Series and Parallel Resistance Formulas

Resistors combine differently depending on how they are wired. In series, current flows through each resistor in turn and the voltage drops add up, so the total resistance is simply the sum. In parallel, current splits between the resistors and the total resistance is always lower than the smallest individual resistor. This page covers both formulas, the two-resistor parallel shortcut, and the worked examples that show why parallel resistance is always less than the smallest branch.

Formulas

Series: R_total = R1 + R2 + R3 + ...

Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

Two parallel: R_total = (R1 × R2) / (R1 + R2)

In series, resistances add directly. Current flows through each resistor sequentially. In parallel, the reciprocals add. Current splits across multiple paths, reducing total resistance. The total parallel resistance is always less than the smallest individual resistor.

Worked Examples

Example 1: Three 100Ω resistors in series

R = 100 + 100 + 100 = 300 Ω

Example 2: Three 100Ω resistors in parallel

1/R = 1/100 + 1/100 + 1/100 = 3/100. R = 100/3 = 33.3 Ω

Example 3: 10Ω and 20Ω in parallel

R = (10 × 20) / (10 + 20) = 200 / 30 = 6.67 Ω

Common Mistakes

Adding resistances in parallel instead of using the reciprocal formula.
Forgetting that parallel resistance is always LESS than the smallest resistor.
Using the two-resistor shortcut formula for three or more resistors.

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This is a formula reference page for educational use. Always consult a licensed electrician and verify compliance with the National Electrical Code (NEC) and local electrical codes before applying any of these formulas to real installations.

Standards & References

This page cites the following electrical codes and standards. Always consult the current edition of your local adopted standard for authoritative requirements.

NIST SP 811: SI Unit Definitions. Definitions of the volt, ampere, watt, ohm, coulomb, and joule under the International System of Units (SI). Authoritative reference for unit conversions and precision.
National Institute of Standards and Technology. Reference →

Disclaimer: The information on this page is provided for reference. Always consult a licensed electrician and the current edition of your local adopted electrical code before performing electrical work.