What Ohm's law actually says
Ohm's law states that the current through a conductor between two points is proportional to the voltage across those two points, and the constant of proportionality is the conductor's resistance. Written as V = I·R, it is the single most-used relationship in electrical work — it sizes an LED's series resistor, explains why a long extension cord dims a heater, and underpins every voltage drop calculation an electrician performs.
Georg Ohm published the relationship in 1827. What made it a law rather than an observation is the discovery that for metals at a constant temperature, the ratio V/I does not change as you vary the voltage. Double the voltage across a 100 Ω resistor and you get exactly double the current. That linearity is what the word ohmic means, and it is also the assumption you are making every time you use this calculator.
Joule's law is the companion relationship. Power — the rate at which electrical energy turns into heat — is the product of voltage and current: P = V·I. Substituting Ohm's law into it gives the two forms that matter most in practice, P = I²·R and P = V²/R. Between them, these three equations connect four quantities, so knowing any two lets you compute the remaining two. That is precisely what this tool does.
The four quantities and the twelve rearrangements
You never memorise twelve formulas. You memorise two — V = I·R and P = V·I — and rearrange them. The reference table below lists all twelve results so you can check your algebra, but understanding where they come from is faster than looking them up.
Start with the pair you know. If you know voltage and resistance, current follows directly: I = V/R. Power then comes from substituting that current back in, giving P = V·(V/R) = V²/R. If instead you know power and resistance, you have to go the other way and take a square root, because power depends on the square of the voltage: V = √(P·R).
That square is the reason two of the six pairings behave differently from the rest. Current and voltage each scale linearly with one another, but power scales with the square. Raise the voltage across a fixed resistor by 40% and the current rises by 40% while the heat rises by 96%. This is the single most useful intuition in the whole subject, and it is why a resistor that is comfortable at 5 V can char at 12 V.
Watch the units. The calculator normalises whatever you pick — milliamperes, kilohms, milliwatts — to volts, amperes, ohms and watts before it does anything, because the equations are only valid in coherent SI units. Enter 20 mA as 20 with the mA unit selected, or as 0.02 with A selected; both give the same answer, and mixing them (entering 20 with A selected when you meant milliamperes) is the most common source of a result that is off by a factor of 1,000.
Worked example: sizing a resistor for a 12 V LED indicator
You want to run a red LED from a 12 V supply. The datasheet gives a forward voltage of 2.1 V at a forward current of 20 mA. Work it through by hand.
- Find the voltage the resistor must absorb. The LED holds 2.1 V, so the resistor takes the rest: 12 − 2.1 = 9.9 V.
- Convert the target current to amperes. 20 mA = 0.020 A.
- Apply Ohm's law for resistance. R = V/I = 9.9 ÷ 0.020 = 495 Ω.
- Pick a real part. 495 Ω is not a stocked value. The nearest standard E24 value below it is 470 Ω, which gives more current, and the nearest above is 510 Ω, which gives less. Choose 470 Ω.
- Recompute the actual current. I = 9.9 ÷ 470 = 0.021064 A = 21.06 mA. That is 5% above the target, which is fine for an indicator LED.
- Compute the resistor's dissipation. P = V·I = 9.9 × 0.021064 = 0.2085 W.
- Check the cross-form. P = V²/R = 9.9² ÷ 470 = 98.01 ÷ 470 = 0.2085 W. The two forms agree, which is the arithmetic check worth doing every time.
Now the part everyone skips: 0.2085 W is more than 80% of a 1/4 W resistor's rating. Applying the usual doubling margin you want a part rated for at least 0.417 W, so fit a 1/2 W resistor. A 1/4 W part will work, run hot, drift upward in value, and eventually discolour the board. For the full LED calculation including multiple LEDs in series, use the LED resistor calculator.
How to read the result: current tells you if it works, power tells you if it survives
Two of the four outputs answer different questions. Current tells you whether the circuit does what you wanted — the LED lights, the relay pulls in, the sensor gets its bias. Power tells you whether the part lives long enough to matter. Beginners check the first and ignore the second, and that is where components fail.
Standard through-hole resistor ratings are 1/8 W, 1/4 W, 1/2 W, 1 W and 2 W; surface-mount parts run 0.063 W for an 0402 up to about 0.25 W for a 1206. Those are ratings at 70 °C ambient in free air, and manufacturers derate them linearly to zero at 155 °C or so. The practical rule of thumb technicians use is to specify a part rated for at least twice the calculated dissipation, which is what the minimum resistor rating output on this page reports. If the part sits inside a sealed enclosure or under a heatsinked device, double it again.
Resistance is worth a sanity check too. If you measured a component and Ohm's law hands back a resistance far from what you expected, you are usually looking at one of three things: a non-ohmic device (see below), a meter loading the circuit, or a measurement taken with the component still soldered in parallel with the rest of the board. Always lift one leg before you measure resistance in circuit.
Finally, treat the voltage figure as a hazard indicator. Anything at or above 50 V is inside the range NFPA 70E treats as an electrical hazard requiring shock protection boundaries and appropriate PPE. Bench work below 50 V and a few amperes is comparatively forgiving; a 240 V circuit is not.
Ohm's law wheel: all twelve rearrangements
| Solve for | From V and I | From V and R | From I and R | From P and one other |
|---|---|---|---|---|
| Voltage V (V) | — | — | V = I · R | V = P / I or V = √(P · R) |
| Current I (A) | — | I = V / R | — | I = P / V or I = √(P / R) |
| Resistance R (Ω) | R = V / I | — | — | R = V² / P or R = P / I² |
| Power P (W) | P = V · I | P = V² / R | P = I² · R | — |
Twelve expressions in total. The two containing a square root are the ones needed when power is known alongside resistance.
What each resistor size can safely dissipate
| Package | Nominal rating | Comfortable working dissipation (half the rating) | Current at 470 Ω before that limit |
|---|---|---|---|
| 0603 SMD | 0.10 W | 0.050 W | 10.3 mA |
| 0805 SMD | 0.125 W | 0.063 W | 11.5 mA |
| 1206 SMD | 0.25 W | 0.125 W | 16.3 mA |
| Axial 1/4 W | 0.25 W | 0.125 W | 16.3 mA |
| Axial 1/2 W | 0.50 W | 0.250 W | 23.1 mA |
| Axial 1 W | 1.00 W | 0.500 W | 32.6 mA |
| Axial 2 W | 2.00 W | 1.000 W | 46.1 mA |
The last column is I = √(P/R) with R = 470 Ω — for example √(0.125 ÷ 470) = 0.0163 A. Nominal ratings are the industry-standard package sizes; always confirm against the manufacturer's datasheet, which specifies the ambient temperature the rating assumes.
Mistakes that produce a wrong answer
- Mixing units. Entering 20 for a 20 mA current with amperes selected is a factor-of-1,000 error, and it makes a 495 Ω resistor look like 0.495 Ω. Set the unit selector before you type.
- Using the supply voltage instead of the voltage across the component. In the LED example the resistor sees 9.9 V, not 12 V. Ohm's law applies to the voltage across the element you are analysing, nothing else.
- Ignoring dissipation. The current can be perfect and the part still fails. Always read the power output and compare it to the package rating.
- Applying it to a non-ohmic device. Diodes, LEDs, lamps, thermistors, transistors and battery internal resistance are all non-linear. Ohm's law gives their operating-point resistance at one specific voltage, not a constant.
- Measuring resistance in circuit. Parallel paths on the board pull the reading low. Lift one lead, or power the circuit and measure V and I instead.
- Forgetting temperature. A copper conductor's resistance rises roughly 0.39% per °C, and an incandescent lamp's cold resistance can be an order of magnitude below its hot resistance. Ohm's law holds at each temperature, not across them.
- Using DC resistance in an AC circuit. With capacitance or inductance present you need impedance, not resistance.
Where Ohm's law stops being enough
Ohm's law is a statement about resistive elements carrying direct current. Three situations take you outside it.
Alternating current with reactance. Once a capacitor or an inductor is in the path, the opposition to current is impedance Z, a complex quantity, and current lags or leads the voltage. The relationship still looks like Ohm's law — V = I·Z — but the magnitudes no longer multiply to give real power, and you need the power factor as well. Work those cases with the RLC impedance calculator and the electrical power calculator.
Networks rather than single elements. Ohm's law applies element by element. To combine elements you need Kirchhoff's two laws: the currents into a node sum to zero, and the voltages around a loop sum to zero. Those give you the standard series and parallel results — see the series resistance calculator and the parallel resistance calculator — and from there the voltage divider calculator.
Non-linear devices. A semiconductor junction's current rises roughly exponentially with voltage, so a diode has no single resistance. What it has is a dynamic resistance, the slope dV/dI at the operating point, which changes with current. When a datasheet gives you a forward voltage at a stated current, that is a point on the curve, not a resistance you can scale.
For practical electrical work rather than bench electronics, the same equations reappear in code-driven form. Conductor voltage drop is Ohm's law applied to the wire's resistance per unit length; NFPA 70 (the National Electrical Code) recommends limiting branch-circuit voltage drop to 3% in an informational note, and the voltage drop calculator handles the round-trip length and material factors for you.
Key terms
- Ohmic
- A device whose resistance is constant across the voltage range of interest, so that V/I does not change. Metal-film resistors and copper conductors are close to ohmic; diodes are not.
- Dynamic resistance
- The slope of a device's V–I curve at a particular operating point, dV/dI. For a non-linear device this is the only resistance that means anything, and it varies with current.
- Dissipation
- The rate at which a component turns electrical energy into heat, in watts. It sets the package size and the temperature rise, not the electrical behaviour.
- Derating
- Operating a component below its nameplate rating to allow for ambient temperature, enclosure, and service life. Halving a resistor's rated power is the common bench margin.
- E24 series
- The standard set of 24 resistor values per decade with 5% tolerance: 10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91 and their decade multiples.
- Impedance
- The AC generalisation of resistance, combining resistance with capacitive and inductive reactance. Measured in ohms, but with a phase angle attached.