The formula this page uses
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ Iₙ = V / Rₙ I_total = ΣIₙ
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Parallel Circuit Calculator
Solve parallel circuit problems with clear steps, notation, and a final check.
Ω
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Evaluate the governing formula locally in your browser. Define each known quantity once, then change values to test another case instantly.
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Applied math
Parallel Circuit Calculator explained
The short version
- In a parallel circuit every branch gets the full supply voltage.
- The reciprocals of the resistances add, so the total is always smaller than the smallest branch.
- Branch currents add up to the total current, which is why adding more appliances trips a breaker.
What each part means
SymbolWhat it means
V — Supply voltageThe same across every branch, in volts.
Rₙ — Branch resistanceIn ohms. Each branch is independent of the others.
R_total — Equivalent resistanceWhat a single replacement resistor would have to be. Always less than the smallest branch.
Iₙ — Branch currentV divided by that branch's resistance. Smaller resistance means bigger current.
Show your work: a full example
- The circuit120 Ω and 240 Ω in parallel across 12 V
- Add the reciprocals1/120 + 1/240 = 2/240 + 1/240 = 3/240
- Flip to get the totalR_total = 240/3 = 80 Ω
- Current in the 120 Ω branch12 ÷ 120 = 0.1 A
- Current in the 240 Ω branch12 ÷ 240 = 0.05 A
- Total current0.1 + 0.05 = 0.15 A
- Check against the equivalent resistance12 ÷ 80 = 0.15 A ✓, and total power is 12 × 0.15 = 1.8 W
A second, different case
- A different case: three branches on 24 V4 Ω, 6 Ω and 12 Ω in parallel
- Put the reciprocals over a common denominator1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12
- FlipR_total = 12/6 = 2 Ω, smaller than the 4 Ω branch
- Branch currents24/4 = 6 A, 24/6 = 4 A, 24/12 = 2 A
- Total6 + 4 + 2 = 12 A
- Check24 ÷ 2 = 12 A ✓
- Read itthe smallest resistor carries the most current, exactly half the total here
Copy-ready example
120 Ω and 240 Ω in parallel across 12 V
The circuit
Questions about the Parallel Circuit Calculator
Why is the total resistance smaller than any single branch?
Each extra branch is another road for current to take. More roads means less opposition overall, so adding a 1000 Ω branch beside a 10 Ω one still lowers the total slightly, from 10 Ω to 9.90 Ω.
Why is house wiring parallel rather than series?
So every socket gets the full 120 V or 230 V, and so switching off a lamp does not cut power to the fridge. The cost is that each appliance adds current, and enough of them together trip the breaker.
Which branch carries the most current?
The one with the least resistance, because they all share the same voltage. In the three-branch example the 4 Ω path takes 6 A while the 12 Ω path takes only 2 A.
When is the product-over-sum shortcut safe?
Only with exactly two resistors: R₁R₂/(R₁ + R₂). For 120 and 240 that gives 28800/360 = 80 Ω. For three or more, either use the reciprocal sum or combine two at a time.