Resistors in Series/Parallel Calculator

Resistors in series and parallel are the two fundamental circuit configurations. Understanding how to calculate equivalent resistance is essential for every electronics project.

Series formula:

R_total = R1 + R2 + R3 + ... + Rn

Parallel formula (two resistors):

R_total = (R1 × R2) / (R1 + R2)

Parallel formula, general case for n resistors:

1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

What each variable means:

• Series: resistors connected end-to-end. The same current flows through all of them, and their voltages add up.
• Parallel: resistors connected side by side across the same two nodes. The same voltage applies to all of them, and their currents add up.
• R_total: the single equivalent resistance that the source “sees”

Worked examples:

Series: Three resistors: 100 Ω, 220 Ω, 470 Ω R_total = 100 + 220 + 470 = 790 Ω

Parallel (two): 1 kΩ and 1 kΩ in parallel: R_total = (1,000 × 1,000) / (1,000 + 1,000) = 1,000,000 / 2,000 = 500 Ω Two equal resistors in parallel always give half the value of one.

Parallel (three): 100 Ω, 200 Ω, 400 Ω: 1/R = 1/100 + 1/200 + 1/400 = 0.01 + 0.005 + 0.0025 = 0.0175 R_total = 1 / 0.0175 = 57.1 Ω

Key rules to remember:

• Series total is always larger than the largest individual resistor
• Parallel total is always smaller than the smallest individual resistor
• Adding a resistor in parallel always reduces total resistance
• Adding a resistor in series always increases total resistance

Why anyone combines resistors in the first place

Almost never for the theory. It is because the value you want does not exist as a part. Standard resistors come in the E-series: E12 gives twelve values per decade (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82), E24 gives twenty-four, and E96 gives ninety-six for 1% parts. If your design calls for 1,250 Ω, nothing in E12 or E24 is closer than 1,200 or 1,300, and two in series or parallel will get you there.

So the calculator also reports the nearest single E24 value to whatever total you build. If that value is within a fraction of a percent, buy the one part rather than soldering two, because every extra joint is another thing to go wrong and the tolerance stacking is worse, not better.

A word on tolerance stacking

Two 5% resistors in series do not give a 10% result. Errors that are independent tend to partly cancel, so the combination is statistically better than the worst case, though the guaranteed bound is still the sum. In parallel it is the low-value resistor that dominates both the total and the error, because it carries most of the current and sets most of the conductance. If you need precision from a combination, put the tight-tolerance part where it matters: the largest resistor in a series string, or the smallest in a parallel bank.

Power does not divide the way resistance does

This is the part that catches people out. In a parallel bank the smallest resistor gets the most current and dissipates the most heat, so sizing all the resistors to the same wattage as the average is a mistake. Work out the dissipation per part, which this calculator does once you give it a supply voltage, and rate the busiest one properly.