How to Calculate Equivalent Resistance: Series & Parallel (R₁ + R₂)

Find equivalent resistance for series (Rₜ = R₁ + R₂) and parallel (1/Rₜ = 1/R₁ + 1/R₂) pairs. Worked examples, traps, and a free calculator.

What Equivalent Resistance Asks

Real circuits often have more than one resistor. Equivalent resistance Rₜ is a single value that behaves like the whole combination — same total current from the battery or same voltage drop across the branch.

For two resistors the rules are: series Rₜ = R₁ + R₂, and parallel 1/Rₜ = 1/R₁ + 1/R₂. All values are in ohms (Ω).

If you already have R₁ and R₂, open the free series & parallel resistance calculator first, then return here for spotting series vs parallel and linking to Ohm's law.

Series vs Parallel

Series: one path — current is the same through each resistor. Resistances add: Rₜ = R₁ + R₂.

Parallel: same two nodes — voltage is the same across each branch. Reciprocals add: 1/Rₜ = 1/R₁ + 1/R₂.

Series total is always larger than either resistor. Parallel total is always smaller than the smallest resistor.

Trace the wire: if current must pass through R₁ then R₂ with no split, it is series. If the wire splits so each resistor has its own path between the same two points, it is parallel.

The Formulas

Series: Rₜ = R₁ + R₂.

Parallel: 1/Rₜ = 1/R₁ + 1/R₂, then invert to get Rₜ.

Two-resistor parallel shortcut: Rₜ = (R₁ R₂) / (R₁ + R₂).

Equal resistors in parallel: two R in parallel give Rₜ = R/2.

After You Find Rₜ

Use equivalent R in Ohm's law V = IR to find total current or voltage across the combination.

For power dissipation, try the electric power calculator with P = I²R or P = V²/R once you know I or V.

When two resistors divide a supply voltage (not the same as parallel), use the voltage divider calculator instead.

Units

Resistances → ohms (Ω). Convert kΩ to Ω (× 1000) before combining.

Do not mix mA with Ω in Ohm's law without converting amperes.

Worked Examples

Example 1: series 100 Ω and 220 Ω

Rₜ = 100 + 220 = 320 Ω.

Example 2: parallel 100 Ω and 100 Ω

1/Rₜ = 1/100 + 1/100 = 2/100, so Rₜ = 50 Ω. Shortcut: equal pair → R/2.

Example 3: parallel 6 Ω and 3 Ω

1/Rₜ = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Rₜ = 2 Ω. Check: (6×3)/(6+3) = 18/9 = 2 Ω.

Example 4: 12 V across 320 Ω series pair

After Example 1, I = V/R = 12/320 = 0.0375 A = 37.5 mA total through both resistors.

Common Mistakes

Adding reciprocals for a series circuit (should add R directly).

Adding R₁ + R₂ for parallel (should use reciprocal rule).

Forgetting to invert after 1/Rₜ = 1/R₁ + 1/R₂.

Confusing parallel combination with a voltage divider on a single supply.

Check It on the Calculator

Series & parallel resistance calculator.

Ohm's law calculator.

Electric power calculator.

Learn Rₜ for series and parallel pairs and confirm every circuit homework number on the calculator.

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