Parallel & Series Resistor Calculator — Build Mixed Circuits
Combine resistors in parallel, series or nested groups. Keep every original part and inspect its DC voltage, current and power.
SERIES & PARALLEL RESISTORS
Build the circuit. Keep every resistor.
Start with a parallel pair, then combine groups while keeping the original parts and their results.
No resistance tolerance entered.
2 original resistors retained
Your circuit
Select a resistor in the diagram or the list below to edit it. Wider circuits scroll inside the diagram.
Circuit inputs
- R1: 100 Ω, tolerance ±0%
- R2: 200 Ω, tolerance ±0%
Resistance-only calculation; no applied voltage.
Nominal DC results
- Total source current
- Source current range from resistance tolerances
- Total nominal dissipation
| Resistor | Voltage | Current | Power |
|---|
Per-resistor voltage, current and power are nominal, not worst-case tolerance maxima. The power result does not select or approve a component rating; check the part’s datasheet and thermal conditions.
Reduce the groups, keep the parts
- Network: R1 (100 Ω) ∥ R2 (200 Ω) = 66.66667 Ω
∥ means parallel. Each group can be replaced by its equivalent for calculation, while the original resistors remain in your circuit.
The parallel example is calculated. Enable JavaScript to edit the circuit.
Formulas, tolerances and model limits
Series resistance is the sum of the resistances, and the same current passes through each part. Parallel resistance is 1 / (1/R₁ + 1/R₂ + …), and each branch has the same voltage. Mixed series-parallel groups are reduced recursively; voltages and currents are then distributed back to every original resistor.
For an exact applied DC voltage V, total current is V / R and power is V × I. The original part’s nominal power is its voltage times its current. R₁ = 100 Ω and R₂ = 200 Ω in parallel give 66⅔ Ω. Add 300 Ω in series: the total is 366⅔ Ω. At 12 V, the original parallel parts share approximately 2.181818 V and carry 21.81818 mA and 10.90909 mA; the series part carries 32.72727 mA.
Each resistor’s stated tolerance gives minimum and maximum resistance. Positive ideal series-parallel resistance increases when any component resistance increases, so setting every part to its minimum or maximum gives the network’s range. This is a bounded range, not a probability distribution or an RSS tolerance. Source-current bounds use this range at the exact entered voltage. Per-part currents and powers are nominal only.
Scope: 1 µΩ–1 TΩ per part, 0–99% resistance tolerance, optional 0–1,000,000 V DC, up to 16 resistors, 2–8 children per group and five nested levels. These are numerical limits, not approved operating voltages. Short circuits, open circuits, bridge networks that cannot be reduced to series-parallel groups, AC impedance, heating, temperature drift, supply internal resistance and physical component approval are outside the model.
Source: OpenStax: resistors in series and parallel. The mixed-network calculations and tolerance propagation are independently derived. Choose a current-limiting resistor for an LED or explore RC timing for those separate circuit tasks.
