12 V across a 4 Ω resistor
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V = 12 V, R = 4 ΩThe current comes from Ohm's law: I = V/R = 12 / 4 = 3 A. With the current known, the power is P = VI = 12 · 3 = 36 W. P = I²R gives the same: 3² · 4 = 36 W.
Ohm's Law Calculator
Any two of voltage, current, resistance and power give the other two.
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Want to solve these without the calculator?
The Coddy physics course teaches the method: you solve each problem in steps on an interactive board, and it tells you which step went wrong.
The Ohm's law formula, and the power formulas that go with it
Ohm's law links the three numbers of a simple circuit: the voltage V across a component, in volts, the current I through it, in amperes, and its resistance R, in ohms. The formula is V = IR, so I = V/R and R = V/I. One ohm is one volt per ampere: a 4 Ω resistor with 12 V across it carries 12 / 4 = 3 A.
Power is the rate the component turns electrical energy into heat or light, in watts, and P = VI. Put V = IR into it and you get two more forms, P = I²R and P = V²/R. Between them, these four formulas mean that any two of V, I, R and P are enough to find the other two, which is what the Ohm's law wheel on a classroom wall shows.
The calculator does exactly that. Fill in any two of the four boxes and leave the other two blank: it finds one blank with whichever formula fits, then uses that answer to find the last one, and shows which formula each step used. Millivolts, milliamps, kilohms and kilowatts are converted to volts, amps, ohms and watts first, as their own step, and each answer is also given in the other units.
What to notice
- V = IR works in volts, amperes and ohms. A current in milliamps or a resistance in kilohms has to be converted first, or the answer is out by a factor of 1000.
- For a fixed resistance, current is proportional to voltage: double the voltage and the current doubles too.
- Power grows with the square of the current or the voltage. Double the current through the same resistor and P = I²R goes up four times.
- Ohm's law describes an ohmic conductor, one whose resistance stays the same as the current changes, like a metal resistor at a steady temperature. A filament lamp and a diode are not ohmic.
- For a component that is not ohmic, R = V/I still gives its resistance at that moment, but the value changes when the current does.
How to use Ohm's law
Pick out the two values you know
Any two of voltage, current, resistance and power. A kettle label gives power and voltage; a resistor's colour bands give its resistance.
Put them in volts, amps, ohms and watts
Milliamps divide by 1000, kilohms multiply by 1000, kilowatts multiply by 1000. 20 mA is 0.02 A and 2 kW is 2000 W.
Choose the formula with your two values and one unknown
V = IR for voltage, current and resistance; P = VI, P = I²R or P = V²/R when power is involved. Rearrange it for the unknown.
Use that answer to find the fourth value
Once you have three of the four, any formula that holds the last one gives it. From V and I, for example, P = VI.
The Ohm's law wheel as a table
Every quantity from every pair of the others. V in volts, I in amperes, R in ohms, P in watts.
| To find | You know | Formula |
|---|---|---|
| Voltage V | I and R | V = IR |
| Voltage V | P and I | V = P/I |
| Voltage V | P and R | V = √(PR) |
| Current I | V and R | I = V/R |
| Current I | P and V | I = P/V |
| Current I | P and R | I = √(P/R) |
| Resistance R | V and I | R = V/I |
| Resistance R | V and P | R = V²/P |
| Resistance R | P and I | R = P/I² |
| Power P | V and I | P = VI |
| Power P | I and R | P = I²R |
| Power P | V and R | P = V²/R |
Worked examples
A 2 kW kettle on 230 V
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V = 230 V, P = 2 kW2 kW is 2000 W. The current is I = P/V = 2000 / 230 = 8.70 A, and then the resistance is R = V/I = 230 / 8.696 = 26.45 Ω. P = V²/R checks it: 230² / 26.45 = 2000 W. That current is why a kettle needs a thicker cable than a lamp.
20 mA through a 220 Ω resistor
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I = 20 mA, R = 220 ΩConvert first: 20 mA = 0.02 A. Then V = IR = 0.02 · 220 = 4.4 V across the resistor, and P = VI = 4.4 · 0.02 = 0.088 W, which is 88 mW. A common quarter watt resistor (250 mW) handles that easily.
A 60 W lamp on 230 V
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V = 230 V, P = 60 WI = P/V = 60 / 230 = 0.261 A, and R = V/I = 230 / 0.26087 = 881.7 Ω. That is the filament's resistance while it glows. Measured cold with a meter it reads much lower, because a filament lamp is not ohmic: its resistance rises as it heats up.
Common mistakes
- Putting milliamps straight into the formula. 20 mA is 0.02 A; using 20 makes the voltage a thousand times too big.
- Forgetting that a resistor value in kΩ means thousands of ohms. 4.7 kΩ is 4700 Ω.
- Multiplying when you should divide. I = V/R, not V · R: a bigger resistance means a smaller current.
- Dropping the square in P = I²R or P = V²/R. With 3 A through 4 Ω the power is 9 · 4 = 36 W, not 12 W.
- Using the supply voltage for one component in a series circuit. V in V = IR is the voltage across that component, which is only part of the supply.
- Treating a filament lamp, a diode or a thermistor as if its resistance were fixed. Ohm's law with a constant R only fits an ohmic conductor.
Ohm's law FAQ
What is Ohm's law?
Ohm's law says the current through a conductor is proportional to the voltage across it, as long as its temperature stays the same. As a formula, V = IR, where V is in volts, I in amperes and R in ohms. It is named after Georg Ohm, who published it in 1827.
What is the Ohm's law formula for current and resistance?
Rearrange V = IR. The current is I = V/R and the resistance is R = V/I. A 9 V battery across a 3 kΩ resistor drives 9 / 3000 = 0.003 A, which is 3 mA.
How do you calculate power from voltage and current?
P = VI, in watts when V is in volts and I in amperes. If you know the resistance instead of one of them, use P = I²R or P = V²/R. All three give the same answer for the same component.
What is the Ohm's law wheel?
A circle split into four quarters, one each for V, I, R and P, holding the twelve formulas that give each quantity from two of the others. The table on this page lists the same twelve formulas.
What is an ohmic conductor?
A conductor whose resistance stays constant, so a graph of current against voltage is a straight line through zero. A metal resistor at a steady temperature is ohmic. A filament lamp is not, because its resistance rises as it heats, and neither is a diode, which barely conducts one way.
Does Ohm's law work for AC?
For a plain resistor, yes, with the RMS values of the voltage and current. The 230 V or 120 V of mains electricity is already an RMS value, which is why the kettle example works. Coils and capacitors need impedance instead, which this calculator does not cover.
What is the unit of resistance?
The ohm, Ω. One ohm is one volt per ampere: a resistance of 1 Ω lets 1 A flow when 1 V is across it. Resistors are often marked in kilohms (1 kΩ = 1000 Ω) or megohms (1 MΩ = 1,000,000 Ω).
