SizingKitElectronics · direct current
Ohm’s Law Calculator
Give this free calculator any two of voltage, current, resistance and power and it returns the other two, printing the exact rearrangement it used on each answer — V = I × R, P = V² ÷ R, and the ten others. No signup, and the wheel of all twelve identities prints on one sheet for the inside of a lid. It solves direct current through a resistance that holds still; where the current alternates, watts stops being volts times amps and a power factor enters the arithmetic.
- 100% free
- No signup
- 12 rearrangements
- V · I · R · P
- Printable wheel
Which two do you have?
Any two of the four fix the other two. Pick the pair you are holding and the page prints the rearrangement it used on each answer.
Default ±5 % — IEC 60062 color-band marking: a gold tolerance band is ±5 %, silver ±10 %, brown ±1 %, red ±2 % and blue ±0.25 %.
Worked circuits
Solved values
Current — I = V ÷ R
10.6 mA
10.1 mA to 11.2 mA across the band
Power — P = V² ÷ R
0.0532 W
0.181 BTU/h of heat
0.0507 W to 0.0560 W across the band
| Voltage (entered) | 5 V |
|---|---|
| Current | 10.6 mA |
| Resistance (entered) | 470 Ω |
| Power | 0.0532 W |
A quarter-watt part is twenty times the dissipation this needs, which is why nobody checks it — until the same resistor is moved to 48 V and the figure goes up by a factor of ninety-two.
The band above is the marked resistance carried through the same algebra at ±5 %. The part's own datasheet is what governs, and a 1 % metal-film part in the same footprint narrows this fivefold. Tolerance is the marking at the reference temperature only — it does not cover drift with temperature, which a separate coefficient in ppm/°C describes, nor aging, nor the change in a wirewound element once it is hot.
Wattage is printed in BTU/h beside watts because a dissipation is a heat load once it is inside an enclosure. One watt is 3.412 BTU/h, from the International Table BTU of 1055.05585262 J and an hour of 3,600 s — a definition, not a measurement.
The twelve rearrangements
Two identities, V = I × R and P = V × I, with one variable eliminated between them each time. The pair selected above is marked; the sheet prints without the calculator.
| Solve for | Knowing | Formula | Where it turns up |
|---|---|---|---|
| V | I, R | V = I × R | A current through a known resistance: the drop across a shunt, a sense resistor, a length of wire. |
| V | I, P | V = P ÷ I | A load whose wattage and draw are both on the plate but whose supply voltage is not. |
| V | R, P | V = √(P × R) | A heating element sold by wattage and measured in ohms — what supply it was built for. |
| I | V, R | I = V ÷ R | The everyday one: a resistor across a supply, and how much goes through it. |
| I | V, P | I = P ÷ V | Nameplate watts against nameplate volts, for picking a fuse or a conductor. |
| I | R, P | I = √(P ÷ R) | The draw of an element you have measured with a meter and read the wattage off. |
| R | V, I | R = V ÷ I | A resistance you infer from a measurement instead of reading it off the bands. |
| R | V, P | R = V² ÷ P | The element that turns a known supply into a wanted wattage. |
| R | I, P | R = P ÷ I² | Sizing a shunt or a ballast to a current you have fixed and a dissipation you can live with. |
| P | V, I | P = V × I | What the supply is delivering, and what the component has to get rid of as heat. |
| P | V, R | P = V² ÷ R | Dissipation in a resistor across a fixed rail — the one that decides its physical size. |
| P | I, R | P = I² × R | Conductor and connection heating, where the current is what is fixed and the resistance is small. |
Volts, amperes, ohms and watts throughout. Every row is exact for direct current through a resistance that is not changing while you measure it — 12 rearrangements of two identities, so none of them can disagree with another.
How to solve a DC circuit from the two figures you have
Every measurement you can take on a resistive branch fixes the whole branch, provided you take two of them.
Say which two you are holding
The pair menu lists the six combinations: voltage with resistance, voltage with current, voltage with power, current with resistance, current with power, resistance with power. Choosing the pair is what selects the two rearrangements out of the twelve, so the page never has to guess which formula you meant.
Type the figures with their prefixes
Each field takes its own unit — millivolts through kilovolts, microamps through kiloamps, ohms through megohms — and a unit typed into the box beats the one selected beside it, so 4k7 written as 4.7 kohm and 4700 in ohms land on the same value. A marked resistance also gets a tolerance field, defaulting to the ±5 % a gold band means.
Read the answer with its identity and its band
Each solved figure carries the rearrangement above it and, where a marked resistor went in, the interval the two answers actually occupy once the tolerance is carried through. Power is printed a second time in BTU/h, because a dissipation inside an enclosure is a heat load somebody has to get rid of.
What this calculator does and refuses
| Identities solved | 12 rearrangements of V = I × R and P = V × I, selected two at a time by which pair of figures you enter. |
|---|---|
| Units accepted | Voltage in mV, V and kV; current in µA, mA, A and kA; resistance in Ω, kΩ and MΩ; power in W, kW, hp and BTU/h. Milliohms are absent site-wide because case-folded unit matching cannot tell mΩ from MΩ. |
| Tolerance band | ±5 % prefilled, from the gold band of the IEC 60062 color code; editable from 0 to 50 %, and applied only when a marked resistance is one of the two inputs. |
| Heat cross-print | Every wattage prints a second time in BTU/h at 3.412142 BTU per watt-hour, from the International Table BTU of 1055.05585262 J divided by 3,600 s. |
| Worked circuits | 3 presets: a 470 Ω pull-down on a 5 V rail, the series resistor in a 12 V LED string carrying 20 mA, and a 1,500 W element on a 120 V supply. |
| Circuit type | Direct current through one resistive element. Power factor, reactance, phase angle and √3 appear nowhere on this page, by design. |
| Zero and negative inputs | Refused with a message naming the reason rather than returned as infinity — 0 Ω is a short circuit, and a negative figure here is a polarity the algebra does not carry. |
| Where it runs | In the tab, with no request to a server after the page loads, so it keeps solving on a phone with two bars in a basement. |
Frequently asked questions
Why does the current I measure not match the current this calculates?
Three things account for almost all of it: the resistor's tolerance, the resistance of everything else in the loop, and the supply sagging under load. A ±5 % part alone puts a 10 % spread on the answer, which the band under each figure shows. Add the leads, the connector and the breadboard rail — a few hundred milliohms in a low-voltage circuit is a real fraction of a 47 Ω load — and a bench supply whose 5.00 V reads 4.87 V at 200 mA, and the gap closes. Measure the voltage across the resistor itself rather than at the supply terminals and the two figures usually agree to within the band.
Does Ohm's law apply to AC circuits?
V = I × R still holds instant by instant, but the R you divide into is no longer a resistance — it is an impedance, and the power identity is the one that breaks. Volts times amps on an alternating supply gives volt-amperes, and the watts a meter bills you for are that figure times the power factor. This page has no power factor in it on purpose; the single-phase AC version is the volts, amps and watts calculator.
Is a lamp filament a resistor?
Not in the sense this page assumes: a tungsten filament's resistance rises by roughly a factor of ten to fifteen between room temperature and its operating temperature, so the cold reading on your meter and the hot value implied by its wattage are two different numbers, and neither is wrong. Ohm's law is a description of materials that hold a constant ratio, not a law that materials obey. Nichrome heating wire barely moves, which is why an element behaves and a bulb does not. A diode, a thermistor and an LED do not hold a ratio at all, and any calculator that returns a resistance for them is returning the slope of one point on a curve.
Should I use P = V² ÷ R or P = I² × R for conductor heating?
Use P = I² × R, because current is the quantity a conductor's heating is fixed by and voltage is not. The drop across a length of wire is a small fraction of the supply, so V in the first formula would have to be the drop rather than the system voltage — a mistake that inflates the answer by orders of magnitude. The square is also why doubling a load quadruples the heat in the same conductor, and why a loose termination that adds a fraction of an ohm gets hot enough to find with a thermal camera.
What wattage resistor do I fit for the dissipation shown?
More than the figure, and how much more comes from the part's own derating curve rather than from a rule of thumb. A resistor's power rating is quoted at a stated ambient — Vishay's CRCW thick-film series, for one, holds its full rating to 70 °C and falls linearly to zero at 155 °C — so a part inside a warm enclosure is already derated before you add margin. Read the curve in the datasheet at your ambient and pick a rating above the answer at that temperature; the standard sizes leave you 0.125, 0.25, 0.5, 1, 2 and 3 W to choose from.
Why is 0 Ω refused instead of returning an infinite current?
Because infinity is not an answer to the question, and printing one would be a claim about a real circuit that no real circuit satisfies. A short across a supply is limited by the supply's own internal resistance, by the conductors, and finally by whatever protective device opens — none of which this page knows about. It says so rather than showing a figure somebody might write down.
Can I use this on a battery that has internal resistance?
Yes, by treating the internal resistance as another resistor in the loop rather than as a property of the battery. Enter the terminal voltage under load rather than the open-circuit voltage and the answer describes the external circuit correctly. If you want the internal resistance itself, take the open-circuit voltage, take the terminal voltage at a known current, and divide the difference by that current — which is the R = V ÷ I row of the chart with the difference standing in for V.
About Ohm's law, and the twelve ways it is written
Georg Ohm published the ratio in 1827, in Die galvanische Kette, mathematisch bearbeitet, and what he established was not a law of nature but a property that some materials have and others do not. A metal at a steady temperature holds a constant ratio of voltage to current; a diode, a thermistor, an arc and a lamp filament do not, and for those the ratio you compute describes exactly one point of a curve. That is the distinction most calculators for this query erase by returning a number for whatever you type. It is also why the presets here are a pull-down resistor, a series resistor and a nichrome element, all three of which genuinely hold their ratio, rather than an LED — picking the resistor that feeds one is the LED resistor calculator, and its subject is the forward voltage, not the ratio.
The twelve formulas people call the wheel are two identities with one variable eliminated between them, which is why they cannot disagree: start from V = I × R and P = V × I, substitute each into the other, and every row of the chart falls out. Knowing that is worth more than memorising the chart, because it tells you which substitution hides an assumption. P = V² ÷ R and P = I² × R give the same answer on a fixed circuit and diverge the moment the resistance changes — hold the voltage and a rising resistance drops the power, hold the current and the same rise raises it. That is the whole behavior of a heating element warming up, and it is invisible if you only ever use P = V × I. Where a pair of resistors splits a rail rather than loading it, the ratio rather than either value is what matters, and that is the voltage divider calculator.
This page stops where direct current stops. On an alternating supply, volts divided by amps returns an impedance and the product of the two returns volt-amperes, which is a different quantity from watts — the volts, amps and watts calculator is where that distinction is worked through, and the three phase power calculator owns the √3 that appears once there are three of them. If you want the five relations one after another with the arithmetic written out rather than a chart to print, the electrical calculator is the console version. And the same three-term algebra runs most of the rest of this site under other names: a driving pressure over a resistance gives a flow, which is why sizing a run of ductwork on the duct size calculator reads so much like sizing a resistor, right down to the square on the loss term.
Where these numbers are worked out
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
The tolerance you type and the pair you select are held in the page’s own memory for as long as the tab is open and are gone when you close it. Nothing is written to local storage, so a shared bench machine keeps no record of what was on the board.