Answer first
What this calculator tells you
Calculate the combined resistance of up to three resistors in series and in parallel. Find one resistor value that stands in for a network on a circuit board. Formula: Series: R = R₁ + R₂ + R₃; parallel: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + 1 ÷ R₃ (a zero-ohm resistor in parallel is a short circuit, so the result is 0). At the worked-example inputs, the series resistance (ohms) is 650. Holding every other input steady, moving resistor 1 (ohms) from 80 to 120 moves the result from 630 to 670.
Transparent method
The formula
Find one resistor value that stands in for a network on a circuit board.
Worked example
Example inputs
How to interpret the result
Resistors add in series and combine in reverse in parallel. Three resistors of 100, 220 and 330 ohms make 650 ohms in a chain, but only about 57 ohms side by side, less than the smallest one. Current takes every path it can, so more paths always lower the total resistance. That is the reason a parallel branch can never raise resistance.
At the worked-example inputs the series resistance (ohms) is 650. It rises with resistor 3 (ohms), resistor 2 (ohms) and resistor 1 (ohms).
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model.
Before you rely on it
What to check
Confirm how the parts are wired. A resistor in line with the current is in series, and one connected across the same two points is in parallel.
The common error
Where people go wrong with series and parallel resistor calculator
Adding resistances in parallel like a series chain. The result is always larger than any single part, which cannot be true when current has extra paths.
Sensitivity evidence
How resistor 1 (ohms) changes the series resistance (ohms)
Holding every other input at the worked-example value, moving resistor 1 (ohms) from 80 to 120 moves the series resistance (ohms) from 630 to 670: a spread of 40, or 6% of the worked-example result.
| Resistor 1 (ohms) | Series resistance (ohms) | Parallel resistance (ohms) |
|---|---|---|
| 80 | 630 | 49.8 |
| 90 | 640 | 53.5 |
| 100worked example | 650 | 56.9 |
| 110 | 660 | 60 |
| 120 | 670 | 62.9 |
Every input, tested
Which input moves the series resistance (ohms) most
Of the 3 inputs, resistor 3 (ohms) moves the series resistance (ohms) most (66 across the range tested) and resistor 1 (ohms) moves it least (20).
| Input | Tested from | To | Series resistance (ohms) at each end | Swing |
|---|---|---|---|---|
| Resistor 3 (ohms) | 297 | 363 | 617 to 683 | 66 (10%) |
| Resistor 2 (ohms) | 198 | 242 | 628 to 672 | 44 (6.8%) |
| Resistor 1 (ohms) | 90 | 110 | 640 to 660 | 20 (3.1%) |
Two variables at once
Series resistance (ohms) by resistor 1 (ohms) and resistor 2 (ohms)
Across the grid the series resistance (ohms) runs from 586 to 714. Moving resistor 1 (ohms) from 80 to 120 shifts it by 40 at the middle column, and moving resistor 2 (ohms) from 176 to 264 shifts it by 88 at the middle row, so resistor 2 (ohms) is the bigger lever here.
| Resistor 1 (ohms) \ Resistor 2 (ohms) | 176 | 220 | 264 |
|---|---|---|---|
| 80 | 586 | 630 | 674 |
| 90 | 596 | 640 | 684 |
| 100 | 606 | 650 | 694 |
| 110 | 616 | 660 | 704 |
| 120 | 626 | 670 | 714 |
The highlighted cell is the worked example: 650.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Resistor 1 (ohms) | 100 | Enter the resistor 1 (ohms) used in this calculation. |
| Resistor 2 (ohms) | 220 | Enter the resistor 2 (ohms) used in this calculation. |
| Resistor 3 (ohms) | 330 | Enter 0 if you only have two resistors. A third value of 0 is left out of both sums. |
| Series resistance (ohms) | 650 | |
| Parallel resistance (ohms) | 56.9 | |
Inputs, definitions and assumptions
Resistor 1 (ohms)
Enter the resistor 1 (ohms) used in this calculation. The prefilled worked-example value is 100.
Resistor 2 (ohms)
Enter the resistor 2 (ohms) used in this calculation. The prefilled worked-example value is 220.
Resistor 3 (ohms)
Enter 0 if you only have two resistors. A third value of 0 is left out of both sums. The prefilled worked-example value is 330.
How to use this calculator
- 1Verify the inputs. Gather resistor 1 (ohms), resistor 2 (ohms) and resistor 3 (ohms) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the series resistance (ohms) at 650. Store your own version of it as Scenario A.
- 3Test one change. Start with resistor 3 (ohms), the input with the biggest effect here: moving resistor 3 (ohms) from 297 to 363 takes the series resistance (ohms) from 617 to 683, a swing of 10% of the worked-example figure.
- 4Check the extremes. At half the example resistor 3 (ohms) (165) the series resistance (ohms) is 485; at double (660) it is 980.
People also ask
Frequently asked questions
How do you calculate series and parallel resistor?
Series: R = R₁ + R₂ + R₃; parallel: 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + 1 ÷ R₃ (a zero-ohm resistor in parallel is a short circuit, so the result is 0). At the worked-example inputs the series resistance (ohms) is 650.
What does the series and parallel resistor result mean?
Find one resistor value that stands in for a network on a circuit board. At the worked-example inputs the series resistance (ohms) is 650. It rises with resistor 3 (ohms), resistor 2 (ohms) and resistor 1 (ohms).
How much does resistor 1 (ohms) change the series resistance (ohms)?
Holding every other input at the worked-example value, moving resistor 1 (ohms) from 80 to 120 moves the series resistance (ohms) from 630 to 670, a spread of 40.
What are the limits of this series and parallel resistor calculator?
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model. The tables on this page test resistor 1 (ohms) only from 80 to 120; a value outside that range is not tabulated here.
Which input moves the series resistance (ohms) most in the series and parallel resistor calculator?
Ranked by how far each moves the series resistance (ohms) across the range tested: resistor 3 (ohms) (66, 10%), resistor 2 (ohms) (44, 6.8%) and resistor 1 (ohms) (20, 3.1%).
If I double resistor 3 (ohms) in the series and parallel resistor calculator, does the series resistance (ohms) double?
Doubling it from 330 to 660 takes the series resistance (ohms) from 650 to 980, which is 1.51 times the worked-example figure. So it grows, but by less than double. Halving it to 165 gives 485.
How much does resistor 2 (ohms) matter in the series and parallel resistor calculator?
The worked example uses 220. Holding every other input at its worked-example value, moving resistor 2 (ohms) from 198 to 242 takes the series resistance (ohms) from 628 to 672, a swing of 6.8% of the worked-example figure.
How much does resistor 3 (ohms) matter in the series and parallel resistor calculator?
The worked example uses 330. With the other inputs left at the worked example, moving resistor 3 (ohms) from 297 to 363 takes the series resistance (ohms) from 617 to 683, a swing of 10% of the worked-example figure.
Which inputs change the parallel resistance (ohms) in the series and parallel resistor calculator?
At the worked-example inputs it is 56.9. Resistor 1 (ohms) takes it from 53.5 to 60, resistor 2 (ohms) takes it from 55.3 to 58.3 and resistor 3 (ohms) takes it from 55.8 to 57.8.
Why does wire gauge affect voltage drop?
A thinner wire (higher AWG number) has more electrical resistance per foot than a thicker one. So it dissipates more voltage as heat over the same run length and current. Long runs or high currents need a thicker gauge to keep voltage drop within an acceptable range.
What does specific gravity actually tell you?
How dense a substance is relative to water. A specific gravity above 1 means it's denser than water and will sink in it. Below 1 means it's less dense and will float. It's a quick, unit-independent way to compare materials.
Sources and evidence
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