Ohm's Law Explained: The Full Formula Wheel and a Worked Example
Ohm’s law says the current through a resistor equals the voltage across it divided by its resistance: I = V / R. Add the power formula P = V x I and you can find any one of voltage, current, resistance, or power from just two of the others. A 9 volt battery pushing current through a 350 ohm resistor, for example, draws 9 / 350 = 0.0257 amps, or about 26 milliamps, and dissipates 9 x 0.0257 = 0.23 watts as heat.
The Ohm’s law wheel: all 12 formulas
Most people only remember V = I x R, but that single equation combined with P = V x I actually expands into twelve formulas, three for each of the four quantities. This is usually drawn as a “formula wheel” or “Ohm’s law pie chart,” and it is the fastest way to find the right equation once you know which two values you already have.
| To find | If you know V and I | If you know V and R | If you know I and R |
|---|---|---|---|
| Voltage (V) | — | — | V = I x R |
| Current (I) | — | I = V / R | — |
| Resistance (R) | R = V / I | — | — |
| Power (P) | P = V x I | P = V² / R | P = I² x R |
The full wheel also covers the pairs that involve power directly:
| To find | If you know V and P | If you know I and P | If you know R and P |
|---|---|---|---|
| Voltage (V) | — | V = P / I | V = √(P x R) |
| Current (I) | I = P / V | — | I = √(P / R) |
| Resistance (R) | R = V² / P | R = P / I² | — |
| Power (P) | — | — | — |
Six quantity-pairs, each solving for the two you don’t have, is why the calculator below only ever needs two inputs. Give it voltage and resistance and it hands back current and power; give it current and power and it works backward to voltage and resistance. You never have to remember which of the twelve formulas applies, the tool picks it for you.
Worked example: sizing a resistor for an LED
The single most common reason people reach for Ohm’s law outside a classroom is figuring out what resistor to put in series with an LED so it doesn’t burn out. Say you’re running a standard red LED off a 9 volt battery. The LED has a forward voltage drop of about 2 volts, and you want to drive it at its typical rated current of 20 milliamps (0.02 amps).
The resistor doesn’t see the full 9 volts, it only sees what’s left after the LED takes its share:
Voltage across resistor = Battery voltage - LED forward voltage
= 9V - 2V = 7VNow apply Ohm’s law to that 7 volts and the target current:
R = V / I = 7V / 0.02A = 350 ohms350 ohms isn’t a standard resistor value, so you round to the nearest one you can actually buy. The two closest standard values, 330 ohms and 390 ohms, both keep the LED safely within range:
| Resistor chosen | Actual current | Actual voltage across resistor |
|---|---|---|
| 330 ohms | 7V / 330Ω = 21.2 mA | 21.2 mA x 330Ω = 7.0V |
| 390 ohms | 7V / 390Ω = 17.9 mA | 17.9 mA x 390Ω = 7.0V |
Either value keeps the LED within a safe range; 330 ohms runs it slightly brighter, 390 ohms slightly dimmer and cooler.
Don’t forget the resistor’s power rating
The last step people skip is checking whether the resistor can actually handle the heat. Using P = I² x R on the 350 ohm target value:
P = I² x R = (0.02A)² x 350Ω = 0.14 wattsStandard resistors are commonly sold in 1/8 watt, 1/4 watt, and 1/2 watt ratings. A 1/8 watt (0.125W) resistor would be running right at its limit here, so a 1/4 watt (0.25W) resistor gives a comfortable safety margin.
Why power jumps faster than voltage
Power scales with the square of voltage across a fixed resistance (P = V² / R), not linearly, which is why a small voltage increase can matter more than it looks like it should. Keep the 350 ohm resistor from the example above but swap in a bigger battery:
| Supply voltage | Current (I = V / R) | Power (P = V x I) |
|---|---|---|
| 6V | 6V / 350Ω = 17.1 mA | 6V x 17.1 mA = 0.103 W |
| 9V | 9V / 350Ω = 25.7 mA | 9V x 25.7 mA = 0.231 W |
| 12V | 12V / 350Ω = 34.3 mA | 12V x 34.3 mA = 0.412 W |
Doubling the supply from 6V to 12V doesn’t double the power, it quadruples it, since power depends on voltage squared. This is exactly why fuses and wire gauges are rated conservatively: a modest voltage bump on a circuit that was already close to its limit can push power dissipation well past what the components were built for.
Calculate your own values
Enter any two of voltage, current, resistance, or power below and the calculator applies the right formula from the wheel automatically, including the power relations.
Enter any two values and the other two are calculated.
Common mistakes and edge cases
Forgetting the resistor’s power rating. Getting the resistance value right isn’t the whole job. A resistor rated below the power it will actually dissipate overheats, drifts out of tolerance, and can fail outright. Always run P = I² x R (or P = V² / R) on your final choice and pick a component rated comfortably above that number.
Treating an LED as a plain resistor. Ohm’s law assumes a linear relationship between voltage and current, which holds for resistors but not for diodes. An LED’s forward voltage stays roughly constant across a range of currents rather than scaling with resistance, which is exactly why you calculate the resistor value from the leftover voltage after the LED’s drop, not the full supply voltage.
Mixing up AC and DC without accounting for it. Ohm’s law in this simple form applies directly to DC circuits and to the purely resistive part of an AC circuit. Real AC loads with inductance or capacitance also involve reactance and phase, so a straight V = I x R calculation won’t capture the full picture for a motor, transformer, or speaker coil.
Assuming zero current gives real numbers. Some quantity pairs cannot be solved: zero current with a resistance value implies infinite voltage or power depending on which formula you’d use, and the calculator correctly refuses to guess in that case. If you get no result, check that neither of your two known values is zero where the formula needs to divide by it.
Ignoring resistor tolerance. A resistor labeled 350 ohms (or the nearest standard value) is rarely exactly that number. Common tolerances are 5% or 1%, so a “350 ohm” resistor could genuinely measure anywhere from about 332 to 368 ohms at 5% tolerance. For LED circuits this rarely matters, but for precision analog work it’s worth accounting for.
Frequently asked questions
What is Ohm’s law in simple terms? Ohm’s law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance: I = V / R. In practice, that means if you double the voltage across a fixed resistance, the current doubles too, and if you double the resistance while keeping voltage constant, the current is cut in half.
What are all the Ohm’s law formulas? Combining V = I x R with the power formula P = V x I produces twelve formulas total, three ways to solve for each of voltage, current, resistance, and power depending on which two other quantities you already know. They’re commonly drawn together as a “formula wheel”: V = IR, V = P/I, V = √(PR); I = V/R, I = P/V, I = √(P/R); R = V/I, R = P/I², R = V²/P; and P = VI, P = I²R, P = V²/R.
How do I calculate the resistor value for an LED? Subtract the LED’s forward voltage from your supply voltage to get the voltage the resistor needs to drop, then divide that by your target current using R = V / I. A 9V supply with a 2V LED drop and a 20mA target current gives R = 7V / 0.02A = 350 ohms, rounded to the nearest standard value, 330 or 390 ohms.
Does Ohm’s law apply to AC circuits? It applies directly to DC circuits and to the purely resistive portion of an AC circuit. For AC loads that include inductance or capacitance, such as motors or speakers, the relationship between voltage and current also depends on reactance and phase angle, so a plain V = I x R calculation understates or overstates the real behavior.
Why did my resistor get hot or burn out? Almost always because its power rating was too low for the actual power it needed to dissipate. Calculate the power with P = I² x R (or P = V² / R) using the real current or voltage in the circuit, then choose a resistor rated well above that figure, a 1/4 watt resistor for a calculated 0.14 watts, for instance, rather than one rated right at or below it.