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Ohm's Law Calculator and Formula

The Ohm's law formula is V = IR: potential difference = current × resistance, with V in volts, I in amps and R in ohms. Rearrange it as I = V/R to find the current or R = V/I to find the resistance.

Ohm's law formula: V = IR

V = I·R
I = VRV = I·RR = VI
I
current, A
V
potential difference, V
R
resistance, Ω

Convert every value to SI units (m, s, kg, A, V, Ω) before substituting into the formula. The calculator does this for you and shows the conversion as a step.

3 A
Icurrent
3 A
current: 3 A
A battery drives a current of 3 A through a resistance of 4 Ω, with a potential difference of 12 V across it. As the current grows, the bulb glows brighter and the dots showing the flow of charge move faster.

Step-by-step solution

  1. FormulaI = VR
  2. SubstituteI = 12 V4 Ω
  3. AnswerI = 3 A

Ohm's law examples

  1. Example 1

    A current of 2 A flows through a 6 Ω resistor. Calculate the potential difference across the resistor.

    Given:I = 2 AR = 6 Ω
    1. FormulaV = I·R
    2. SubstituteV = 2 A · 6 Ω
    3. AnswerV = 12 V

  2. Example 2

    The heating element of a hairdryer has a resistance of 46 Ω and is connected to the 230 V mains supply. Calculate the current in the element.

    Given:V = 230 VR = 46 Ω
    1. FormulaI = VR
    2. SubstituteI = 230 V46 Ω
    3. AnswerI = 5 A

  3. Example 3

    A torch bulb is connected to a 3 V battery and the current through it is 250 mA. Calculate the resistance of the bulb.

    Given:V = 3 VI = 250 mA
    1. FormulaR = VI
    2. In SI unitsI = 250 mA = 0.25 A
    3. SubstituteR = 3 V0.25 A
    4. AnswerR = 12 Ω

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What is Ohm's law?

V = IR links three quantities in a circuit. Potential difference V, measured in volts, is the energy transferred per unit of charge; current I, in amps, is the rate of flow of charge; resistance R, in ohms, tells you how strongly a component opposes the current. For a fixed potential difference, a bigger resistance means a smaller current. For a fixed resistance, doubling the potential difference doubles the current.

Strictly, Ohm's law says that the current through a conductor is directly proportional to the potential difference across it, provided the temperature stays constant. Components that behave like this, such as a fixed resistor or a wire at constant temperature, are called ohmic conductors, and their I–V graph is a straight line through the origin. A filament lamp is not ohmic: as it heats up, its resistance rises and the graph curves. V = IR still gives its resistance at any one moment, but that resistance is not constant.

A real-life picture: a phone charger, a kettle and a hairdryer all run from the same UK mains supply, yet they draw very different currents because their resistances differ. It is also why a short circuit is dangerous: the resistance becomes very small, so the current becomes very large, and the fuse melts to break the circuit.

Common mistakes

  • Forgetting to convert mA to A: 250 mA is 0.25 A, not 250 A.
  • Leaving kΩ unconverted: 2.2 kΩ is 2200 Ω.
  • Rearranging the wrong way, for example writing R = I/V or I = R/V. Check that I × R gives back V.
  • Using the supply potential difference for one component in a series circuit. Use the potential difference across that component only.
  • Assuming every component obeys Ohm's law. A filament lamp or a diode has a resistance that changes, so its I–V graph is not a straight line.

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Frequently asked questions

V = IR, where V is the potential difference in volts, I is the current in amps and R is the resistance in ohms. It rearranges to I = V/R or R = V/I.

Divide the potential difference by the resistance: I = V ÷ R. For example, a 12 V supply across a 4 Ω resistor gives a current of 3 A.

Not quite. V = IR defines resistance and applies to any component at a given moment. Ohm's law is the statement that, at constant temperature, current is directly proportional to potential difference, so R stays constant; only ohmic conductors obey it.

The ohm, symbol Ω. A resistance of one ohm lets a current of one amp flow when the potential difference across it is one volt; 1 kΩ = 1000 Ω.

Yes. GCSE specifications use 'potential difference' (p.d.), measured in volts, while 'voltage' is the everyday word. Both use the symbol V.

Connect an ammeter in series with the component and a voltmeter in parallel across it, then calculate R = V ÷ I. This is the method used in the GCSE required practicals on resistance.