Resistors in Parallel Calculator
Calculate the equivalent resistance of up to 4 resistors wired in parallel using 1/R = 1/R₁ + 1/R₂ + … Also shows the series equivalent for comparison.
How to use this tool
- Enter resistor r₁, resistor r₂, resistor r₃ (optional) and resistor r₄ (optional) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your parallel resistance and the full breakdown beneath it.
For resistors in parallel: 1/R = 1/R₁ + 1/R₂ + …. The equivalent resistance is always less than the smallest individual resistor. For two resistors: R = R₁R₂/(R₁+R₂).
Formula
1/Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4
Equivalent parallel resistance: Rp = 1 ÷ (1/R1 + 1/R2 + …). Series reference: Rs = R1 + R2 + …
How it works
When resistors are wired in parallel, each provides an independent current path, so the total conductance (reciprocal of resistance) is the sum of individual conductances. The calculator sums 1/R for every non-zero input value and inverts the total to get the parallel equivalent resistance.
A series sum is also shown for quick comparison. Results are rounded to 5 decimal places. The formula is exact for ideal resistors; real-world values have tolerance ratings (e.g. ±5%) that affect the true equivalent.
Worked example
- Given: R₁ = 10 Ω, R₂ = 20 Ω.
- Sum of conductances: 1/10 + 1/20 = 0.1 + 0.05 = 0.15 S.
- Parallel resistance: Rₚ = 1 / 0.15 = 6.6̇ Ω ≈ 6.66667 Ω.
- Series resistance (reference): Rₛ = 10 + 20 = 30 Ω.
Parallel resistance = 6.66667 Ω; Series resistance = 30 Ω.
Common mistakes to avoid
- Adding the resistances directly for parallel combinations as if they were in series; parallel equivalent resistance is always less than the smallest individual resistor.
- Forgetting to take the reciprocal at the end of the 1/R_total calculation, leaving the answer as a conductance (in siemens) rather than resistance (in ohms).
- Assuming equal power dissipation across parallel resistors; each resistor shares the same voltage but carries different current (and dissipates different power) if the resistances differ.
Key terms
- Parallel circuit
- A circuit configuration where components share the same two nodes, providing multiple independent current paths.
- Conductance (S)
- The reciprocal of resistance (1/R), measured in siemens (S). In parallel, conductances add directly.
- Equivalent resistance
- A single resistance value that produces the same electrical behaviour as the combination of resistors in a circuit.
- Series circuit
- A circuit where components are connected end-to-end in a single path; total resistance is the sum of individual resistances.
- Ohm (Ω)
- The SI unit of electrical resistance. A resistance of 1 Ω allows 1 A of current to flow under 1 V of potential difference.
Frequently asked questions
- Why is parallel resistance always less than any individual resistor?
- Adding a parallel path gives current more routes to flow, increasing total conductance (1/R). Higher conductance = lower resistance.
- What is the formula for exactly two resistors in parallel?
- R = R₁ × R₂ / (R₁ + R₂). Quick shortcut: two equal 10 Ω resistors in parallel give 5 Ω.