How to Calculate Series and Parallel Resistors
Resistors in series add up: R = R1 + R2 + … (the value increases). Resistors in parallel combine as 1/R = 1/R1 + 1/R2 + … (the value is smaller than the smallest resistor). For two resistors the handy shortcut is R = (R1 × R2) / (R1 + R2). For example, 100 Ω and 220 Ω give 320 Ω in series and ~68.75 Ω in parallel.
By wiring resistors in series or parallel you can obtain a value you do not have on hand and set how current and power are shared. The two arrangements change the total resistance in opposite directions: series increases it, parallel decreases it. Below are the formulas, handy shortcuts and worked examples.
Series resistors: the values add up
In a series connection the resistors are placed end to end and the same current flows through all of them. The total (equivalent) resistance is simply the sum:
Rtotal = R1 + R2 + … + Rn
The result is always larger than the biggest resistor. In a series circuit the source voltage is shared between the resistors in proportion to their values (series vs parallel circuits).
Parallel resistors: reciprocals decrease the value
In a parallel connection the resistor terminals are common and the same voltage is applied to all of them; the current splits between branches. The equivalent resistance is the reciprocal of the sum of reciprocals:
1 / Rtotal = 1/R1 + 1/R2 + … + 1/Rn
The result is always smaller than the smallest resistor. Two common shortcuts:
| Case | Shortcut |
|---|---|
| Two resistors (R1, R2) | R = (R1 × R2) / (R1 + R2) |
| n EQUAL resistors (R) | Rtotal = R / n |
Formula summary
| Connection | Formula | Total resistance | Shared quantity |
|---|---|---|---|
| Series | R = R1 + R2 + … | Increases | Same current |
| Parallel | 1/R = 1/R1 + 1/R2 + … | Decreases | Same voltage |
Worked examples
- Series: 100 Ω + 220 Ω = 320 Ω.
- Parallel (equal): 100 Ω ‖ 100 Ω = 100 / 2 = 50 Ω.
- Parallel (unequal): 1 kΩ ‖ 2 kΩ = (1000 × 2000) / (1000 + 2000) = 2,000,000 / 3000 ≈ 667 Ω.
How to solve a mixed (series + parallel) circuit
In mixed circuits simplify from the inside out: first reduce parallel groups to a single resistor, then add the series values. Example: 100 Ω in series with a (300 Ω ‖ 600 Ω) parallel group.
- Parallel group: (300 × 600) / (300 + 600) = 180,000 / 900 = 200 Ω.
- Series total: 100 Ω + 200 Ω = 300 Ω.
Common mistakes
- Forgetting the reciprocals in parallel: the parallel result is not the average of the two values; work with reciprocals.
- Using the shortcut for more than two resistors: R1×R2/(R1+R2) is for TWO resistors only; use the full reciprocal formula for three or more.
- Ignoring power sharing: in a series circuit the largest resistor dissipates the most power; check each resistor's power rating.
Use the calculator
To enter several resistors in series or parallel and get the equivalent value instantly, use our Parallel/Series Resistor Calculator.