How it works
In series the same current flows through every resistor, so the resistances simply add. In parallel each resistor sees the same voltage and the currents add, so the conductances (1/R) add.
A parallel combination is always smaller than the smallest resistor in it. Two equal resistors in parallel give half the value; n equal resistors give R ÷ n.
Combining standard values is a common way to make an odd resistance, or to spread heat across several parts so each one stays within its wattage rating.
Formula
Series: R = R₁ + R₂ + … + Rₙ Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ
Questions people ask
Is there a shortcut for two resistors in parallel?
Yes: R = (R₁ × R₂) ÷ (R₁ + R₂), the "product over sum". For 100 Ω and 220 Ω that is 22,000 ÷ 320 = 68.75 Ω.
Why is parallel resistance lower than any single resistor?
Each added resistor gives current another path, so the total current rises for the same voltage. More current at the same voltage means less resistance.
How does power split between them?
In series the largest resistor dissipates the most power (P = I²R). In parallel the smallest resistor dissipates the most (P = V²/R).