Series and Parallel Resistance Calculator
Equivalent resistance of any number of resistors in series or in parallel.
What is Equivalent Resistance?
Resistors in series add up directly; resistors in parallel add up as reciprocals. The parallel case is the one that surprises people — the equivalent resistance is always smaller than the smallest resistor in the network, because every extra branch gives the current another path.
How it works
For series, R = R₁ + R₂ + …, and the same current flows through every resistor so the voltage divides in proportion to resistance. For parallel, 1/R = Σ(1/Rᵢ) — the reciprocal form rather than the two-resistor shortcut, so it scales to any number of rows — and the same voltage is across every resistor, so the current divides in proportion to conductance. That share is reported per resistor, since it is the number that reverses intuition: most of the current takes the smallest resistor.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
Why is parallel resistance smaller than any single resistor?
Because each additional branch is another path for the current, so more current flows for the same voltage — which is exactly what a lower resistance means.
What is the equivalent resistance of two 100 Ω resistors in parallel?
50 Ω. The reciprocal sum gives 1/100 + 1/100 = 0.02 S, and 1 ÷ 0.02 = 50 Ω. In series the same pair would be 200 Ω.
Can I mix series and parallel in one calculation?
Not in this tool — each calculation is purely series or purely parallel. For a mixed network, reduce the innermost parallel group first and then add the results in series.