Series & Parallel Resistance
Find equivalent resistance for two resistors in series or in parallel. Clear formulas and steps for circuit homework and electronics practice.
Key formula
Series: R_t = R1 + R2; Parallel: 1/R_t = 1/R1 + 1/R2
How do you calculate equivalent resistance?
Series (one path): Rₜ = R₁ + R₂. Parallel (same two nodes): 1/Rₜ = 1/R₁ + 1/R₂, then invert for Rₜ. For two resistors in parallel you can also use Rₜ = (R₁ R₂)/(R₁ + R₂). Equal resistors in parallel give Rₜ = R/2.
About this tool
Series and parallel combinations are the foundation of most resistor networks. This page keeps Rₜ = R₁ + R₂ and 1/Rₜ = 1/R₁ + 1/R₂ visible so you can find equivalent resistance for a two-resistor pair before applying Ohm's law.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: series 100 Ω and 220 Ω
Rₜ = R₁ + R₂ = 100 + 220 = 320 Ω. Total current from a battery sees 320 Ω of opposition.
Example 2: parallel 100 Ω and 100 Ω
1/Rₜ = 1/100 + 1/100 = 0.02, so Rₜ = 50 Ω. Equal pair shortcut: R/2 = 50 Ω.
Example 3: parallel 6 Ω and 3 Ω
1/Rₜ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Rₜ = 2 Ω. Product-over-sum: (6×3)/(6+3) = 2 Ω.
Frequently asked questions
What is the series resistance formula?
For resistors in series, Rₜ = R₁ + R₂ + … . Current is the same through each; voltages add across them. For two resistors: Rₜ = R₁ + R₂.
What is the parallel resistance formula?
For resistors in parallel, 1/Rₜ = 1/R₁ + 1/R₂ + … . Voltage is the same across each branch. Two-resistor form: Rₜ = (R₁ R₂)/(R₁ + R₂).
How do I tell series from parallel?
Series: one path — current through R₁ must also pass through R₂. Parallel: the wire splits so each resistor has its own path between the same two junctions.
Why is parallel resistance smaller?
Parallel branches give current more paths, so the combination draws more current from the same voltage — that means lower equivalent R by Ohm's law.
What do I do after finding Rₜ?
Treat Rₜ like a single resistor in Ohm's law (V = IR) or electric power (P = I²R, P = V²/R). Use the voltage divider calculator when two resistors divide a supply, not for a simple parallel pair.