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    Resistors in Parallel Calculator

    GCSE PhysicsAQAEdexcelOCRA-level and some GCSE courses

    Find the total resistance of two resistors in parallel, or a missing resistor, using 1/Rtotal = 1/R1 + 1/R2. The working shows each reciprocal and the final flip.

    Quick answer

    In parallel, 1/Rtotal = 1/R1 + 1/R2, and the total is always smaller than the smallest resistor. For example, 6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 0.5, so R = 2 Ω.

    By Engr. Mehmood Kakar · Updated

    1/Rtotal = 1/R1 + 1/R2
    Find:

    Simulation

    Parallel branches share the current

    Set two resistors in parallel and the supply pd. Each branch gets the full pd; the currents add up, so the total resistance is less than either resistor.

    4 Ω
    12 Ω
    6 V

    Adding a branch gives the charge another path, so the total current goes up for the same pd and the total resistance goes down. (AQA GCSE asks for this explanation, not the 1/R equation.)

    Put these numbers in the calculator above

    How to calculate resistance in parallel

    When two resistors are connected in parallel, side by side between the same two points, the current has two paths. That makes the total resistance smaller than either resistor. To calculate it, add the reciprocals:

    1/Rtotal = 1/R1 + 1/R2

    • All resistances are in ohms (Ω)

    For 6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 0.5, so R = 1 ÷ 0.5 = 2 Ω. The last step, flipping the answer back, is the one students forget.

    A quick check: two equal resistors in parallel always give half of one of them. Two 10 Ω resistors give 5 Ω.

    Which course needs this? AQA GCSE Physics only asks you to explain why the total resistance in parallel is less than the smallest resistor, not to calculate it. The reciprocal formula is used at A-level and in some other GCSE courses, so check your own specification.

    Common mistakes that cost marks

    1. Forgetting to flip the answer. 1/6 + 1/3 = 0.5 is 1/R, not R. R = 1 ÷ 0.5 = 2 Ω.
    2. Adding the resistances. That is the series rule. A parallel total bigger than either resistor is a sign something went wrong.
    3. Not converting kΩ first. Change everything to ohms before taking reciprocals.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A 6 Ω resistor and a 3 Ω resistor are connected in parallel. Calculate the total resistance.[2 marks]
    1. 1/R = 1/6 + 1/3 = 0.5
    2. R = 1 ÷ 0.5
    3. R = 2.0 Ω
    Q2Two 10 Ω resistors are connected in parallel. Calculate the total resistance.[2 marks]
    1. 1/R = 1/10 + 1/10 = 0.2
    2. R = 1 ÷ 0.2
    3. R = 5.0 Ω
    Q3Two resistors in parallel have a total resistance of 4 Ω. One is 12 Ω. Calculate the other.[3 marks]
    1. 1/R₂ = 1/4 − 1/12 = 0.25 − 0.0833 = 0.1667
    2. R₂ = 1 ÷ 0.1667
    3. R₂ = 6.0 Ω

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    How do you calculate resistance in parallel?

    Use 1/Rtotal = 1/R1 + 1/R2. Add the reciprocals of each resistance, then take the reciprocal of the answer to get Rtotal.

    Why is the total resistance in parallel smaller?

    Each extra branch gives the current another path, so more current flows from the same potential difference. More current for the same p.d. means a lower total resistance.

    Do I need this formula for AQA GCSE Physics?

    No. AQA GCSE only asks you to explain why the total is less than the smallest resistor. The formula is used at A-level and in some other courses.

    Is there a shortcut for two resistors?

    Yes: Rtotal = (R1 × R2) ÷ (R1 + R2), often called product over sum. It gives the same answer.