Resistors in Series/Parallel Calculator
Calculate total resistance for up to 5 resistors in series or parallel.
Returns equivalent resistance, current at a given voltage, and power dissipation.
Resistors in series and parallel are the two fundamental circuit configurations. Understanding how to calculate equivalent resistance is essential for every electronics project.
Series formula:
R_total = R1 + R2 + R3 + ... + Rn
Parallel formula (two resistors):
R_total = (R1 × R2) / (R1 + R2)
Parallel formula (general — n resistors):
1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn
What each variable means:
- Series — resistors connected end-to-end; the same current flows through all; voltages add up
- Parallel — resistors connected side-by-side sharing the same two nodes; the same voltage applies to all; currents add up
- R_total — the single equivalent resistance that the source “sees”
Worked examples:
Series: Three resistors: 100 Ω, 220 Ω, 470 Ω R_total = 100 + 220 + 470 = 790 Ω
Parallel (two): 1 kΩ and 1 kΩ in parallel: R_total = (1,000 × 1,000) / (1,000 + 1,000) = 1,000,000 / 2,000 = 500 Ω Two equal resistors in parallel always give half the value of one.
Parallel (three): 100 Ω, 200 Ω, 400 Ω: 1/R = 1/100 + 1/200 + 1/400 = 0.01 + 0.005 + 0.0025 = 0.0175 R_total = 1 / 0.0175 = 57.1 Ω
Key rules to remember:
- Series total is always larger than the largest individual resistor
- Parallel total is always smaller than the smallest individual resistor
- Adding a resistor in parallel always reduces total resistance
- Adding a resistor in series always increases total resistance