Generated on: June 17, 2026 at 05:24 PM

Series and Parallel Resistor Calculator

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Physics

Series and Parallel Resistor Calculator

Add any number of resistors and get both the series total (R₁ + R₂ + …) and the parallel total (1 / (1/R₁ + 1/R₂ + …)) at once. Works with ohms, kilohms and megohms.

Inputs

Resistors

  • #1
    Resistor
    Output
  • #2
    Resistor
    Output

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Series and parallel resistors

Resistors combine in two basic ways. In series they sit one after another on a single wire; in parallel they bridge the same two points. The two arrangements behave oppositely, and this calculator reports both totals at once for any number of resistors you enter.

Series: resistances add

When resistors are in series the same current flows through every one, and their resistances simply add:

Rseries=R1+R2+R3+⋯R_{series} = R_1 + R_2 + R_3 + \cdots

The total is always larger than the largest single resistor. Two 100 Ω100\ \Omega resistors in series make 200 Ω200\ \Omega.

Parallel: reciprocals add

When resistors are in parallel they share the same voltage, and the reciprocals of the resistances add:

1Rparallel=1R1+1R2+1R3+⋯\frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots

so

Rparallel=11R1+1R2+⋯R_{parallel} = \frac{1}{\dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots}

The total is always smaller than the smallest single resistor, because adding another path makes it easier for current to flow. Two 100 Ω100\ \Omega resistors in parallel make 50 Ω50\ \Omega.

Worked example

Three resistors of 100 Ω100\ \Omega, 200 Ω200\ \Omega and 300 Ω300\ \Omega:

Rseries=100+200+300=600 ΩRparallel=11100+1200+1300=10.01833…≈54.5 Ω\begin{aligned} R_{series} &= 100 + 200 + 300 = 600\ \Omega \\ R_{parallel} &= \frac{1}{\frac{1}{100} + \frac{1}{200} + \frac{1}{300}} \\ &= \frac{1}{0.01833\ldots} \approx 54.5\ \Omega \end{aligned}

The two-resistor shortcut

For exactly two resistors in parallel, the reciprocal formula simplifies to the product over the sum:

Rparallel=R1⋅R2R1+R2R_{parallel} = \frac{R_1 \cdot R_2}{R_1 + R_2}

This is quick to do by hand, but it only works for two resistors at a time; for more, the full reciprocal formula is needed. This calculator uses the general formula, so you can add as many resistors as your circuit has.

Why it matters

Combining resistors is one of the most common steps in circuit analysis. Series strings set a total resistance or divide a voltage; parallel branches lower resistance, share current, or set a precise value that no single standard resistor provides. Reducing a network to a single equivalent resistance is usually the first move before applying Ohm's law.

Limitations

The formulas assume ideal resistors and ignore the resistance of the connecting wires, which is normally negligible. Real resistors also have a tolerance — often 1 % or 5 % — so a measured combination will differ slightly from the calculated value. Power ratings still apply to each resistor individually and must be checked separately.

Frequently Asked Questions (FAQ)

How do you add resistors in series?

Resistors in series simply add: R = R₁ + R₂ + R₃ + … The same current flows through each one, and the voltages across them add up to the supply. Two 100 Ω resistors in series make 200 Ω. The series total is always larger than the largest individual resistor.

How do you add resistors in parallel?

For resistors in parallel the reciprocals add: 1/R = 1/R₁ + 1/R₂ + 1/R₃ + … so R = 1 / (1/R₁ + 1/R₂ + …). Each resistor sees the same voltage, and the branch currents add. Two 100 Ω resistors in parallel make 50 Ω. The parallel total is always smaller than the smallest individual resistor.

What is the difference between series and parallel?

In series the components form a single path, so the same current passes through all of them and resistances add. In parallel they share the same two connection points, so they see the same voltage and the currents split between them. Series raises the total resistance; parallel lowers it.

Is there a shortcut for two resistors in parallel?

Yes — for exactly two resistors the parallel value is the product over the sum: R = (R₁·R₂)/(R₁+R₂). For 100 Ω and 200 Ω that is (100×200)/(100+200) = 20000/300 ≈ 66.7 Ω. For three or more resistors, use the full reciprocal formula, which this calculator applies automatically as you add rows.

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