About the Series and Parallel Resistor Calculator
This series and parallel resistor calculator finds the equivalent resistance of any number of resistors. Type the values separated by commas or spaces — you can use shorthand such as 4.7k, 4k7, 1M or 330R — and it returns both the parallel total and the series total, along with total conductance.
Enter a voltage to see how current divides between the resistors when they are wired in parallel, how much power each one dissipates, and what the supply must deliver. That makes it handy for building a non-standard value from parts in your drawer, checking heater or load banks, sizing shunts, and working through circuits homework.
Resistances in series simply add, so the total is always larger than the biggest resistor. In parallel the reciprocals add, so the total is always smaller than the smallest resistor, and the lowest resistor carries the most current. The calculator assumes ideal resistors and ignores tolerance and temperature drift.
With the default inputs, the parallel total is 59.977 Ω. Change any value above to recalculate instantly.
How to use the series and parallel resistor calculator
- 1Type the resistor values separated by commas, spaces or new lines.
- 2Use k for kilo-ohms and M for mega-ohms, e.g. 4.7k or 1M.
- 3Optionally enter the applied voltage to see currents and power.
- 4Read the parallel and series totals, then check the per-resistor table.
Formula and method
In series the same current flows through every resistor, so their voltage drops add and the total resistance is the plain sum. In parallel every resistor sees the same voltage and the branch currents add, so it is the conductances (1/R) that add; the equivalent resistance is the reciprocal of that sum. For two resistors this simplifies to R₁ × R₂ ÷ (R₁ + R₂).
With a voltage applied, each parallel branch carries I = V ÷ R and dissipates V² ÷ R. In series the current is V ÷ R_total, each resistor drops I × R, and dissipates I² × R.
- R
- Equivalent (total) resistance
- Rₙ
- Individual resistor values
- 1/R
- Conductance in siemens (S)
Worked examples
100 Ω, 220 Ω and 470 Ω
In parallel, 1/R = 1/100 + 1/220 + 1/470 = 0.016673 S, so R ≈ 59.98 Ω. In series they add to 790 Ω. At 12 V the parallel network draws about 0.2 A.
Two 1 kΩ resistors in parallel
Two equal resistors in parallel give half the value: 1,000 × 1,000 ÷ 2,000 = 500 Ω. In series they make 2 kΩ. At 5 V the parallel pair draws 10 mA and the series pair 2.5 mA.
Making 3.9 kΩ from 4k7 and 22k
Putting 4.7 kΩ in parallel with 22 kΩ gives 4,700 × 22,000 ÷ 26,700 ≈ 3,873 Ω — within 1% of a 3.9 kΩ value you might not have on hand.
Frequently asked questions
How do you calculate resistors in parallel?+
Add the reciprocals of each resistance and take the reciprocal of the sum: 1/R = 1/R₁ + 1/R₂ + … For two resistors, R = R₁ × R₂ ÷ (R₁ + R₂).
How do you calculate resistors in series?+
Simply add them: R = R₁ + R₂ + R₃ + … Three 100 Ω resistors in series make 300 Ω, and the same current flows through each one.
Why is parallel resistance less than the smallest resistor?+
Each extra parallel branch gives current another path, so the total conductance rises and the equivalent resistance falls. It is always lower than the smallest individual resistor.
What is the parallel resistance of identical resistors?+
N identical resistors of value R in parallel give R ÷ N. For example, four 1 kΩ resistors in parallel make 250 Ω, and each carries a quarter of the current.
How do I handle a mixed series-parallel network?+
Reduce it step by step: calculate each parallel group to a single equivalent value, then add those in series (or vice versa), working from the innermost group outwards.