Parallel Resistor Calculator
Two 100 ohm resistors wired in parallel give a total resistance of 50 ohms, while the same pair in series gives 200 ohms. This parallel resistor calculator finds the equivalent resistance of a group of resistors connected either in parallel or in series. Enter two to four resistor values in ohms, choose the wiring mode, and the tool returns the single resistance that the whole network behaves like. Parallel wiring always lowers the total below the smallest resistor because current has more than one path to flow through, while series wiring adds every resistor end to end so the total climbs above the largest single value. The math is simple once you know the two rules, but reciprocals are easy to get wrong by hand, especially with three or four resistors, so this tool does the arithmetic and rounds the answer to four decimal places for you. Use it to check a breadboard design, plan a resistor substitution, or study for an electronics exam.
Quick answer
Resistors in series add up directly, so the total resistance equals the sum of every resistor value.
What this tells you
- •Resistors in series add up directly, so the total resistance equals the sum of every resistor value.
- •Resistors in parallel combine by reciprocals, so one over the total equals the sum of one over each resistor.
- •A parallel network always has a lower resistance than its smallest resistor because current splits across several paths.
- •A series network always has a higher resistance than its largest resistor because current flows through each one in turn.
- •Two identical resistors in parallel give exactly half of one resistor value, a handy shortcut worth memorizing.
- •This tool ignores blank or zero entries so you can enter two, three, or four resistors without extra steps.
How to Use
- 11. Choose the wiring mode. Select Parallel if the resistors share the same two nodes, or Series if they are connected end to end in a single line.
- 22. Enter your first resistance in ohms in the Resistor 1 field. The default is 100 ohms.
- 33. Enter your second resistance in the Resistor 2 field. At least two positive values are required for a valid result.
- 44. Add a third or fourth resistor if your circuit has them. Leave any unused field blank or at 0 and the tool skips it.
- 55. Press Calculate and read the total resistance as the primary result, with the resistor count and sum shown underneath.
How It Works
Formula
Series: Rt = R1 + R2 + ... . Parallel: 1/Rt = 1/R1 + 1/R2 + ... , so Rt = 1 / (1/R1 + 1/R2 + ...)In series, the same current passes through every resistor, so the voltage drops add and the total resistance is the plain sum of each value. In parallel, every resistor sees the same voltage but shares the current, so the conductances (the reciprocals of resistance) add instead. That is why the parallel formula works with reciprocals. To find the total, you add one over each resistance, then take one over that sum. For two resistors this simplifies to the product over the sum, R1 times R2 divided by R1 plus R2, which is a quick way to check a two-resistor parallel result by hand. The calculator rounds the final total to four decimal places while keeping full precision during the calculation.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Two equal resistors in parallel
One over 100 plus one over 100 equals 0.02. One divided by 0.02 gives 50 ohms. Two identical resistors in parallel always halve the value, so this is a fast sanity check.
Mixed pair in parallel
Using the product over sum shortcut, 100 times 220 is 22000, and 100 plus 220 is 320. 22000 divided by 320 gives 68.75 ohms, safely below the smaller 100 ohm resistor.
Three resistors in parallel
One over 100 plus one over 200 plus one over 300 equals about 0.018333. One divided by that sum gives roughly 54.5455 ohms. Adding more parallel paths keeps pulling the total down.
The same three resistors in series
In series you simply add the values, so 100 plus 200 plus 300 gives 600 ohms. Notice how the same three resistors give 600 ohms in series but only about 54.5 ohms in parallel.
Common Two-Resistor Results
Total resistance for popular resistor pairs in both wiring modes.
| Resistor 1 (ohms) | Resistor 2 (ohms) | Parallel (ohms) | Series (ohms) |
|---|---|---|---|
| 100 | 100 | 50.00 | 200 |
| 100 | 200 | 66.67 | 300 |
| 100 | 220 | 68.75 | 320 |
| 220 | 330 | 132.00 | 550 |
| 1000 | 1000 | 500.00 | 2000 |
| 470 | 1000 | 319.73 | 1470 |
Parallel values are rounded to two decimals here for readability. The calculator itself rounds to four decimal places.
Why parallel resistance drops and series resistance climbs
The difference between series and parallel comes down to how current moves. In a series circuit there is only one path, so every electron must pass through each resistor one after another. Each resistor adds its own opposition to that single path, which is why the total resistance is just the sum of all the values and always ends up larger than any one resistor on its own.
In a parallel circuit the resistors sit side by side between the same two points, giving current several routes at once. More routes mean it is easier for current to flow overall, so the combined resistance drops. Adding another parallel resistor never raises the total, it can only lower it, because you are opening one more path. This is why the parallel result is always smaller than the smallest resistor in the group.
A practical use of this is building a resistance value you do not have on hand. If you need roughly 68 ohms but only own 100 ohm resistors, putting a 100 ohm and a 220 ohm in parallel gets you to 68.75 ohms. If you need a large value, chaining resistors in series adds them together. Understanding both rules lets you reach almost any target resistance from a small parts bin.
Common mistakes
- Adding resistances in parallel as if they were in series. Parallel resistors combine by reciprocals, not by a plain sum, so two 100 ohm resistors give 50 ohms in parallel, not 200.
- Forgetting to take the final reciprocal in parallel mode. Adding one over each resistor gives the total conductance, and you still have to divide one by that sum to get resistance.
- Entering a zero or blank resistor and expecting it to count. The tool ignores those entries, and in a real circuit a zero-ohm path would short out the network entirely.
- Mixing up which value should be smaller. A correct parallel result is always below the smallest resistor, so if your answer is larger than every input you have used the wrong mode.
- Assuming two resistors in parallel always halve the value. That shortcut only works when both resistors are equal, unequal pairs need the full reciprocal formula.
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