Ohm's Law Calculator

V = I × R, rearranged as I = V / R and R = V / I

V

The voltage across the component, in volts, with millivolts and kilovolts selectable in the same box. It is the potential difference between the two ends of the thing the current is flowing through, so it is a measurement across a component and never a measurement of the supply on its own. Leave this box empty when the voltage is the answer you are after, which is the usual case when you know the current a circuit draws and the resistor standing in its way

I

The current through the component, in amps or milliamps. The name comes from intensity, and the amp is the coulomb per second, which is why this is the quantity that pairs with time whenever you go on to energy or battery life. Milliamps matter more than amps in most electronics work, so the box offers both: a 20 mA LED current is 0.02 A, and choosing milliamps in the dropdown is how you type the number you actually read off the meter

R

The resistance, in ohms, kiloohms or megohms, and it is the main row of the result panel because resistance is the answer people come here for most often. One ohm is one volt per amp. The box accepts zero, which is a piece of wire and not an error, but it does not accept a negative value: a negative resistance is not a component, it is a circuit that supplies power, and this page has nothing to say about those

V / R

The three rearrangements are the whole content of the page, and they are worth reading as one sentence rather than three formulas: fix the voltage and the current falls as the resistance rises, fix the resistance and the current rises with the voltage, and fix the current and the voltage rises with the resistance. Two of the three quantities always determine the third, and that is why the page asks for exactly two

Use this page whenever two of the three quantities are known and the third is what you need, which covers most of the arithmetic that comes up around a circuit: sizing a series resistor for an LED when you know the supply and the current you want, working out what current a 10 kiloohm load will draw from a 5 V rail, or checking whether a resistor you have in a drawer will do. It is deliberately three quantities rather than four, so if the question mentions watts or kilowatt hours, the electrical power calculator is the page you want, and it starts from the same two boxes.

1. The defaults: 12 V and 0.02 A

   1. Voltage 12 V, current 0.02 A, resistance left empty
   2. The known pair is V and I, so the rearrangement to use is R = V / I
   3. R = 12 / 0.02 = 600 ohms
   4. The panel prints 600 in the main row, and echoes the two values you typed underneath so you can see what the answer was built from

   600 ohms is a standard value you can buy, and 20 mA is a typical LED current, so this is the calculation behind a great many small circuits: a 12 V supply, a resistor, and an indicator. Notice the direction the page went. You did not need to know the resistance to use it; you needed to know what current you wanted, and the resistance fell out. That is the shape of most real uses of Ohm's law, and it is why the field you leave empty matters more than the ones you fill.

2. 230 V across 23 ohms: how much current flows

   1. Voltage 230 V, resistance 23 ohms, current left empty
   2. The known pair is V and R, so the rearrangement to use is I = V / R
   3. I = 230 / 23 = 10 amps
   4. The panel prints 10 in the current row

   Ten amps on a 230 V supply is 2.3 kilowatts of heating, which is a kettle or a small immersion heater, and it is drawn through a 23 ohm element. That is what a resistive appliance is: a piece of wire with a known resistance, chosen so that the supply voltage drives the current the appliance needs. The arithmetic here is why mains appliances are described by their power rather than their resistance — 2.3 kW is a more useful label than 23 ohms, and the two describe the same object.

3. 0.02 A through 470 ohms: the voltage it takes

   1. Current 0.02 A, resistance 470 ohms, voltage left empty
   2. The known pair is I and R, so the rearrangement to use is V = I × R
   3. V = 0.02 × 470 = 9.4 volts
   4. The panel prints 9.4 in the voltage row

   This is the third direction and the one people reach for least, though it is the one that answers the practical question of how much of a supply a component will drop. Push 20 mA through 470 ohms and 9.4 V disappears across it, which leaves very little room if the supply is 12 V and none at all if it is 5 V. That is the calculation that tells you a resistor is too large for the rail you have, and it is the same arithmetic as the first example read backwards.

4. All three filled in, and they agree

   1. Voltage 12 V, current 0.02 A, resistance 600 ohms — all three boxes filled
   2. The page picks the first pair it can use, which here is V and I, and derives R = 12 / 0.02 = 600 ohms
   3. That agrees with the 600 ohms you typed, so the row is reported rather than rejected
   4. Change any one of the three and the same check fails instead

   Filling all three is allowed and is the fastest way to check a measurement: type what the meter said for all three and the page tells you whether they are consistent. What it does not do is average them or pick a winner. If you type 12 V, 0.02 A and 500 ohms it reports the disagreement rather than quietly deriving from two of them and ignoring the third, because the third is the one you measured and the mismatch is the information you came for. A page that silently preferred two boxes would hide exactly the broken assumption you were trying to catch.

Ohm's law holds for components whose resistance does not change with voltage or temperature, and plenty of real ones do change: a filament lamp's resistance rises as it heats, a diode's falls sharply once it conducts, and a thermistor is designed to vary. Alternating current brings in reactance, so a capacitor or an inductor has an impedance that depends on frequency and this page's arithmetic no longer applies to it. Everything here is a steady, single value at one instant, and no component is ideal.

What is the ohms law formula?

V = I × R: voltage equals current times resistance. The other two forms are the same statement solved for a different quantity, I = V / R and R = V / I, and the page shows all three in its first table because which one you need depends entirely on which two values you started with. A 12 V supply driving 0.02 A through a resistor means the resistor is 12 / 0.02 = 600 ohms. The formula is the definition of resistance as much as it is a law about electricity: one ohm is one volt per amp.

What is the ohms law triangle?

It is the mnemonic for the three rearrangements, drawn as a triangle with V on top and I and R below. Cover the quantity you want and what is left shows the arithmetic: cover V and the remaining pair sits side by side, so multiply them; cover I or R and the other two are stacked, so divide the top by the bottom. It is a way of remembering the three forms without writing them out, and it contains exactly the three expressions this page's first table lists. Nothing about the triangle is physics; it is a lookup aid for the algebra.

Which boxes do I fill in?

Any two, and leave the third empty. The empty box is the one the page solves for, so the tool is answering the question you came with rather than checking your arithmetic. Fill in voltage and current to get resistance, voltage and resistance to get current, or current and resistance to get voltage. If you fill all three the page checks them against each other instead, and reports a mismatch rather than picking two of them to believe, which makes it usable as a consistency check on a set of meter readings.

How do I work out watts from this?

That is a fourth quantity and this page deliberately leaves it out, because electrical power has its own page and adding it here would duplicate it. The bridge is P = V × I: take the voltage and current you have just found and multiply them. Ten amps on 230 V is 2.3 kilowatts. The electrical power calculator does that multiplication from the same two boxes and goes on to energy and running cost; on the mechanical side, the horsepower calculator reaches power through P = W / t instead, dividing work by time.

Does it work for AC?

Only where the load is purely resistive, such as a heater or an incandescent lamp. Alternating current through a capacitor or an inductor produces a phase shift between voltage and current, and the ratio of the two is then an impedance rather than a resistance: it depends on the frequency as well as on the component. The arithmetic on this page would give a number and the number would be wrong. For that case the impedance of an RLC circuit is the right page, and for the size of the voltage itself the RMS voltage calculator is the one to use.

Why does it refuse a negative resistance?

Because no component has one. Zero is accepted, since a zero ohm resistor is a piece of wire and the arithmetic handles it perfectly well, but a negative value is not a component you can hold: a circuit with a negative resistance is one that supplies power rather than dissipating it, which in practice means an amplifier or a power source, and describing it with this formula would be a category error. The page rejects the value rather than returning a negative answer that looks like a result.

• Ohm's Law: Resistance and Simple Circuits (College Physics 2e, §20.2) — the definition of resistance as voltage divided by current, the three rearrangements, and the statement that the law applies only to components whose resistance is constant — OpenStax
• Ohm's law — the history of the 1827 statement, the triangle mnemonic, and the distinction between ohmic and non-ohmic conductors — Wikipedia
• NIST Guide for the Use of the International System of Units (SI), Appendix B.8 — Factors for Units Listed Alphabetically: the ampere and ohm definitions the base units of this page rest on — NIST