Parallel Resistor Calculator

Use the reciprocal formula: 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn. Add the reciprocals (1/R) of each resistor value, then take the reciprocal of that sum to find the total parallel resistance. For example, two resistors of 100Ω and 200Ω in parallel: 1/Rt = 1/100 + 1/200 = 0.015, so Rt = 1/0.015 = 66.67Ω.

Each resistor in a parallel circuit provides an additional path for current to flow. More paths mean less overall opposition to current flow, so the total resistance decreases. Mathematically, adding any positive term to the sum 1/R1 + 1/R2 + ... makes the sum larger, and since Rt = 1/(sum), Rt gets smaller. The total is always less than the smallest individual resistor.

When all resistors have the same value R, the total parallel resistance is simply Rt = R / n, where n is the number of resistors. For example, four 1,000Ω resistors in parallel give 1,000 / 4 = 250Ω. This shortcut is commonly used in circuit design to create precise resistance values not available as standard components.

For exactly two resistors, there is a simplified “product over sum” formula: Rt = (R1 × R2) / (R1 + R2). This is mathematically equivalent to the reciprocal formula but easier to compute by hand. For example, 100Ω and 200Ω: Rt = (100 × 200) / (100 + 200) = 20,000 / 300 = 66.67Ω.

If any resistor in a parallel combination is zero ohms (a short circuit), the total parallel resistance becomes zero regardless of the other resistor values. All current takes the path of least resistance through the short, effectively bypassing every other resistor in the parallel group.