Resistor Network Calculator
Combine up to 10 resistors in series or parallel. Live SVG schematic, total resistance, conductance, and optional current and power from an applied voltage.
- 1 / Rtotal = 1/R1 + 1/R2 + … + 1/Rn
- Gtotal = 1 / Rtotal
How It Works
- 1
Pick series or parallel
Series for current-sharing chains (voltage ladders, sense-resistor stacks). Parallel for voltage-sharing banks (splitting dissipation, lowering R below a single standard value).
- 2
Add each resistor and its unit
Use the + button for up to 10 resistors. Pick Ω, kΩ, or MΩ per row. The diagram and total update as you type.
- 3
Optional: apply a voltage for I and P
Tick the voltage box to compute total current I = V / R_total and total dissipation P = V² / R_total. Useful for checking whether a parallel bank clears its power rating.
Series and parallel resistor networks
Two rules cover almost every resistor network a working engineer needs to simplify. In series, resistances add: R_total = R1 + R2 + … + Rn. In parallel, conductances add: 1/R_total = 1/R1 + 1/R2 + … + 1/Rn. Both follow directly from the circuit laws Gustav Kirchhoff published in 1845. Series resistors share the same current, so their voltage drops stack; parallel branches share the same voltage, so their currents sum. These combinations show up in voltage reference ladders, sensor dividers, current-sense shunts banked in parallel to split heat, pull-up and pull-down stacks on digital buses, and resistor arrays that scale a single precision part into an arbitrary ratio. A deeper result — Thévenin's theorem (Léon Charles Thévenin, 1883) — says any passive two-terminal network of resistors and sources reduces to a single voltage source in series with a single equivalent resistance. The series-parallel rules are the algorithmic path to that equivalent. The common pitfall is tolerance stack-up: ten 1% resistors in series do not give 0.1% accuracy — the standard deviation adds in quadrature, so expect roughly 3.2% worst-case drift, and if the parts come from the same reel the drift is correlated, not averaged. Stick to 0.1% or 0.01% parts when the ratio needs to hold across temperature. For high-power parallel banks, match the resistances within a percent or better — the hottest resistor draws more current, heats up faster, and fails first in a thermal runaway.
Common pitfalls
Swapping series and parallel rules. Parallel resistors share the same voltage, currents sum. Series resistors share the same current, voltages sum. A 10 kΩ and 10 kΩ in parallel is 5 kΩ; in series it is 20 kΩ. Check the topology before the math.
Believing series stacking improves tolerance. Ten 1% resistors in series give a standard deviation that adds in quadrature, worst case ~3.2%, not 0.1%. If they come from the same reel, drift is correlated and the tolerance does not average out at all. Buy 0.1% or 0.01% parts when the ratio matters.
Ignoring power dissipation in the parallel bank. Two 100 Ω 1/4 W resistors in parallel still dissipate 1/4 W each; putting 24 V across the 50 Ω pair burns 11.5 W, far past the 0.5 W combined rating. Mismatched parts run hotter than matched ones and fail first (thermal runaway).
Forgetting voltage rating in series stacks. Stacking four 200 V-rated MELF resistors for 800 V only works if leakage and parasitic capacitance balance the voltage across each part. Manufacturers (e.g. Vishay PVC) make dedicated high-voltage series parts; do not roll your own from jellybean resistors.
Using the wrong reference point for R_total in voltage-divider math. V_out/V_in = R_bottom / (R_top + R_bottom), not R_bottom / R_top. Mix this up and the ratio inverts.
Frequently Asked Questions
When do resistors combine in series versus parallel?
Series is any chain where the same current flows through every resistor — a voltage-divider ladder, a current-sense stack, a string of LEDs sharing one limiter. Parallel is any branch where the same voltage appears across every resistor — banks of pull-ups, multiple shunts splitting current, a single load resistance built from two or more in parallel to spread the heat.
Why does adding a second equal resistor in parallel halve the total?
In parallel, conductance (1/R) is the quantity that adds. Two equal resistors supply twice the conductance of one, and the total resistance is the reciprocal — half the original. Three equal in parallel gives one third, ten equal gives one tenth, and so on. The general rule for n equal parallel resistors is R_total = R / n.
How accurate is a series or parallel network built from 1% resistors?
Tolerances add in quadrature, not linearly. Ten 1% resistors in series give a one-sigma spread of about 3.2%, and the worst case can exceed 10% at the tails. Resistors from the same reel are correlated, which helps some ratios and hurts others. For precision dividers and sense networks, spend on 0.1% or 0.01% parts rather than averaging more 1% parts.
Can I parallel two resistors to get twice the power rating?
Yes, but only if the resistances match closely. Two 200 Ω 1/4 W resistors in parallel give 100 Ω at 1/2 W total — but the resistor with the lower value hogs more current, heats up faster, and drifts further from its rated value. Matching the parts within a percent keeps dissipation even. For high-current shunts, prefer a single higher-rated part over a parallel bank.
What happens if one resistor opens or shorts?
In series, an open resistor breaks the chain — total resistance is infinite and no current flows. A short in one series element drops that section out of the sum. In parallel, an open resistor removes its branch — the total goes up. A short in one parallel branch shorts the whole network to zero ohms, which this calculator flags as a short.
How is this connected to Kirchhoff's laws and Thévenin's theorem?
Kirchhoff's current law says currents into a node sum to zero, which gives the parallel conductance rule. Kirchhoff's voltage law says voltages around a loop sum to zero, which gives the series resistance rule. Gustav Kirchhoff published both in 1845. Thévenin's theorem (Léon Charles Thévenin, 1883) goes further and says the whole network reduces to one voltage source and one resistance. The series-parallel rules are how you compute that equivalent by hand.
Does this calculator handle mixed series-parallel networks?
Not directly. You can work in stages: compute the parallel combination of a sub-branch here, then use that value as one element of a series calculation in another session. For more complex graphs (Wheatstone bridges, ladder networks), mesh or nodal analysis handles the whole circuit in one pass.
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