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Resistors and capacitors in series and parallel

Equivalent resistance or capacitance in series or parallel, and the voltage divider, with the series/parallel duality and the effect of a load on the output.

Parameters

One or more values per line, separated by spaces, all in the same unit (Ω, kΩ, F, µF…).

Result

Equivalent resistance

56.8966

Calculation
1/Req = Σ(1/Rᵢ) (3 values) → Req = 56.8966
Number of components
3 · The result is in the unit of the entered values.
100220330is equivalent toR_eq = 56.8966
Note

The equivalent (56.8966) is always smaller than the smallest value (100), every added branch gives the current one more path.

Calculation, assumptions and sources

OverviewAny number of values, in one unit, give the equivalent resistance or capacitance in series and in parallel, with the calculation and the sanity guard.

Any number of values, in one unit, give the equivalent resistance or capacitance in series and in parallel, with the calculation and the sanity guard. The voltage divider is computed unloaded; a connected load pulls the output down.

Method & formulasresistors: series R_eq = ΣRᵢ, parallel 1/R_eq = Σ(1/Rᵢ)
resistors: series Req = ΣRᵢ, parallel 1/Req = Σ(1/Rᵢ)capacitors: series 1/Ceq = Σ(1/Cᵢ), parallel Ceq = ΣCᵢvoltage divider: Vout = Vin × R₂ / (R₁ + R₂)

Capacitors follow the resistor formulas, swapped: in series, the inverses of the capacitances add (same charge, voltages add); in parallel, the capacitances add. Two values in parallel give R₁R₂/(R₁+R₂), n equal values give R/n.

Equivalent
the single value that, replacing the whole combination, leaves the rest of the circuit unchanged: same currents, same voltages at the terminals.
Sanity guard
a parallel combination is smaller than the smallest value, a series larger than the largest.
Unloaded divider
the formula V_out = V_in·R₂/(R₁+R₂) assumes no current leaves the midpoint. Any connected load sits in parallel with R₂ and lowers V_out.
Validity domainDC or instantaneous values only: complex impedances (capacitors under sinusoidal drive, inductors) are not handled.

DC or instantaneous values only: complex impedances (capacitors under sinusoidal drive, inductors) are not handled. Components are ideal, with no series resistance and no tolerance; real values deviate from the computed equivalent by the component tolerance (±5%, ±1%…). The idealisations 0 and ∞ (short circuit, open circuit) are outside the calculation.

The loaded voltage dividerA 10 kΩ/10 kΩ divider on 12 V gives 6 V unloaded.

A 10 kΩ/10 kΩ divider on 12 V gives 6 V unloaded. A 10 kΩ load at the output sits in parallel with R₂ (10 kΩ ∥ 10 kΩ = 5 kΩ) and the output drops to 4 V. The divider is only a voltage source if the load is much larger than R₂. It is therefore unsuited to powering a load; it serves to provide a reference to a high-impedance input.