Series and parallel resistor calculator

How to calculate resistors in series and parallel

In series, resistances add: R = R₁ + R₂ + …. In parallel, reciprocals add: 1/R = 1/R₁ + 1/R₂ + …. So 100 Ω, 220 Ω and 470 Ω resistors give 790 Ω in series and 59.98 Ω in parallel, below the smallest resistor, since each branch adds a path for current.

Working the parallel formula by hand

1. Take each reciprocal: 1/100 = 0.01, 1/220 = 0.004545 and 1/470 = 0.002128.
2. Add them: 0.016673 siemens.
3. Invert the sum: 1 ÷ 0.016673 = 59.98 Ω.

For exactly two resistors, product over sum is quicker: R = R₁R₂ ÷ (R₁ + R₂). 100 Ω and 220 Ω in parallel give 22,000 ÷ 320 = 68.75 Ω.

Equal resistors divide neatly: n of them give R/n in parallel and nR in series, so four 100 Ω resistors in parallel give 25 Ω. OpenStax derives both rules from current and voltage.

Capacitors and inductors in series and parallel

• Resistors and inductors: values add in series; reciprocals add in parallel.
• Capacitors: values add in parallel; reciprocals add in series.

So 10 µF and 22 µF give 32 µF in parallel but 6.875 µF in series, less than the smaller part. Three 100 nF capacitors in parallel give 300 nF (OpenStax).

Series capacitors carry the same charge, so the smaller one takes the larger share of the voltage. Across 12 V, the 10 µF part sees 8.25 V and the 22 µF part 3.75 V.

Inductors follow the resistor rules while their magnetic fields stay apart: 10 mH and 4.7 mH give 14.7 mH in series and 3.197 mH in parallel.

Coils that share flux need a mutual-inductance term, added or subtracted depending on the winding direction (HyperPhysics).

Mixed series-parallel networks

Reduce the network one group at a time. For 100 Ω in series with a parallel pair of 220 Ω and 470 Ω, combine the pair first: 220 × 470 ÷ 690 = 149.86 Ω. Then add the series part: 100 + 149.86 = 249.86 Ω.

Some networks, such as an unbalanced bridge with a resistor across its middle, cannot be reduced by series and parallel steps alone. Those need nodal analysis.

Power sharing in parallel resistors

Equal resistors in parallel share current, and power, equally. Unequal ones split it unequally: at 10 V, a 100 Ω resistor in parallel with a 220 Ω one dissipates 1.0 W against 0.45 W.

The smaller resistor carries the larger current, so with equal ratings it reaches its power limit first.

What a zero value does

A 0 Ω link in parallel shorts the whole group, so the equivalent is 0 Ω. A 0 F capacitor in series blocks the path, so the series capacitance is 0.

Equivalent values for the examples

Default is 100, 220 and 470 Ω in parallel, and series resistors is the same three in series. Series capacitors is 10 µF and 22 µF, and series inductors is 10 mH and 4.7 mH with no coupling.

Common mistakes

• Doubling the multiplier. Typing 1k with kΩ selected means 1,000 kΩ, so two in parallel give 500 kΩ, not 500 Ω.
• Using the resistor rule for capacitors. Capacitors add in parallel and combine by reciprocals in series.
• Judging the connection by the drawing. Parts drawn side by side are in parallel only if both ends share the same two nodes.
• Mixing units in one list. Convert 4.7 kΩ to 4,700 Ω, or type 4.7k, before combining it with values in ohms.
• Accepting a parallel total above the smallest part. That result means a value or the arrangement is wrong.

Value formats and units

• Separate values with commas or spaces, such as 100, 220, 470.
• Suffixes scale a value before the unit applies: 4.7k is 4,700 of the selected unit.
• One unit applies to the whole list, and values cannot be negative.
• Capacitor units run from pF to F, and inductor units from nH to H.

To find current and power once you know the resistance, use the Ohm's law calculator. The resistor color code calculator reads a resistor's value from its bands.