Parallel resistor calculator

Type the resistances separated by commas: `100, 220` or `4.7k, 10k, 22k`. The total appears with its working, and Show the steps draws the circuit. Pick In series from the menu to add them end to end instead.

Values can use k for kilohms and M for megohms, or the code printed on many parts, where the letter stands in for the decimal point. 4k7 is 4.7 kΩ and 4R7 is 4.7 Ω.

Side by side, resistors give the current more than one path, so the total is lower than any one of them. Add up the reciprocals and take the reciprocal of the answer, so 1/R = 1/R₁ + 1/R₂ + 1/R₃ and so on.

For exactly two there's a shortcut, product over sum. 100 Ω and 220 Ω in parallel is (100 × 220) ÷ (100 + 220) = 22,000 ÷ 320 = 68.75 Ω. Equal resistors are easier still. n of them in parallel give one of them divided by n, so two 10 kΩ make 5 kΩ.

End to end, the same current goes through every resistor and the resistances simply add. 4.7 kΩ, 220 Ω and 100 Ω in series is 5.02 kΩ. Series is how you make a value you don't have in the drawer, and parallel is how you get one lower than any you have, or spread the heat across several parts.

Both rules follow from the circuit laws Gustav Kirchhoff published in 1845, in his early twenties. Current flowing into a junction equals current flowing out, so parallel branches share the current. The voltages round any closed loop add to zero, so series resistors share the voltage. Every circuit calculator, this one included, is those two sentences plus Ohm's law.