Resistors and capacitors in series and parallel
resistors: series R_eq = ΣRᵢ, parallel 1/R_eq = Σ(1/Rᵢ)
Paste your values (as many as you like, in the unit of your choice) and get the equivalent resistance or capacitance in series and in parallel, with the calculation displayed and the sanity guard (a parallel combination is always smaller than the smallest value, a series always larger than the largest). The voltage divider completes the tool, with its assumption stated: the formula holds unloaded, a connected load pulls the output down.
56.8966
- Calculation
- 1/R_eq = Σ(1/Rᵢ) (3 values) → R_eq = 56.8966
- Number of components
- 3, The result is in the unit of your values.
The equivalent (56.8966) is always smaller than the smallest value (100), every added branch gives the current one more path.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasresistors: series R_eq = ΣRᵢ, parallel 1/R_eq = Σ(1/Rᵢ)
resistors: series R_eq = ΣRᵢ, parallel 1/R_eq = Σ(1/Rᵢ)
capacitors: series 1/C_eq = Σ(1/Cᵢ), parallel C_eq = ΣCᵢ
voltage divider: V_out = V_in × R₂ / (R₁ + R₂)
Capacitors follow exactly the resistor formulas, swapped: that is the series/parallel duality. The physical reason: in series, resistors add their oppositions to the same current, while capacitors add their inverses (same charge, voltages add); in parallel it is the other way round. Useful special cases: two values in parallel give the “product over sum” R₁R₂/(R₁+R₂), and n equal values give R/n.
- Equivalent
- · the single value that, replacing the whole combination, leaves the rest of the circuit strictly unchanged. Same currents, same voltages at the terminals.
- Sanity guard
- · a parallel combination is always smaller than the smallest value; a series always larger than the largest. A result violating this rule is an input mistake, the tool shows the bound for an at-a-glance check.
- 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 here.
DC or instantaneous values only: complex impedances (capacitors under sinusoidal drive, inductors) are not handled here. Components are assumed ideal, no equivalent series resistance of a real capacitor, no tolerance: the computed equivalent is exact for the entered values, and real values deviate by the component tolerance (±5%, ±1%…). The idealisations 0 and ∞ are refused, and the refusal says why.
Common pitfall: 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. Connect a 10 kΩ load at the output: it sits in parallel with R₂ (10 kΩ ∥ 10 kΩ = 5 kΩ) and the output drops to 4 V, a third less. A voltage divider is only a voltage source if the load is much larger than R₂, which is why it is never used to power anything, only to provide a reference to a high-input-impedance circuit.