Beginner
Parallel Resistance Formula
Calculate total resistance for parallel resistors — two-resistor shortcut and general formula for any number of resistors.
Formulas
1/Rt = 1/R₁ + 1/R₂ + 1/R₃ + ...
General parallel resistance formula
Rt = (R₁ × R₂) / (R₁ + R₂)
Two-resistor shortcut (product over sum)
Rt = R / N (equal resistors)
N equal resistors in parallel
Variable Definitions
Rt=Total parallel resistance(ohms (Ω))
R₁, R₂...=Individual resistor values(ohms (Ω))
N=Number of equal resistors(count)
Worked Example
Three resistors in parallel: 10Ω, 20Ω, and 30Ω.
- 1/Rt = 1/10 + 1/20 + 1/30
- 1/Rt = 0.100 + 0.050 + 0.033 = 0.183
- Rt = 1/0.183 = 5.45Ω
Answer: 5.45Ω (always less than the smallest resistor)
When to Use
- •Calculating parallel conductor impedance for voltage drop
- •Ground fault loop impedance with multiple ground paths
- •Parallel battery bank internal resistance
- •Any circuit with multiple parallel current paths
Standards & References
- Fundamental — applies to all parallel conductor calculations per NEC 310.10(G)