Parallel Resistance Calculator
Calculate the equivalent resistance of 2 to 4 resistors in parallel. Uses 1/Rp = 1/R1 + 1/R2 + … Enter R3 and R4 as 0 to ignore them.
How to use this tool
- Enter r1, r2, r3 (optional) and r4 (optional) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your equivalent resistance and the full breakdown beneath it.
Resistors in parallel share the same voltage. The equivalent resistance is 1/Rp = 1/R1 + 1/R2 + …. The result is always less than the smallest individual resistor. For two equal resistors the result is exactly half of one resistor.
Formula
1 / Rp = 1/R1 + 1/R2 + 1/R3 + 1/R4
Equivalent resistance: Rp = 1 / (1/R1 + 1/R2 + …)
Total conductance: G = 1/Rp (siemens, S). R3 and R4 are included only when greater than zero.
How it works
Resistors in parallel share the same voltage, so their currents add; by Ohm's law this means their conductances (reciprocals of resistance) add, giving the reciprocal-sum formula 1/Rp = Σ(1/Ri).
The calculator supports two to four resistors; R3 and R4 are ignored when set to zero, allowing the tool to also solve two-resistor combinations. All resistors are assumed to be ideal, linear, and at the same temperature.
Worked example
Worked example — two 1000 Ω resistors in parallel
- R1 = 1000 Ω, R2 = 1000 Ω (R3 and R4 set to 0, so ignored).
- Reciprocal sum = 1/1000 + 1/1000 = 0.001 + 0.001 = 0.002 S.
- Equivalent resistance R_p = 1 / 0.002 = 500 Ω.
- Total conductance G = 0.002 S.
Equivalent resistance = 500 Ω; conductance = 0.002 S.
Key terms
- Parallel circuit
- A circuit configuration where all components share the same two nodes, so each sees the same voltage; total current divides among branches.
- Conductance (G)
- The reciprocal of resistance (G = 1/R), measured in siemens (S); conductances add directly in parallel, whereas resistances do not.
- Equivalent resistance
- A single resistance value that produces the same current draw from the source as the full parallel combination.
- Reciprocal-sum formula
- 1/R_p = 1/R1 + 1/R2 + …; the standard rule for calculating the equivalent resistance of parallel resistors.
- Siemens (S)
- The SI unit of electrical conductance; 1 S = 1 A/V, equal to the reciprocal of one ohm.
Frequently asked questions
- Why is the result always lower than the smallest resistor?
- Adding parallel paths gives current more routes to flow, reducing total opposition. Each additional resistor adds conductance (1/R) to the total.
- What is the quick formula for two resistors in parallel?
- Rp = (R1 × R2) / (R1 + R2) — the product over sum. Works only for two resistors.