Resistors in parallel and in series
When you combine resistors, the circuit behaves as if it contained a single resistor with an equivalent value. How you work that value out depends on whether the resistors share the same current (series) or the same voltage (parallel).
Parallel resistors
Resistors are in parallel when both ends of each one connect to the same two points. The current splits between them, and the total resistance is the reciprocal of the sum of reciprocals:
1 / Rtotal = 1 / R1 + 1 / R2 + … + 1 / Rn
For exactly two resistors this simplifies to the product over the sum, R1 × R2 ÷ (R1 + R2). Two equal resistors in parallel give half the value, and n equal resistors give R ÷ n. The total is always lower than the smallest resistor in the group, because each extra path lets more current through.
Each resistor carries current in proportion to its conductance (1/R), so the smallest resistor carries the largest share. The percentages next to each value above show that split.
Series resistors
Resistors are in series when they are connected end to end so the same current flows through each one. Their values simply add: Rtotal = R1 + R2 + … + Rn. The supply voltage divides between them in proportion to their resistance, which is how a voltage divider works.
Why combine resistors?
- To make a value you do not have, such as 5 kΩ from two 10 kΩ resistors in parallel.
- To share heat: two resistors in parallel or series can each dissipate their full rating, doubling the total.
- To trim a value precisely by adding a large resistor in parallel with a slightly-too-high one.
Using this calculator
Type values with SI prefixes such as 4.7k, 4k7 or 1M. Press Enter to add a new row, Backspace in an empty row to remove it, and the arrow keys to move between rows. The quick-add buttons append common E12 values.
