Science calculator

Series and parallel resistance.

Compare the equivalent resistance of 2–8 resistors connected all in series or all in parallel. Enter each value in the units you have.

Connection

Number of resistors

Series resistance Rₛ

—

Rₛ = ΣRᵢ

Parallel resistance Rₚ: —

Result unit

Display precision

R_{s} = \sum_{i = 1}^{n} R_{i}

\frac{1}{R_{p}} = \sum_{i = 1}^{n} \frac{1}{R_{i}}

R_s equivalent series resistance · R_p equivalent parallel resistance · R_i each resistor · n number of resistors

Assumptions

Every component is an ideal, ohmic resistor with constant resistance.
For the series result, all resistors are connected end to end with no branches, so the same current passes through each one.
For the parallel result, every resistor is connected across the same two nodes, so each has the same potential difference.
Connecting wires have zero resistance; source and meter resistances are not included.
Resistance values are non-negative. A zero-ohm parallel branch is an ideal short circuit, giving zero equivalent resistance.

How it works

Series resistances add because the same current loses energy across each component in turn. The equivalent resistance is therefore larger than any individual resistor in the chain.

Parallel branches share the current while keeping the same potential difference. Their conductances, 1/R, add, so the equivalent resistance is smaller than the smallest branch resistance. This page compares the two arrangements; it does not simplify a mixed series–parallel circuit.

Results use up to three significant figures by default (adjustable above), without padding with trailing zeroes. Each input is converted to ohms before calculation, so mixed mΩ, Ω, kΩ and MΩ entries are valid.

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