Circuits and conductors
Parallel resistance
- where
- total resistance (Ω)
- individual resistances (Ω)
Explain this equation
Works out the combined resistance of three branches connected across the same two points. Useful for parallel elements, earth paths and loads.
Rₜ is the combined resistance. R₁, R₂ and R₃ are the branch resistances, all with the same voltage across them. 1/R is conductance: how easily each branch passes current.
Each branch offers an extra path, so their conductances add. Taking the reciprocal of the total conductance turns it back into resistance.
Sense check: 10, 20 and 30 Ω in parallel give about 5.45 Ω. The answer is always smaller than the smallest branch.
Watch out: do not stop after adding the reciprocals. That figure is conductance; flip it to get ohms.
Parallel branches share the same two connection points. Add their conductances, then take the reciprocal to return to resistance.
For positive resistances the answer is smaller than the smallest branch resistance. Use this check before submitting.
Enter your values to see the result.
Common mistake
Stopping after adding reciprocals: that result is conductance, not resistance.
Limits
Three finite positive resistor branches across the same two nodes.
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.