Ohm's Law Calculator — Voltage, Current, Resistance & Power

The law

V = I × R

Voltage equals current times resistance, where V is volts, I is amps and R is ohms. Rearranged:

I = V / R          R = V / I

Georg Ohm published this in 1827 and it remains the single most useful equation in electrical work — not because it is difficult, but because almost every practical question reduces to it.

Adding power: the wheel

Power joins the set through P = V × I, and substituting Ohm's law into it gives two more forms. Which of the three you reach for depends entirely on which pair of quantities you actually have:

• P = V × I — you have voltage and current. Most measurements.
• P = I² × R — you have current and resistance. This is the one behind cable heating: double the current and the losses go up four times.
• P = V² / R — you have voltage and resistance. This is the one behind heaters: a fixed-resistance element dissipates four times as much at 230 V as at 115 V.

Ohm's law and those three make twelve rearrangements in all, which is what the power wheel on a workshop wall is a picture of:

V = I × R        P = V × I
I = V / R        P = I² × R
R = V / I        P = V² / R

I = P / V        V = P / I        V = √(P × R)
R = V² / P       R = P / I²       I = √(P / R)

The bottom block is the half people forget. Knowing resistance and power — a 47 Ω load rated 5 W — gives the voltage and current directly, without routing through a quantity you were never given. The calculator covers all twelve and names the one it used, because on a page about a relationship, a number without its formula teaches nothing.

Worked examples

A 12 V circuit drawing 2 A.

R = V / I = 12 / 2 = 6 Ω
P = V × I = 12 × 2 = 24 W

A 230 V heater element measuring 35 Ω cold.

I = V / R = 230 / 35 = 6.6 A
P = V² / R = 52,900 / 35 = 1511 W

So roughly a 1.5 kW heater drawing 6.6 A. Note cold — that resistance will not stay at 35 Ω, for the reason in the temperature section below.

Volt drop in a cable run. A 50 m run of 2.5 mm² copper has a resistance of about 0.74 Ω there and back. At 16 A:

V = I × R = 16 × 0.74 = 11.8 V

That is 5.1 % of 230 V — over the limit for a power circuit, so the cable needs to be larger. The voltage drop calculator does this properly, with the manufacturer's mV/A/m figures rather than a nominal resistance.

And the power lost in that cable.

P = I² × R = 256 × 0.74 = 189 W

A hundred and eighty-nine watts of heat in the wall, continuously, doing nothing. Over a year at eight hours a day that is 552 kWh — worth more than the larger cable would have cost.

Series and parallel

Ohm's law applies to any part of a circuit, but you have to give it the right resistance to apply to.

Series — resistances add, current is common:

R_total = R₁ + R₂ + R₃ …

Parallel — conductances add, voltage is common:

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ …

two only:  R_total = (R₁ × R₂) / (R₁ + R₂)

Two sanity checks worth memorising: resistances in series always total more than the largest one, and resistances in parallel always total less than the smallest. If an answer breaks either rule, the arithmetic is wrong.

The commonest series case is a voltage divider, where two resistors split a supply in proportion to their resistances — and where the parallel shortcut above is exactly what a connected load does to the lower resistor.

Where Ohm's law stops applying

It holds for linear, resistive components at constant temperature. Three common situations break that:

• Temperature. Copper's resistance rises about 0.4 % per °C, so a motor winding at 100 °C has roughly 30 % more resistance than at rest. A filament lamp is the extreme: cold resistance can be a tenth of hot, which is why filament lamps draw a large inrush and why they nearly always fail at switch-on.
• Non-linear devices. Diodes, transistors, LEDs and varistors have no fixed resistance — current does not follow voltage proportionally. An LED does not have “a resistance” you can put in the formula; it has a forward voltage, and you set the current with a series resistor sized from whatever is left over.
• AC with reactance. With inductance or capacitance in circuit, the opposition to current is impedance, not resistance, and voltage and current fall out of step. Ohm's law generalises to V = I × Z, but power stops being V × I and becomes V × I × cos φ — the difference being the power factor. That is why every AC conversion on this site carries a power factor term; see the kW, kVA and kVAr converter.

What it is actually used for on a job

• Fault finding. A circuit drawing far more current than V / R predicts has a short somewhere; far less means an open or a bad connection. A loose terminal is a small resistance in series, and P = I² × R tells you exactly why it gets hot enough to char an enclosure.
• Earth loop impedance. The fault current available at a point is the supply voltage divided by the loop impedance — Ohm's law again. It decides whether a protective device disconnects in the required time, and it underpins earthing conductor sizing.
• Checking an element. Measure resistance, apply P = V² / R, compare with the nameplate. A large discrepancy means a partially failed element.
• Measuring current indirectly. A known low resistance in circuit — a shunt — turns a current measurement into a voltage measurement.

Four ways people get it wrong

• Mixing units. Milliamps with volts gives milliwatts, not watts. Kilohms with volts gives milliamps. Keep everything in base units, or be deliberate about the conversion.
• Using cold resistance for a hot component. Motor windings, filament lamps and heater elements all move substantially with temperature.
• Applying it to AC without a power factor. V × I in an AC circuit gives VA, not watts.
• Forgetting the return conductor. Volt drop and I²R loss happen in both directions. A 50 m run is 100 m of conductor.

Working at scale

The same four quantities run a distribution board as run a breadboard, but the useful arrangement changes. For three-phase work, current comes from P / (√3 × V × pf × η) — Ohm's law with a power factor and an efficiency carried through it.