Ohm's Law Calculator

Every electrical question eventually collapses into one of four numbers: voltage, current, resistance, or power. Will this resistor survive? How much current is that heater actually pulling? What resistor tames an LED? Ohm's law connects all four, and this calculator is the whole connection in one box — enter any two values and it solves the other two, showing the formula it used for each step so the answer arrives with its math attached.

The point of solving all four at once is that real questions rarely name what they're really asking. You measure 12 V across a resistor and know 0.5 A flows — what you actually want to know is whether 6 W of heat is too much for the part. The tool hands you R = 24 Ω and P = 6 W together, in the same instant, from the same two inputs.

It's free, browser-based, and instant. Nothing to install, nothing uploaded — electricians on a job site and students at a desk get the same sub-second response with zero setup.

Voltage (V, measured in volts) is electrical pressure — how hard the source pushes. Current (I, in amperes) is the flow rate — how much charge actually moves through the wire. Resistance (R, in ohms, symbol Ω) is what impedes that flow, turning the pushed energy into heat. Power (P, in watts) is the transfer rate — one watt is one joule of energy per second moving from source to load.

The plumbing analogy is old but earns its keep. Voltage is water pressure at the tap, current is liters per minute flowing, resistance is the skinny pipe restricting the flow. Squeeze the pipe (raise R) and flow drops; raise the pressure (V) and flow climbs. One caution before the analogy outstays its welcome: water flows visibly and electricity doesn't, which is precisely why the arithmetic matters more in the electrical case.

• V = I × R — the core statement: pressure equals flow times opposition.
• I = V ÷ R — more pressure or less resistance means more current.
• R = V ÷ I — resistance is what's left when you divide pressure by the flow it produced.
• P = V × I — power is pressure times flow, the rate energy gets delivered.

The units themselves encode the relationships, which is worth a slow look. One ohm is defined as one volt per ampere — the resistance that lets one volt push exactly one ampere through. One watt is one volt-ampere. When you write V = IR you are almost rearranging unit definitions, which is why the formula is dimensionally airtight and why no coefficient ever appears in it. Physics equations rarely come this clean, and the cleanliness is a hint about how fundamental the relationship underneath actually is.

Enter two of the four quantities and the tool derives the rest — the only real decision is which two you happen to know.

1. 1

   Pick your two knowns

   Any pair works: V and I, V and R, P and V, P and I, and so on. The input fields you leave blank are the ones the calculator fills in.

2. 2

   Enter values with units in mind

   Volts, amperes, ohms, watts — plain units, no prefixes needed. For milliamperes, enter 0.02 rather than 20 mA; the tool works in base units throughout.

3. 3

   Read the solved outputs

   The two unknown quantities appear immediately, each labeled with its unit and the formula that produced it — R = V ÷ I, P = V × I, whichever path your inputs opened.

4. 4

   Check the sanity line

   The output flags physically implausible results, like a resistance that implies current beyond what real wiring could carry, before you act on the number.

5. 5

   Swap scenarios live

   Change voltage from 12 to 9 and watch current and power recompute instantly — comparing supply options is the most common reason people keep this tab open.

6. 6

   Copy the worked solution

   One click copies the values and formulas for a lab writeup, repair ticket, or forum post where showing the method matters.

Worked micro-scenarios make the flow concrete. Bench electronics: enter 9 and 470 to see what current a battery-resistor pair actually produces — about 19 mA — and whether the part stays under its wattage rating. Household load planning: enter 120 and 1440 to confirm a heater draws 12 A before plugging it into a crowded circuit. LED first build: enter 3 and 0.02, get 150 Ω, and buy the right parts the first time. Same tool, three worlds.

Four quantities, taken two at a time, give six pairs, and each pair determines the remaining two — twelve formulas in total, traditionally printed on a color wheel that electricians stick inside their toolbox lids. You don't need the poster when the algebra is this shallow, but seeing all twelve together shows the symmetry of the system.

Cross-check the wheel on a worked case: with V = 12 and I = 0.5, resistance is 24 Ω by division. Power follows as P = V × I = 6 W. Now the derived formulas must agree — P = I² × R gives 0.25 × 24 = 6 W, and P = V² ÷ R gives 144 ÷ 24 = 6 W. Three separate routes, one answer, and that agreement is the calculator's built-in verification: every solution the tool displays has been checked through an alternate formula before it reaches you.

Each case below was computed by hand and cross-checked through a second formula from the wheel. Type the same inputs into the calculator and compare line by line.

Look at what the heater example is quietly teaching. Twelve amperes on a standard 15 A US circuit is 80% of the breaker's rating — the exact ceiling the National Electrical Code sets for continuous loads — which is why 1440 W shows up on heater nameplates so often. The number is not a marketing choice; it's code compliance expressed in watts. On a 230 V European outlet, the same 1440 W needs only 6.26 A and a 36.1 Ω element, which is why appliances rated for both worlds list different currents.

And the 60 W incandescent bulb deserves its own farewell calculation: at 240 V it draws 0.25 A through a 960 Ω filament — a resistance that shifts as the tungsten heats, incidentally, which makes the bulb a fine example of a non-ohmic device and a reminder that the equation describes cold arithmetic, not always hot reality.

Resistance problems are electronics problems; power problems are billing problems. Your electric meter counts kilowatt-hours — energy, not current — and every appliance's running cost is its wattage times hours times your rate. A 1440 W heater running 5 hours a day consumes 7.2 kWh daily; at the US average residential rate, that real money adds up over a winter month, and it all started as P = V × I on a spec sheet.

Power also sets the physical limits of components. A resistor is rated in watts because its job is converting electrical energy to heat, and exceeding the rating cooks it — sometimes literally, with smoke and a smell you remember. The 150 Ω LED resistor dissipating 0.06 W is loafing; a quarter-watt part there is overkill by design, which is exactly what good design looks like.

Ohm's law is a statement about one resistance at one voltage. The moment a circuit contains two resistors, you compute their combined effect first, then apply V = IR. In series, resistances add: two 10 Ω parts in a row present 20 Ω to the source, and at 12 V that's 0.6 A through everything. In parallel, conductance adds, which works out to halving: those same two 10 Ω parts side by side present 5 Ω, and the source pushes 2.4 A total.

The parallel case is why your house is wired that way. Every outlet is a parallel branch, so each device sees the full 120 V while drawing only its own current — the toaster doesn't dim the lights by stealing their voltage. It's also why adding devices eventually trips a breaker: parallel branches add currents, and the total crosses the line. A space heater's 12 A plus a hair dryer's 12.5 A exceeds 15 A comfortably, and the breaker does in milliseconds what the arithmetic predicts.

• Series: R_total = R1 + R2 — same current everywhere, voltage divides between them.
• Parallel (two resistors): R_total = (R1 × R2) ÷ (R1 + R2) — same voltage everywhere, current divides.
• Two identical resistors in parallel always halve: 10 Ω + 10 Ω → 5 Ω.
• Compute the combined resistance first, then apply Ohm's law to the simplified circuit.

Georg Simon Ohm published the relationship in 1827, in a book whose title translates to The Galvanic Circuit Investigated Mathematically. The reception was brutal — the Prussian minister of education publicly dismissed it, and the physics establishment of the day was hostile enough that Ohm resigned his teaching post in Cologne. The mathematics of a schoolteacher, they implied, was not how physics progressed.

Time settled the argument in his favor completely. Ohm ended his career as a professor in Munich, and in 1881 — well after his death in 1854 — the International Electrical Congress in Paris named the unit of resistance the ohm in his honor. Every multimeter dial with a Ω symbol is carrying the apology the man never received in print.

The formula is simple enough that mistakes concentrate in the inputs and the assumptions rather than the algebra itself.

• Mixing unit scales — entering 20 for 20 mA instead of 0.02 A inflates current a thousandfold; the tool works in base units and assumes you did too.
• Treating an LED as a fixed resistance — diodes hold roughly constant forward voltage, not constant R, so the series resistor must be computed from the voltage difference as in the 150 Ω example.
• Ignoring temperature dependence — filament lamps and thermistors shift resistance with heat, so cold measurements mislead about hot behavior.
• Using peak instead of RMS values in AC — a 170 V peak US outlet is a 120 V RMS circuit; the equations want RMS.
• Forgetting the 80% continuous-load rule — a 15 A circuit is a 12 A circuit for sustained loads like heaters, and the 1440 W ceiling exists for exactly this reason.
• Assuming battery voltage is constant — a 9 V battery sags under load and ages downward, so measured current drifts from predicted current in real builds.

Most of these share one root cause: the equation is honest about exactly what you feed it and nothing more. Garbage precision in, garbage precision out, wearing a confident face. The defense is the same in every case — note the units next to each input before computing, confirm the device is actually ohmic, and treat the result as a starting estimate rather than a verdict.

Electronics hobbyists and trade professionals both end up here, usually for slightly different halves of the formula wheel.

• Electronics hobbyists — sizing LED resistors, checking whether a 1/4 W part survives a circuit, and sanity-checking breadboard measurements against theory.
• Electricians and apprentices — converting nameplate watts to amperes for load calculations, like verifying that a 1440 W heater stays inside a 15 A circuit's continuous limit.
• Physics and trade-school students — the lab exercise of measuring V and I, computing R, and comparing against the resistor's color code is a rite of passage.
• EV and solar owners — estimating charge currents and inverter loads: a 7.2 kW charger on 240 V is a 30 A calculation, and the tool answers it in one step.
• Appliance shoppers — translating watts to yearly cost, which starts with P = V × I and ends at the electricity bill.
• Makers and repair technicians — establishing whether a mystery transformer winding is a few hundred or a few thousand ohms, using a measured voltage and current.
• Home DIYers — checking whether adding a bathroom fan and a light to an existing circuit stays within its ampacity before anyone touches a breaker.

The wheel chart, mental math, and the calculator each have a place; they differ mainly in error surface and convenience.

The wheel chart row is affectionate rather than dismissive — that laminated disc is a genuinely good design that predates every calculator here, and it works with gloves on in the rain. What software adds is the cross-check: computing 6 W through three independent formulas and refusing to display a result when they disagree is a form of honesty paper cannot offer.

This calculator does exact arithmetic on idealized components, and real circuits are only ideal on paper. Battery voltage sags, resistors carry tolerance — often ±5% or ±10%, which the color code on the part encodes — and conductors themselves add small resistances the schematic omits. Treat results as the center of a band, not the edge of a fact.

Component tolerance deserves one worked illustration: a 150 Ω resistor with ±5% tolerance ranges from 142.5 to 157.5 Ω, so the LED current lands between roughly 19 and 21 mA. The circuit works across the whole band, which is why designers choose values with margin instead of values at the edge.

The more serious limit is scope. Ohm's law arithmetic does not make anyone qualified to wire a panel, size a breaker, or bond a ground — those are code questions with life-safety consequences, and the National Electrical Code exists because voltage is unforgiving of shortcuts. Use this tool to understand, to estimate, and to check; use a licensed electrician for the parts of the system that can hurt you.

Straight answers to the questions that actually get searched about Ohm's law.

One resistor question always leads to another; these are the natural next tabs.

• Resistor Color Code Calculator — decode the colored bands on the physical part you just computed a value for, including 4-band and 5-band precision resistors.
• Caffeine Half-Life Calculator — the other kind of estimate engineers run at 2 a.m. when the soldering session runs long.

The formulas, the history, and the code context all trace to these references.