Parallel Resistance

1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

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Result
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Formula

1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

Description

Parallel resistors share the same voltage across them, and the total resistance is found by the reciprocal of the sum of reciprocals. The result is always less than the smallest individual resistor because each additional path provides more ways for current to flow. For two resistors the shortcut formula Rtotal = (R1 × R2) / (R1 + R2) is often used. Two equal resistors in parallel yield exactly half of one resistor's value.

Variables

  • Rtotal — Total equivalent resistance (Ω)
  • R1, R2, ... Rn — Individual resistor values (Ω)

Practical Notes

Parallel combinations are used to create lower resistance values, increase power handling capacity, and reduce the effective tolerance of a resistor network. In PCB design, parallel resistors are also used as termination networks for high-speed signal lines.

Related Formulas

Series Resistance LED Resistor Resistor Power Derating Resistive Attenuator Resistor Tolerance Range Resistor Thermal Noise (Johnson–Nyquist)

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