Series & Parallel Resistor Calculator

When two resistors are wired together, their combined — or equivalent — resistance depends on how they are connected. This calculator gives both results at once: the equivalent resistance of R₁ and R₂ in series and in parallel.

Series and parallel resistance

In series, the same current flows through both resistors one after another, so their resistances simply add:

• R series = R₁ + R₂

The series total is always greater than either resistor on its own.

In parallel, the current splits between the two paths. For two resistors the convenient product-over-sum form is:

• R parallel = (R₁ × R₂) / (R₁ + R₂)

The parallel total is always smaller than the smaller of the two resistors, because adding another path makes it easier for current to flow.

How to use this calculator

1. Enter Resistor 1 (R₁) in ohms.
2. Enter Resistor 2 (R₂) in ohms.
3. Read the parallel and series equivalent resistances.

Examples

100 Ω and 200 Ω. In series: 100 + 200 = 300 Ω. In parallel: (100 × 200) / 300 ≈ 66.67 Ω.

Two equal resistors. 1 kΩ and 1 kΩ in series give 2 kΩ; in parallel they give 500 Ω — exactly half, which holds for any two equal resistors.

Very different values. 10 Ω in parallel with 1 MΩ is ≈ 10 Ω: the much larger resistor carries almost no current, so the small one dominates.

Frequently asked questions

Why is parallel resistance smaller than either resistor? Adding a second path gives current another way through, lowering the overall opposition — so the equivalent is always below the smallest branch.

Can I extend this to three or more resistors? Yes — combine two at a time. For three in parallel, find the parallel of two, then combine that result with the third using the same product-over-sum rule.

What units should I use? Enter both resistors in the same unit (ohms here); the results come out in that unit.

References

• Resistors in Series and Parallel — Basic Electronics Tutorials
• Simple Parallel Circuits — All About Circuits