Series & Parallel Resistors
Equivalent resistance of resistors in series or parallel, the voltage, current and power in each one at your supply, and the resistor to add to hit a target.
One equivalent value for the network, a per-resistor table of volts, amps and watts when a voltage is applied, and the extra resistor that reaches a target value.
Example: 100 Ω, 220 Ω and 330 Ω in parallel are 56.90 Ω; on 12 V the network draws 210.9 mA and the 100 Ω part dissipates 1.44 W. In series they are 650 Ω.
Sum the ohms,
or sum the siemens.
The two rules, how the voltage and current divide, how the “resistor to add” is found, and what an ideal resistor leaves out.
Series and parallel
In series the same current flows through every resistor, so resistances add: R = R₁ + R₂ + … In parallel every resistor sees the same voltage, so conductances add: 1/R = 1/R₁ + 1/R₂ + …, which is why the parallel total is always below the smallest resistor. For two resistors this is the familiar R₁R₂ ÷ (R₁ + R₂). Mixed networks are solved by reducing one group at a time; enter each group here and carry the result forward.
With a voltage applied
The total current is V ÷ R. In series each resistor drops I × Rᵢ, and the drops add up to the supply; in parallel each branch carries V ÷ Rᵢ, and the branch currents add up to the total. Each part dissipates V × I. The page flags any part above 0.25 W because small through-hole resistors are commonly rated at that level — the rating that applies is the manufacturer's for the part you use.
The resistor to add
Given a target value, one more resistor in the same arrangement reaches it: in series add R_target − R; in parallel add 1 ÷ (1/R_target − 1/R). A series addition can only raise the total and a parallel addition can only lower it, so the page says when a target is on the wrong side. The result is an exact value; the nearest stock value and its tolerance are yours to choose.
What the number does not settle
Resistors are treated as ideal and at their nominal value: tolerance bands, temperature coefficient, self-heating and lead or contact resistance are not modelled. Reactive parts (capacitors, inductors) do not combine this way at AC. Inputs stay in your browser; the same four anonymous usage counts as the rest of the site apply.