Parallel Resistance Calculator
Ω
Ω
Ω
Total Resistance56.8966 Ω
Total Conductance0.017576 S
Resistors3
The Parallel Resistance Calculator finds the single equivalent resistance of any number of resistors wired side by side across the same two nodes. When resistors share both ends, current splits between them, so the combined resistance is always lower than the smallest individual resistor. Add as many resistor values as your circuit has, and the tool sums their reciprocals to return the equivalent resistance along with the total conductance.
Formula
1 / Rt = 1/R1 + 1/R2 + … + 1/Rn
- Rt
- Equivalent parallel resistance (ohms)
- R1…Rn
- Each individual resistor in the parallel network (ohms)
How it works
- Enter each resistor value in ohms, using the add button to extend the list to as many parallel branches as you need.
- The calculator adds up the reciprocal of every resistance to get the total conductance, then takes the reciprocal of that sum to produce the equivalent parallel resistance.
- The result is always smaller than the lowest resistor in the set, and adding more branches lowers it further.
Worked example
A 60 Ω and a 30 Ω resistor connected in parallel.
- Sum of reciprocals = 1/60 + 1/30 = 0.016667 + 0.033333 = 0.05 S.
- Equivalent resistance = 1 ÷ 0.05 = 20 Ω.
The two resistors in parallel behave as a single 20 Ω resistor.
Frequently asked questions
- Why is the parallel resistance lower than every resistor?
- Adding a parallel branch gives current another path, so more total current flows for the same voltage. More current at the same voltage means less resistance, so the combined value drops below the smallest resistor.
- What is the quick rule for two equal resistors?
- Two equal resistors in parallel give exactly half the value of one. For example, two 100 Ω resistors in parallel equal 50 Ω. For N equal resistors the result is R divided by N.
- What is conductance and why is it shown?
- Conductance is the reciprocal of resistance, measured in siemens. Parallel resistances add directly as conductances, which is why the calculator reports the summed conductance alongside the equivalent resistance.
- Can I mix very different resistor values?
- Yes. The math handles any positive values, but a much smaller resistor dominates the result because it carries most of the current, so a large resistor in parallel barely changes the total.