Ohm's Law Calculator

What Is Ohm's Law?

Ohm's law is a statement about materials rather than about circuits. For a conductor held at a fixed temperature, the current flowing through it is directly proportional to the voltage across it, and the constant that links the two is what we call resistance. Every electronics textbook writes it the same way: V = I × R.

The consequence is that the three quantities are not independent. Fix any two and the third is decided for you, which is why one equation with three rearrangements covers most of the arithmetic in low-voltage work — sizing a series resistor, checking whether a cable can carry a load, working out why a 12 V accessory does nothing on a 5 V supply.

Volts, Amps and Ohms: What Each One Measures

• Voltage is a difference in electrical potential between two points — the push. It is always measured across something, which is why a voltmeter goes in parallel with the component you care about.
• Current is the rate at which charge moves past a point. It is measured through something, so an ammeter goes in series and the circuit has to be opened to insert it.
• Resistance is how strongly a conductor opposes that flow. It is not a free-floating number: for a uniform wire it works out to resistivity times length divided by cross-sectional area, so the same material resists more as a longer wire and less as a thicker one.

The plumbing analogy — pressure, flow rate, and the narrowness of the pipe — survives contact with the details better than most teaching analogies. It starts to fail in AC, where the water would have to slosh back and forth fifty or sixty times a second, and where a pipe can oppose the sloshing without opposing steady flow at all.

Resistance is nothing more than the ratio of volts to amps, so the same proportional reasoning behind it drives the Ratio Calculator.

The Four Units and How They Are Defined

The SI definitions are unusually revealing here, because two of them contain Ohm's law outright.

Look at the resistance row again. The ohm is defined as one volt per ampere, so R = V ÷ I is not a discovery about circuits — it is the definition of the unit, and it would be true of any material whatsoever at any single operating point. What Ohm actually discovered is the part the definition does not give you: that for a metal wire the ratio stays the same as you change the voltage.

Why It Is Called a Law but Is Not One

OpenStax's University Physics is blunt about the status of the thing: many materials do not show the relationship, "so despite being called Ohm's law, it is not considered a law of nature, like Newton's laws or the laws of thermodynamics." It is an experimental observation that happens to hold across a large and extremely useful class of materials.

Georg Simon Ohm (1787–1854) demonstrated the proportionality by measuring the voltage across and current through circuits built from various lengths of wire, publishing the result in 1827. Anything that behaves the way those wires behaved is called ohmic; anything that does not is nonohmic. Which of the two you are holding decides whether the number this page gives you describes your circuit or merely describes one instant of it.

How Do You Calculate Ohm's Law?

Three of the four quantities on the wheel are in this calculator: voltage, current and resistance. Give it any two and it performs the division or the multiplication, then reports the power as well.

The Ohm's Law Formula and Its Rearrangements

One equation solved three ways. Which form gets used depends entirely on which box you left at 0.

V = I × R      volts = amps × ohms
I = V ÷ R      amps  = volts ÷ ohms
R = V ÷ I      ohms  = volts ÷ amps

P = V × I      watts = volts × amps

Power is not a fourth rearrangement of Ohm's law. It is a separate relationship, P = I × V, that happens to be built from the same quantities. Substitute V = IR into it and you get the two forms printed on datasheets — P = I²R and P = V² ÷ R — which are the reason a resistor's wattage matters as much as its resistance. This calculator always reports the plain form, P = V × I, using the pair it holds once the missing value has been found.

Step by Step

The page opens with a result already showing, because voltage and current arrive pre-filled and the calculator runs once on load when every box has something in it. After that it recalculates only when you press Calculate — nothing updates as you type.

• Identify which two of the three you know. A printed label, a datasheet figure or a meter reading all count.
• Convert them to plain volts, amps and ohms. There is no unit selector and no prefix parsing: 20 mA is 0.02, and 4.7 kΩ is 4700.
• Type those two values, and put 0 in the box for the quantity you want back.
• Press Calculate.
• Read the hero line for all three values, the line under it for the rearrangement used, and the power line for the watts.

Only the resistance box tolerates being left empty; a blank there is read as zero, exactly the same as typing one. Voltage and current are required fields, and clearing either stops the calculation before the formula runs, with the panel naming the box it is waiting for.

Worked Example: Resistance From 12 V and 2 A

This is the example the page loads with — voltage 12, current 2, resistance 0.

Panel output

V 12 V · I 2 A · R 6 Ω

Under the hero line the panel prints "Solved: R = V ÷ I = 12 ÷ 2" and "Power: P = V × I = 24 W". Twelve volts across six ohms is twenty-four watts of heat, which is worth pausing on: a resistor asked to do that job would have to be a chassis-mount wirewound part, not the quarter-watt film resistor that comes in a hobby kit.

Worked Example: Current Through a 470 Ω Resistor

Leave the current box at 0 and enter 12 and 470.

Panel output

V 12 V · I 0.026 A · R 470 Ω

The rearrangement line reads "Solved: I = V ÷ R = 12 ÷ 470" and the power line reads "Power: P = V × I = 0.306 W".

Multiply the two displayed figures together and you get 0.312 W, not the 0.306 W on the screen. Both are correct: 12 ÷ 470 is 0.025532 A, and the power is calculated from that unrounded value before anything is rounded for display. Whenever a current has been squeezed into three decimal places, expect the power line to sit slightly away from what you can reproduce by hand from the printed numbers.

Worked Example: Voltage From Current and Resistance

Set the voltage box to 0, then enter a current of 0.5 and a resistance of 24.

Panel output

V 12 V · I 0.5 A · R 24 Ω

This time the lines read "Solved: V = I × R = 0.5 × 24" and "Power: P = V × I = 6 W". It is the direction you use when you know what a component is and how hard you are driving it, and you want the voltage that will appear across it — the voltage-drop calculation, under another name.

What Happens When You Double the Voltage

Hold the resistance at 6 Ω and change only the supply. At 12 V the panel returns "V 12 V · I 2 A · R 6 Ω" with a power line of 24 W. At 24 V it returns "V 24 V · I 4 A · R 6 Ω" with 96 W.

Twice the voltage, twice the current, four times the power. That asymmetry is why overvoltage destroys parts so much faster than intuition suggests: current rises in step with V, but heating rises with V², because P = V² ÷ R. A component running comfortably on 12 V is not being asked for double on 24 V — it is being asked for quadruple.

Ohm's Law Chart: All Twelve Formulas

The Ohm's law wheel that hangs on workshop walls is one equation and one power relationship, rearranged for every pair of quantities you might already have. Sorted by what you know rather than by what you are solving for, the whole wheel fits in a table.

Every Formula, Sorted by What You Already Know

Six starting positions, two unknowns each, twelve formulas. The first three rows are the ones this calculator implements. The last three all begin from a wattage, and the tool does not accept watts as an input — so when a label gives you power, convert before you type: divide by the voltage for amps (P ÷ V), or divide the voltage squared by the wattage for resistance (V² ÷ P).

Current and Power at Common Supply Voltages

Five stock resistor values against three common supply rails. Every pair of figures is what this calculator returns for that combination.

Two patterns are worth reading off the grid. Along the 100 Ω row, doubling the rail from 12 V to 24 V doubles the current from 0.12 A to 0.24 A and quadruples the power from 1.44 W to 5.76 W. Down the 12 V column, moving from 100 Ω to 1,000 Ω divides both figures by ten — the current because it is inversely proportional to resistance, the power because the voltage did not move.

Power figures in this grid come from unrounded currents, so a few will not reproduce from the two printed numbers: 220 Ω on 24 V shows 2.618 W, where multiplying the displayed 0.109 A by 24 gives 2.616 W.

Ohm's Law Examples From Real Circuits

Seven circuits you could plausibly meet this week, each one run through this calculator. The "entered" column is the pair that was typed in; everything to the right of it came back from the tool.

None of those rows required knowing anything about what the device does internally, which is the appeal of the law and also its trap. Only two of them — the 600 Ω resistor and the cable run — come close to reporting a resistance that is a fixed property of a real component. Everywhere else the figure is an equivalent resistance: the ratio the device happens to present at that moment, at that temperature, doing that job.

Why the Heater Row Is Really About the Breaker

A 1,500 W heater on a 120 V supply pulls 1500 ÷ 120 = 12.5 A. Feed those two figures in and the calculator confirms it: "V 120 V · I 12.5 A · R 9.6 Ω", with a power line of "Power: P = V × I = 1500 W".

That 12.5 A is 83% of a 15 A branch circuit. US wiring practice does not allow anything like that continuously — the National Electrical Code requires a breaker feeding a continuous load to be rated at least 125% of the load, which is the same thing as never loading a breaker past 80% of its rating, or 12 A on a 15 A circuit. A single 1,500 W heater is already over that limit with nothing else on the outlet, and two of them would ask a 15 A breaker for 25 A.

On a 230 V supply the same heater draws 1500 ÷ 230 = 6.52 A. Type 230 and 6.52 and the panel returns 35.28 Ω with a power line of 1499.6 W; the four-tenths of a watt missing from 1,500 is the rounding inside that 6.52, not a disagreement with the law.

Sizing the Series Resistor for an LED

An LED is not a resistor, and that is precisely why it needs one. Below its forward voltage almost nothing flows; above it, the current climbs steeply for a very small further rise in voltage. Nothing about the device limits its own current, so the series resistor is what makes the branch predictable.

• Subtract the LED's forward voltage from the supply. A red indicator LED typically sits near 2 V and blue or white parts nearer 3 V, but the figure varies by color and manufacturer — read the datasheet rather than assuming.
• Choose the current. Standard indicator LEDs are rated around 20 mA, which is 0.02 in the current box.
• Enter the resistor's share of the voltage together with that current, leaving resistance at 0.

For a 2 V LED on a 12 V supply the resistor takes the remaining 10 V, so the entry is 10 and 0.02. The panel returns "V 10 V · I 0.02 A · R 500 Ω" and "Power: P = V × I = 0.2 W".

500 Ω is not an E12 value, so round up to 560 Ω — up rather than down, because rounding down raises the current through the LED. Re-enter 10 and 560 and you get "V 10 V · I 0.018 A · R 560 Ω" with 0.179 W. Both dissipations fit a quarter-watt resistor, though 0.2 W is 80% of that rating and the part will run noticeably warm.

Voltage Drop Along a Cable Run

Measure between the two ends of a live cable and you are measuring what the cable is taking for itself. A run carrying 10 A that shows 0.2 V end to end has 0.02 Ω of its own resistance — entering 0.2 and 10 returns "V 0.2 V · I 10 A · R 0.02 Ω" — and it is converting 2 W into heat along its length.

What matters is rarely the 0.2 V itself but its share of the supply. On a 12 V system it is 1.67% of the available voltage, lost before the load sees any of it. The identical drop on a 5 V logic rail is 4%, which is a different kind of problem entirely.

Turning a drop into a percentage of supply, or a percentage budget back into volts, is the job of the Percentage Calculator.

How to Read Your Result

A successful calculation always prints four lines, in the same order, and none of them are conditional.

The Four Lines the Panel Returns

• The hero line carries all three quantities together — "V 12 V · I 2 A · R 6 Ω". The value you left at 0 is now filled in, and nothing marks which one it was.
• The rearrangement line shows the form that was used with your own numbers already substituted: "Solved: R = V ÷ I = 12 ÷ 2".
• The power line is always voltage times current, worked out after the missing quantity has been found: "Power: P = V × I = 24 W".
• The fourth line is a standing caveat — "Holds for resistive (ohmic) loads — reactive AC circuits need impedance, not plain resistance". It appears on every result and is not a judgment about the circuit you entered.

How the Figures Are Rounded

Rounding is decided per number, not per line. Anything below 10 is shown to three decimal places, anything from 10 upward to two, and trailing zeros are dropped. One result can therefore mix precisions: 230 V across 26.45 Ω returns "V 230 V · I 8.696 A · R 26.45 Ω", three decimals on the current beside two on the resistance.

The three-decimal floor has a consequence at the small end. A 1,000,000 Ω resistor on a 240 V supply passes 0.00024 A, and the hero line reports "V 240 V · I 0 A · R 1000000 Ω" — a rounded zero, not a claim that nothing flows. The power line on that same result still reads 0.058 W, which is the giveaway. Below roughly half a milliamp, take the power figure and divide by the voltage rather than trusting the current display.

If You Fill In All Three Boxes

A third value is not used as a check. When none of the three boxes holds a zero, the calculator discards the resistance you typed, recomputes it from V ÷ I, and says so on the rearrangement line: "Solved: all three entered — R recomputed from V ÷ I for consistency". Put in 12 V, 2 A and a deliberately wrong 99 Ω and the hero line still reads "V 12 V · I 2 A · R 6 Ω".

There is therefore no way to ask this tool whether three measurements agree with each other. To do that, enter two of them and compare the third against what comes back.

When a Warning Replaces the Answer

Two conditions inside the formula swap the result for an amber "Check your inputs" panel.

• Fewer than two non-zero values, which returns "Enter any two values (leave the unknown at 0)". This is also the message you get when a single entry is negative and the other two are zero, because the count is tested first.
• A negative value once two are present, which returns "Use positive values".

A third case never reaches the formula at all. Voltage and current are required fields, so clearing one stops the calculation and the panel names whichever box it is missing. Resistance is the only optional box: clear it and it is treated exactly as a typed 0, which is the same instruction to solve for resistance.

What the Boxes Actually Accept

All three are plain text fields with no minimum, no maximum and no browser validation, and every character that is not a digit, a dot or a minus sign is stripped before the number is read. That is forgiving in a useful way — "12V" is read as 12 and "1,500" as 1500 — and hazardous in exactly one way.

An engineering suffix loses its multiplier without a word. Against a 5 V supply, "10k" in the resistance box is read as 10 Ω and returns "V 5 V · I 0.5 A · R 10 Ω" with 2.5 W. Typing 10000 instead returns "V 5 V · I 0.001 A · R 10000 Ω" with 0.003 W. Same intended question, answers a thousandfold apart, and nothing on screen flags the first as wrong. Write the zeros out; a comma is harmless, a k is not.

Limits: Where Ohm's Law Stops Holding

Everything above rests on resistance being a constant. Where it is not, the arithmetic still runs and the panel still prints three tidy figures — the failure mode is silence, which is what makes this section the one worth reading twice.

Components That Are Not Ohmic

A component is ohmic if current stays proportional to voltage across the range you are using it in, and nonohmic if it does not. The nonohmic category is larger than most people expect.

• Incandescent filaments. OpenStax works the case explicitly: a tungsten filament measuring 0.350 Ω at 20 °C reaches about 4.8 Ω at 2850 °C, roughly fourteen times its cold value. The switch-on inrush is correspondingly large, and a cold resistance measurement predicts none of the running behavior.
• Diodes and LEDs. Below the forward voltage almost no current flows; above it, current rises steeply while the voltage barely moves. There is no single resistance to quote, because V ÷ I gives a different answer at every operating point.
• Semiconductors in general. Their resistivity falls as they warm — the temperature coefficient is negative, the reverse of a metal — which is the mechanism behind thermal runaway in a hot transistor.
• Motors. A spinning motor generates a back-EMF opposing the supply, so the current it draws while running is far below what its winding resistance alone implies. Measure the winding cold and you have computed the stall current, not the working one.
• Batteries and power supplies. Internal resistance makes the terminal voltage sag under load, so the voltage you measured with nothing connected is not the voltage the circuit will see.

AC, Reactance and Impedance

Alternating current introduces a second way of opposing current flow. Capacitors and inductors resist change rather than flow, and the combination of resistance with that reactance is impedance, symbol Z, measured in ohms just as resistance is. OpenStax gives the series form and calls it the AC analog of resistance in a DC circuit.

Z = √(R² + (XL − XC)²)
I₀ = V₀ ÷ Z

Z    impedance, in ohms
XL   inductive reactance, in ohms
XC   capacitive reactance, in ohms

Two consequences follow for anyone using this page. First, mains figures are rms values rather than peaks — appliances and devices are commonly quoted in rms — and for a purely resistive AC load, entering rms volts and rms amps gives both the correct resistance and the correct average power. That is exactly what the kettle and space-heater rows above do. Second, where a load has reactance, V ÷ I returns impedance rather than resistance, and V × I overstates the real power: average power is the rms voltage times the rms current times cos φ, the power factor. Multiply 120 V by 10 A and you get 1,200, but at a power factor of 0.8 only 960 W of that is real.

The caveat the panel prints on every result is making precisely this point. It is not detecting reactance in your circuit, because it cannot — it is reminding you that the calculation assumed there was none.

Resistance Moves With Temperature

To a first approximation resistance follows R = R₀(1 + α ΔT): a reference resistance at a reference temperature, adjusted by the material's temperature coefficient times the change. OpenStax takes 20 °C as the usual reference. For metals the coefficient is positive, so they resist more when hot; for the semiconductors in its table the coefficient is negative.

In practice that means a measurement taken on a cold bench does not describe a circuit that has been running for an hour. Heating elements, filaments, motor windings and long cable runs all present a higher resistance hot than cold, and the wattage a device is rated for is the hot figure, not the cold one.

Datasheet temperatures arrive in whichever scale the manufacturer prefers, and moving between them is the job of the Temperature Converter.

What This Calculator Will Not Do

• It will not solve a network. Combine the resistors yourself first — in series they add, in parallel their reciprocals add — then enter the single equivalent resistance.
• It will not take watts. Convert a wattage to amps with P ÷ V, or to a resistance with V² ÷ P, before typing anything.
• It will not parse prefixes or convert units. The three boxes are volts, amps and ohms, and nothing else.
• It will not handle phase, reactance or power factor, and it does not distinguish AC from DC.
• It will not tell you whether a circuit is safe. It reports arithmetic. Conductor sizing, breaker coordination and insulation ratings are separate questions governed by their own standards, and a plausible-looking result here is not permission to build anything.