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Resistors in parallel formula
A parallel circuit is characterized by a common potential difference (voltage) across the ends of all resistors. The equivalent resistance for this kind of circuit is calculated according to the following formula:
- is the equivalent parallel resistance
- are the resistances of individual resistors numbered .
The units of all values are Ohms (symbol: Ω). 1 Ohm is defined as electrical resistance between two points that, when applied with a potential difference of 1 volt, produces a current of 1 ampere. Hence,
1 Ω = 1 V / 1 A or, in SI base units,
Ω = kg·m²/(s³·A²).
The formula for resistors in parallel is similar to the formula for inductors in parallel.
How to calculate parallel resistance
The parallel resistor calculator has two different modes. The first mode allows you to calculate the total resistance equivalent to a group of individual resistors in parallel. In contrast, the second mode allows you to set the desired total resistance of the bunch and calculate the one missing resistor value, given the rest.
To keep it simple, we only show you a few rows to input numbers, but new fields will magically appear as you need them. You can input up to 10 resistors in total.
Let's look at an example for the second, slightly more complicated, mode:
Calculate missing resistorunder Mode.
- Now input the total resistance you want your circuit/collection of resistors to have.
- Start by introducing the values of the resistors you already know (new fields will appear as needed).
- The calculator automatically gives you the required missing resistor after each input.
Other uses of the parallel resistor calculator
The principle is the same as when determining capacitance in series or induction in parallel – you can use it for these calculations too. Just remember that the units are not the same!
How do you calculate two resistors in parallel?
Take their reciprocal values, add the two together and take the reciprocal again. For example, if one resistor is 2 Ω and the other is 4 Ω, then the calculation to find the equivalent resistance is 1 / (1/2 + 1/4) = 1 / (3/4) = 4/3 = 1.33.
Is the voltage the same in a parallel circuit?
Yes, the voltage across all the components is the same in a parallel circuit.
Why does resistance decrease in parallel?
This phenomenon happens because the current has many more paths that it could take. Imagine a shop opens up several new check-out tills. The overall resistance to people going through the check-out will decrease as the workload is shared in parallel.
How do you find an unknown resistor in a parallel circuit?
Rearrange the parallel resistor formula 1/R = 1/R₁ + 1/R₂ + ... + 1/Rn in terms of Rn, given that you know the desired overall resistance. That gives you Rn = (1/R - 1/R₁ + 1/R₂ + ...)-1.
For example, if you have R1 = 4, R2 = 2 and want R = 1, then R4 = 1 / (1 - 1/4 - 1/2) = 4 Ω.