How this calculator works
- Step 1SeriesR₁ + R₂ + …One path: resistances add.
- Step 2Parallel1 ÷ (1/R₁ + 1/R₂ + …)Several paths: conductances add.
- Step 3CheckR∥ < smallestParallel is always below the smallest.
In series, current has one path through every resistor, so the resistances simply add. In parallel, current splits between paths, so it is the conductances, 1/R, that add.
That is why the parallel total is always less than the smallest resistor in the group.
Worked example: 100, 220 and 470 Ω
- Series
R₁ + R₂ + R₃- Parallel
1 ÷ (1/R₁ + 1/R₂ + 1/R₃)
- Series100 + 220 + 470790.0000 Ω
- Conductances1/100 + 1/220 + 1/4700.016673 S
- Parallel1 ÷ 0.01667359.9768 Ω
Read the result
n equal resistors in parallel give R ÷ n: two 1 kΩ give 500.0000 Ω, ten 100 Ω give 10.0000 Ω.
- 4.7k, 10k, 2k216.9000 kΩIn series. 4k7 means 4.7 kΩ.
- Same three in parallel1.3033 kΩBelow the 2.2 kΩ resistor.
Assumptions and limits
- Ideal partsExactly their marked values.
- ToleranceReal resistors vary by ±1% to ±5%.
- Simple groupsMixed networks: combine groups step by step.
- WattageCheck each resistor’s power rating separately.
Related electrical tools
Once resistors are combined, Ohm's law gives the current.
To relate voltage, current and resistance, use the Ohm’s law calculator. The RC time constant calculator adds a capacitor, and the voltage drop calculator covers cables.
Common mistakes
Mistake: Adding resistances in parallel.
Instead: Add their reciprocals, then take the reciprocal.
Mistake: Reading 4k7 as 47 kΩ.
Instead: The k marks the decimal point: 4.7 kΩ.
Checking the method
A separate script combines parallel resistors two at a time with the product-over-sum rule in exact fractions, and matches every golden total.
Read how we test our calculators, or browse more maths calculators.