Parallel Resistance Calculator Formula

Understand the math behind the parallel resistance calculator. Each variable explained with a worked example.

Formulas Used

Total Resistance

total_resistance = 1 / (1/r1 + 1/r2)

Variables

VariableDescriptionDefault
r1Resistor 1(Ω)100
r2Resistor 2(Ω)200

How It Works

Parallel Resistance

Resistors in parallel share the same voltage, and the reciprocals of their resistances add.

Formula

1/R_total = 1/R1 + 1/R2 + ...

For two resistors: R_total = (R1 * R2) / (R1 + R2)

The total is always less than the smallest individual resistor.

Worked Example

Two resistors in parallel: 100 Ω and 200 Ω.

r1 = 100r2 = 200
  1. 011/R = 1/100 + 1/200 = 0.01 + 0.005 = 0.015
  2. 02R = 1 / 0.015 = 66.67 Ω
  3. 03Or: R = (100 * 200) / (100 + 200) = 20000 / 300 = 66.67 Ω

Frequently Asked Questions

Why is parallel resistance lower than either individual resistor?

Each parallel path provides an additional route for current to flow, reducing the overall opposition to current.

What if two equal resistors are in parallel?

The total resistance is exactly half of either one. For example, two 100 Ω resistors in parallel give 50 Ω.

How does this apply to household wiring?

Outlets in a house are wired in parallel so each receives the full supply voltage and can operate independently.

Ready to run the numbers?

Open Parallel Resistance Calculator