W) resistor makes it work at 80 % of its limit and it will get warm: a 1/2 W model stays cool. For the build you therefore need a 470 Ω 1/2 W resistor, the LED, and a multimeter to verify the 21 mA in series in the branch. The color code calculator helps identify the bands before soldering.

Common mistakes and pitfalls

The number one source of absurd results is units. Writing R = 10 / 20 instead of 10 / 0.020 gives 0.5 Ω instead of 500 Ω, a factor of 1000 off. Remember: 1 kΩ = 1,000 Ω, 1 MΩ = 1,000,000 Ω, 1 mA = 0.001 A. The calculator above handles the prefixes, but on paper you need to convert everything to V, A and Ω.

• Power overlooked. A 10 Ω resistor under 12 V lets through I = 1.2 A and dissipates P = 14.4 W. No ordinary axial package can handle that: you need a wire-wound or metal-cased power resistor, chosen with a margin of at least double the calculated power.
• Tolerance. A 470 Ω ±5 % resistor can measure anywhere between 446 and 494 Ω; for an LED this makes no difference, but for a current-sense shunt you need ±1 %.
• In-circuit measurement. An ohmmeter only gives an accurate reading out of circuit and with power off, otherwise neighboring components distort the reading.
• AC. On 220 V AC, U and I are RMS values; as soon as there is a capacitor or an inductor, the resistance becomes an impedance and the real power is no longer simply U × I.