Resistors in series add up: Rtotal = R1 + R2 + …. Resistors in parallel combine as 1 ÷ (1/R1 + 1/R2 + …), and the total is always smaller than the smallest resistor. For example, 10 kΩ and 4.7 kΩ give 14.7 kΩ in series but only 3.2 kΩ in parallel. This free calculator handles up to 12 resistors, finds the resistor you need to reach a value, and shows the current and power in each one.
Series and parallel resistor calculator
Add up to 12 resistors to get the total resistance, or find the resistor you need in parallel to reach a value. Type values like 470, 10k, 4.7k, 4k7 or 1M.
Series and Parallel Resistor Formulas
| To find | Formula |
|---|---|
| Resistors in series | Rtotal = R1 + R2 + R3 … |
| Resistors in parallel | Rtotal = 1 ÷ (1/R1 + 1/R2 + 1/R3 …) |
| Two resistors in parallel | Rtotal = (R1 × R2) ÷ (R1 + R2) |
| n equal resistors in parallel | Rtotal = R ÷ n |
| n equal resistors in series | Rtotal = R × n |
| Resistor to add in parallel | R2 = 1 ÷ (1/Rtotal − 1/R1) |
Worked Example: Three Resistors in Parallel
- Take 1 kΩ, 2.2 kΩ and 4.7 kΩ.
- Work out each inverse: 1/1000 = 0.001, 1/2200 = 0.000455, 1/4700 = 0.000213.
- Add them: 0.001 + 0.000455 + 0.000213 = 0.001668.
- Take the inverse: 1 ÷ 0.001668 = about 600 Ω, lower than the 1 kΩ resistor.
In series, the same three resistors simply add up to 1 + 2.2 + 4.7 = 7.9 kΩ.
Worked Example: Finding a Parallel Resistor
Say you need 7.5 kΩ and you have a 10 kΩ resistor. R2 = 1 ÷ (1/7500 − 1/10000) = 30 kΩ, which is a standard E24 value. Put a 30 kΩ in parallel with the 10 kΩ and you get exactly 7.5 kΩ. The Find mode in the calculator does this for you and suggests the nearest standard values.
Make a Resistor Value You Do Not Have
Resistors come in standard series such as E12 and E24, so odd values are not always in your parts box. These combinations use common values.
| Value you need | How to make it | Result |
|---|---|---|
| 50 Ω | Two 100 Ω in parallel | 50 Ω |
| 165 Ω | Two 330 Ω in parallel | 165 Ω |
| 500 Ω | Two 1 kΩ in parallel | 500 Ω |
| 600 Ω | 1 kΩ and 1.5 kΩ in parallel | 600 Ω |
| 2.5 kΩ | Four 10 kΩ in parallel | 2.5 kΩ |
| 5 kΩ | Two 10 kΩ in parallel | 5 kΩ |
| 7.5 kΩ | Two 15 kΩ in parallel, or 10 kΩ and 30 kΩ in parallel | 7.5 kΩ |
| 13.9 kΩ | 10 kΩ and 3.9 kΩ in series | 13.9 kΩ |
| 20 kΩ | Two 10 kΩ in series | 20 kΩ |
| 200 kΩ | Two 100 kΩ in series | 200 kΩ |
Remember the tolerance. Two 5% resistors still give a result within about 5%. If you need an exact value, measure the combination with your multimeter before you solder it in.
Series vs Parallel: How They Behave
| Series | Parallel | |
|---|---|---|
| Total resistance | More than the largest resistor | Less than the smallest resistor |
| Current | The same through every resistor | Splits; the smallest resistor takes the most |
| Voltage | Splits in proportion to each resistor | The same across every resistor |
| Power | The largest resistor gets the most | The smallest resistor gets the most |
| If one resistor breaks open | Current stops in the whole chain | The others keep working, and the total goes up |
The split of voltage in series is what a voltage divider uses. To get the current or power for one resistor on its own, use the Ohm’s law calculator.
Mixed Series and Parallel Circuits
Work from the inside out. Combine each parallel group into one value first, then add the series parts.
- Example: a 1 kΩ resistor in series with two 2.2 kΩ resistors that are in parallel.
- The parallel pair: 2.2 kΩ ÷ 2 = 1.1 kΩ.
- Add the series part: 1 kΩ + 1.1 kΩ = 2.1 kΩ.
With the calculator, use Parallel mode for each group, write down the result, then use Series mode to add everything up.
Why Your Multimeter Reads Low on a Resistor in a Circuit
When a resistor is still soldered into a board, other parts are often connected across it. Your meter measures all those paths at once, which is the same as measuring resistors in parallel, so the reading is lower than the marked value. A 10 kΩ resistor with another 10 kΩ across it reads 5 kΩ.
- Turn the power off and let any large capacitors discharge.
- Measure in circuit first. If the reading matches the marked value, the resistor is fine.
- If it reads low, lift one leg of the resistor and measure again. That reading is the true value.
- Check the marked value with the resistor color code calculator.
- For values under about 10 Ω, touch the probes together first and subtract that reading, because the test leads add a little resistance.
Step-by-step help is in my guide on how to measure resistance with a multimeter.
Power Rating in Series and Parallel
Equal resistors share the power equally. Two 100 Ω, 1/4 W resistors in parallel make a 50 Ω resistor that can handle 1/2 W, and two in series make 200 Ω that can also handle 1/2 W. With different values the sharing is uneven: in parallel the smaller resistor gets hotter, and in series the larger one does. Add a voltage in the calculator to see the power in each resistor, and choose a rating at least twice that figure.
Frequently Asked Questions
How do you calculate resistors in parallel?
Add up the inverse of each resistor and take the inverse of the result: Rtotal = 1 ÷ (1/R1 + 1/R2 + 1/R3 …). For example, 1 kΩ, 2.2 kΩ and 4.7 kΩ in parallel give about 600 Ω.
What is the formula for two resistors in parallel?
Multiply them and divide by their sum: Rtotal = (R1 × R2) ÷ (R1 + R2). For 10 kΩ and 4.7 kΩ, that is 47 ÷ 14.7 = 3.2 kΩ.
Is the total resistance in parallel always lower than the smallest resistor?
Yes. Each extra resistor gives the current another path, so the total always ends up below the smallest single resistor in the group.
How do I calculate resistors in series?
Just add them: Rtotal = R1 + R2 + R3 …. A 1 kΩ, a 2.2 kΩ and a 4.7 kΩ in series give 7.9 kΩ. The order does not matter.
How can I make a resistor value I do not have?
Combine standard values. Two equal resistors in parallel give half the value, so two 10 kΩ make 5 kΩ. Two resistors in series add up, so 10 kΩ plus 3.9 kΩ makes 13.9 kΩ. The Find mode in the calculator shows which resistor to put in parallel to reach a value.
Why does my multimeter show a lower resistance in the circuit?
Other parts connected across the resistor form parallel paths, and parallel paths always lower the reading. Turn the power off and lift one leg of the resistor to read its true value.
Can I put resistors in parallel to get a higher wattage?
Yes, if they are the same value. Two equal resistors in parallel share the power equally, so two 1/4 W resistors act like one 1/2 W resistor at half the value. With different values, the smaller resistor takes more of the power.