Series and Parallel Resistor Calculator

How it works

Resistors in series carry the same current one after another, so their resistances add: R = R1 + R2 + …. The supply voltage divides between them in proportion to their resistance, so the largest resistor drops the most voltage.

Resistors in parallel each sit across the full supply voltage, so their conductances (1 ÷ R) add: 1/R = 1/R1 + 1/R2 + …. The equivalent is always smaller than the smallest resistor, and the current divides inversely to resistance, so the smallest resistor carries the most current.

With the supply voltage entered, the calculator applies Ohm's law to the equivalent resistance for the total current and to each resistor for its own voltage, current and power.

Formula

series:    R = R1 + R2 + … + Rn
           I = V ÷ R;   Vk = I × Rk
parallel:  1/R = 1/R1 + 1/R2 + … + 1/Rn
           two resistors: R = R1 × R2 ÷ (R1 + R2)
           Vk = V;   Ik = V ÷ Rk
power:     Pk = Vk × Ik;   P = V × I

Example

Three resistors of 3 kΩ, 10 kΩ and 5 kΩ in series on 9 V, the defaults, add to 18,000 Ω. The current is 9 ÷ 18,000 = 0.0005 A (0.5 mA), and the voltage drops are 1.5 V, 5 V and 2.5 V, which add back to 9 V. Total power is 9 × 0.0005 = 0.0045 W.

Resistors of 10 kΩ, 2 kΩ and 1 kΩ in parallel on 9 V give 1 ÷ (0.0001 + 0.0005 + 0.001) = 625 Ω. The branch currents are 0.0009 A, 0.0045 A and 0.009 A, totalling 0.0144 A (14.4 mA), and the total power is 0.1296 W.

Assumptions and limitations

• Resistors are ideal and constant: values are taken as entered, with no tolerance band or change with temperature. A 5% resistor can be 5% off its marked value.
• All resistors are either all in series or all in parallel. Mixed networks can be reduced in steps by running the calculator on each group.
• The supply is an ideal DC source (or the RMS value of an AC source driving resistors only), and wiring resistance is ignored.
• Power figures show what each resistor dissipates; they do not check it against the resistor's power rating.

Frequently asked questions