Hong Life CalculatorsUnderstanding the resistors in series and parallel calculator — concept and principle
When several resistors are connected together, they can be replaced by a single equivalent resistance that draws the same current from the same voltage. This calculator gives that equivalent value for any list of resistors connected all in series or all in parallel. It is used to build a value you do not have in stock, to share power across several parts and to simplify a circuit before analysing it.
How it is calculated
- Series: R = R₁ + R₂ + … + Rₙ
- Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ, so R = 1 / Σ(1/Rᵢ)
Enter the resistances in ohms, separated by commas. For exactly two resistors in parallel the formula reduces to the familiar "product over sum": R = R₁R₂ / (R₁ + R₂).
The principle
In series, the same current I flows through every resistor, and the voltages add (Kirchhoff's voltage law): V = IR₁ + IR₂ + … = I(R₁ + R₂ + …), so the resistances add. In parallel, every resistor sees the same voltage V, and the branch currents add (Kirchhoff's current law): I = V/R₁ + V/R₂ + … = V(1/R₁ + 1/R₂ + …). The reciprocals, the conductances, add. Intuitively, a series chain is a longer path, so resistance grows; parallel branches are extra lanes for the current, so resistance falls.
Worked example
- Inputs: 100 Ω, 220 Ω and 470 Ω.
- Series: 100 + 220 + 470 = 790 Ω.
- Parallel: 1/100 + 1/220 + 1/470 = 0.0100000 + 0.0045455 + 0.0021277 ≈ 0.0166731 S.
- R = 1 / 0.0166731 ≈ 59.98 Ω (59.97679814).
How to read the result
The series value is always larger than the largest resistor, and the parallel value is always smaller than the smallest one: here 59.98 Ω is below 100 Ω. In parallel, the smallest resistor dominates; adding a very large resistor in parallel changes almost nothing. Two equal resistors in parallel give half the value, and n equal resistors give R/n. In series the current is the same in each part and the largest resistor dissipates the most power; in parallel the voltage is the same and the smallest resistor dissipates the most.
Common mistakes
- Adding parallel resistors directly or forgetting to take the reciprocal at the end.
- Using "product over sum" for three or more resistors at once; apply it in pairs or use the reciprocal sum.
- Mixing kΩ and Ω in the same list.
- Treating a mixed series-parallel network as purely one or the other; reduce it step by step.
Frequently asked questions
How do I make 150 Ω from standard values?
Two 300 Ω resistors in parallel, or 100 Ω and 47 Ω in series (147 Ω), depending on the accuracy you need.
Does connecting resistors in parallel increase the power rating?
Yes. Equal resistors in parallel share the power equally, so two identical 0.25 W resistors handle 0.5 W in total.
What happens if one parallel resistor is 0 Ω?
It is a short circuit: the equivalent resistance becomes 0 Ω and all the current flows through it.
Sources: G. Kirchhoff, Annalen der Physik und Chemie 64 (1845), on current distribution in networks · P. Horowitz and W. Hill, The Art of Electronics, Cambridge University Press