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Resistors in parallel calculator
Electricity
The total resistance of two resistors in parallel, found from the sum of the reciprocals.
1 / Rtotal = 1 / R1 + 1 / R2
This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equation1 / Rtotal = 1 / R1 + 1 / R2
- Rearrange to make Rtotal the subjectRtotal = 1 / (1 / R1 + 1 / R2)
- Substitute the valuesRtotal = 1 ÷ (1 ÷ 6 + 1 ÷ 12)
- CalculateRtotal = 4 Ω
- Give the answer to 3 significant figuresRtotal = 4.00 Ω
Worked example
Find Rtotal, the total resistance. Given: resistance R1 = 6.00 Ω; resistance R2 = 12.0 Ω.
- Write the equation1 / Rtotal = 1 / R1 + 1 / R2
- Rearrange to make Rtotal the subjectRtotal = 1 / (1 / R1 + 1 / R2)
- Substitute the valuesRtotal = 1 ÷ (1 ÷ 6 + 1 ÷ 12)
- CalculateRtotal = 4 Ω
- Give the answer to 3 significant figuresRtotal = 4.00 Ω
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| Rtotal | Total resistance | Ω |
| R1 | Resistance | Ω |
| R2 | Resistance | Ω |
Resistors in parallel: rearranged
- To find total resistance: Rtotal = 1 / (1 / R1 + 1 / R2)
- To find resistance: R1 = 1 / (1 / Rtotal − 1 / R2)
- To find resistance: R2 = 1 / (1 / Rtotal − 1 / R1)
Exam tip
The total is always smaller than the smallest single resistor. Do not forget the final reciprocal.
Common questions
What is the formula for resistors in parallel?
The equation is 1 / Rtotal = 1 / R1 + 1 / R2, where Rtotal is the total resistance (Ω); R1 is the resistance (Ω); R2 is the resistance (Ω).
What units should I use for resistors in parallel?
In SI units: total resistance in Ω, resistance in Ω, resistance in Ω. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange 1 / Rtotal = 1 / R1 + 1 / R2?
Rearranging gives these forms: to find total resistance: Rtotal = 1 / (1 / R1 + 1 / R2). to find resistance: R1 = 1 / (1 / Rtotal − 1 / R2). to find resistance: R2 = 1 / (1 / Rtotal − 1 / R1).
Practise resistors in parallel questions
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Related
Read the full explanation on the Resistors in parallel formula page. More electricity equations: Charge, current and time, Ohm’s law, Electrical power, Electrical power, Energy transferred, Resistors in series, Resistivity, EMF and internal resistance. See the full list on the physics equation calculator page.