Parallel Resistor Calculator

Resistors in parallel: equivalent resistance

For resistors in parallel, the equivalent resistance is given by 1/Rtotal = 1/R₁ + 1/R₂ + ... + 1/Rn. For exactly two resistors, the product-over-sum shortcut applies: R = (R₁·R₂) / (R₁ + R₂). The parallel total is always smaller than the smallest individual resistor. In series, by contrast, resistances simply add: Rtotal = R₁ + R₂ + .... This follows from Kirchhoff's current law (KCL): currents entering a node equal currents leaving it; in parallel each resistor sees the same voltage, in series each carries the same current. Examples: 100 Ω || 100 Ω = 50 Ω; 1 kΩ || 2 kΩ ≈ 666 Ω.

Applications: power, redundancy, custom values

Paralleling resistors splits the dissipated power across multiple components, useful when a single resistor would burn out. It also adds redundancy: if one resistor opens, the others keep conducting. Engineers use it to build non-standard values from E12/E24 series — e.g., 333 Ω from two 1 kΩ and a 1 kΩ, or 75 Ω from two 150 Ω in parallel.

FAQ

Why is the parallel total smaller than the smallest resistor? Adding another path for current to flow always lowers overall resistance — more "lanes" for electrons.

How is power shared? Each resistor dissipates P = V²/R with the same voltage, so smaller resistors burn more power. Match resistor wattage to the share each one will take.

Series or parallel for higher precision? Series is usually easier to tune (just add small values); parallel is preferred when you need to lower a resistance without changing the existing one.