Parallel resistor calculator: total resistance in parallel

For resistors in parallel, add the reciprocals of the resistances to get the reciprocal of the total: 1/R = 1/R₁ + 1/R₂ + .... For two resistors this is the product over the sum, so 6 Ω and 3 Ω in parallel make (6 × 3) ÷ (6 + 3) = 2 Ω. The total is always less than the smallest resistor. This parallel resistor calculator is the Resistor network mode of our Circuit Builder: it finds the equivalent resistance, the supply current and the current and voltage for every resistor.

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How to use the parallel resistor calculator

1. Open the Circuit Builder. It starts in Build a circuit, so choose Guided circuits and then Resistor network. Or pick Mixed network (series and parallel) from Load an example.
2. Each Branch is one path between the supply's terminals. Type its resistance in the box. Press Parallel branch to add another branch, up to four.
3. To put resistors in series within a branch, press Series resistor, up to four per branch. The bin icon removes one.
4. Set the Supply voltage.
5. Read the Equivalent resistance, the Supply current and the total power, then each resistor's voltage and current. The working adds each branch in series, then adds the reciprocals of the branches.

The network opens with 220 Ω and 330 Ω in series in branch 1, in parallel with 1000 Ω in branch 2, on a 5 V supply: example 5 below. You can also build parallel circuits part by part in Build a circuit and measure them with meters.

Parallel resistance formula

Work out the right-hand side, then take the reciprocal: that last step is the one most often forgotten. For exactly two resistors there is a shortcut, the product over the sum:

Why it works: every branch has the full supply voltage across it, so each draws its own current, V ÷ R. The currents add, and each extra branch gives the current another path, which lowers the total resistance. For comparison, resistors in series just add: R = R₁ + R₂ + ....

Worked examples you can check in the calculator

Example 1: two equal resistors

Two 100 Ω resistors in parallel: 1/R = 1/100 + 1/100 = 2/100, so R = 50 Ω. Any number of equal resistors in parallel gives one resistor's value divided by how many there are: three 1000 Ω resistors make 333 Ω.

Example 2: product over sum

6 Ω and 3 Ω in parallel make 2 Ω, less than either one.

Example 3: three resistors

So 1/R = 1/2 and R = 2 Ω. The product over sum shortcut is only for two at a time: for three, use reciprocals, or combine two and then the third.

Example 4: the current in each branch

The 6 Ω and 3 Ω resistors are connected to a 12 V supply. Each branch has the full 12 V, so the currents are 12 ÷ 6 = 2 A and 12 ÷ 3 = 4 A. The supply delivers 2 + 4 = 6 A, which matches 12 V ÷ 2 Ω. More current flows through the smaller resistor.

Example 5: series and parallel together

In the calculator's opening network, branch 1 has 220 Ω and 330 Ω in series, which add to 550 Ω. That branch is in parallel with 1000 Ω:

The equivalent resistance is 354.8 Ω, and the 5 V supply delivers 5 ÷ 354.8 = 14.1 mA. Always combine series resistors inside a branch first, then the branches in parallel.

Example 6: finding the resistor you need

You have a 100 Ω resistor and need 75 Ω. What should go in parallel with it? Rearrange: 1/R₂ = 1/75 − 1/100 = 4/300 − 3/300 = 1/300, so R₂ = 300 Ω. Type 100 and 300 as two branches to check that the calculator gives 75 Ω.

Try one, then press Mark to check your answer in the Circuits course.

Quick check

Rules for parallel circuits

• The total resistance is less than the smallest resistor. If your answer is bigger, something has gone wrong.
• Every branch has the same voltage: the supply voltage.
• The branch currents add up to the current from the supply.
• Adding a branch lowers the total resistance and raises the supply current.
• A very small resistance in one branch dominates. 1 Ω in parallel with 1000 Ω is just under 1 Ω.

Common mistakes

• Forgetting the last reciprocal. 1/6 + 1/3 = 0.5 is 1/R. The resistance is 2 Ω.
• Adding parallel resistors as if they were in series. Series resistors add; parallel ones add as reciprocals.
• Using product over sum for three or more. It only works for a pair.
• Splitting the voltage between parallel branches. It is the current that splits; every branch has the full voltage.
• Mixing Ω and kΩ. Convert to the same unit before you combine.

Read next

Physics · Electricity and magnetismSeries and parallel circuits: rules, resistors, examplesSeries and parallel circuits explained: current, potential difference and resistance rules, resistors in parallel, and worked GCSE and A-level examples.