Circuits and conductors
Two parallel resistors
- where
- total resistance (Ω)
- individual resistances (Ω)
Explain this equation
Works out the combined resistance of exactly two resistances in parallel. A quick shortcut for pairs.
Rₜ is the combined resistance. R₁ and R₂ are the two branch resistances connected across the same two points.
Product over sum is the reciprocal rule 1/Rₜ = 1/R₁ + 1/R₂ rearranged for two branches. It gives the same answer with less working.
Sense check: 10 Ω and 20 Ω give 200/30 ≈ 6.67 Ω. Two equal resistances give half of one. The result is always below the smaller one.
Watch out: product over sum does not work for three resistors at once. Combine a pair first, then add the third.
For exactly two parallel resistors, product divided by sum is a convenient rearrangement of the reciprocal formula.
Do not extend product-over-sum directly to three resistors. Reduce a pair first or use reciprocals.
Enter your values to see the result.
Common mistake
Using the product of three resistors divided by their sum.
Limits
Exactly two positive resistors in parallel.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.