Calculate the total resistance of up to five resistors connected in series or parallel.
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When more than one electrical resistor is connected in a single circuit, the way total resistance is calculated differs depending on the type of connection. In a series connection, the same current flows through all the resistors, and the total resistance is simply the sum of all the resistances (R_total = R1 + R2 + ... + Rn). In a parallel connection, the current branches between the resistors and the total voltage drops equally across each of them, and the total resistance is calculated by adding the reciprocal of each resistance and then taking the reciprocal of the result (1/R_total = 1/R1 + 1/R2 + ... + 1/Rn), with the resulting total resistance always being smaller than the smallest individual resistance in the group. This calculator supports up to five resistors in the same calculation, letting you quickly evaluate both simple two-resistor combinations and more complex networks without working through the reciprocal arithmetic by hand for each additional component added.
The two basic ways to combine resistors — series and parallel — produce genuinely opposite effects on total resistance, and understanding why each rule works the way it does, rather than just memorizing the formulas, makes circuit analysis far more intuitive.
In a series connection, resistors are chained one after another, forcing the same current to pass through each one sequentially. Since each resistor independently opposes that current flow, and the same current has to overcome each resistor's opposition one after another, the total opposition simply adds up — which is why series resistance is just the straightforward sum of the individual values, with total resistance always exceeding any single resistor in the chain.
Parallel connections work completely differently: each resistor forms an independent path for current between the same two circuit nodes, meaning current has multiple simultaneous routes to flow through rather than one forced sequential path. Adding more parallel paths gives current more total ways to flow, which reduces the overall opposition the circuit presents — exactly why parallel resistance calculations always produce a result smaller than the smallest individual resistor in the group.
An intuitive way to see why parallel resistance decreases: adding a second, identical resistor in parallel with a first effectively doubles the cross-sectional 'width' available for current flow, which by definition halves the total resistance (two identical resistors in parallel always give exactly half the resistance of one alone) — adding more parallel paths continues this same pattern of ever-decreasing total resistance, though each additional identical resistor contributes progressively less reduction than the one before it.
This series-versus-parallel distinction has direct practical design consequences: circuit designers deliberately choose parallel resistor combinations when they need a resistance value lower than any single standard component provides, or when they need to distribute power dissipation across multiple physical resistors rather than concentrating it (and the resulting heat) into just one component — a common technique in power electronics where a single resistor might not be able to safely dissipate the required heat on its own.
Adding a parallel path always gives current an extra route to flow through, which increases total current for the same voltage — equivalent to reducing overall resistance below the smallest individual resistor.
This calculator handles a single group of resistors that are either all in series or all in parallel. For mixed networks, break the circuit into series and parallel sub-groups and calculate each stage separately.
No — the order in which resistors are connected does not affect the total resistance in either a pure series or pure parallel arrangement.