Resistors in series and parallel — formulas, current and power sharing, making values from standard resistors

A value your schematic needs is not in the series, a bus reads half the termination you expected, a resistor runs too hot — all of these come down to series and parallel combinations. The formulas are two lines, but how current and power divide is where they become useful.

Series: add

R = R1 + R2 + … + Rn
1 kΩ + 2.2 kΩ = 3.2 kΩ

In series the same current flows through every resistor and the voltage divides in proportion to resistance. The total is always above the largest resistor. Power is also proportional to resistance (P = I²R), so the larger one runs hotter.

Parallel: add reciprocals

1/R = 1/R1 + 1/R2 + … + 1/Rn
Two:   R = R1 × R2 ÷ (R1 + R2)
n equal values:   R ÷ n

10 kΩ ∥ 4.7 kΩ = 47,000,000 ÷ 14,700 ≈ 3.197 kΩ
10 kΩ ∥ 10 kΩ = 5 kΩ
10 kΩ ∥ 1 MΩ ≈ 9.90 kΩ (−1 %)

In parallel every resistor sees the same voltage and current divides in inverse proportion to resistance. The total is always below the smallest resistor. A large resistor in parallel lowers the value only slightly, which is handy for trimming.

How current and power divide in parallel

The smallest resistor takes the most current and power. To share power, use equal values: n of them each take 1/n. With different values, check the power rating of the smallest one first.

Making a value from two standard resistors

Resistors come in series values such as E12 (12 per decade), E24 (24) and E96 (96) — the IEC 60063 tables in Vishay document 28372. If the value you need is not in the series, join two in series or parallel. The partner comes from solving the formula backwards.

Series partner:    R2 = Rt − R1          (R1 < Rt)
Parallel partner:  R2 = R1 × Rt ÷ (R1 − Rt)   (R1 > Rt)

What in parallel with 10 kΩ gives 6 kΩ?  10k × 6k ÷ 4k = 15 kΩ
Exact from E12:  5 kΩ = 10k ∥ 10k,   3.3 kΩ = 1.8k + 1.5k

6.04 kΩ is an E96 value. Two E24 resistors get within 0.1 %, but if you need that precision a single E96 part is usually simpler. For a divider where the ratio matters, use the Voltage Divider Calculator's pairs, which match the ratio rather than one value.

What happens to tolerance

If two resistors have the same tolerance (say ±5 %) and both drift fully the same way, the series sum (R1 + R2) and the parallel value (R1R2 ÷ (R1 + R2)) both move by the same ±5 % — scaling both values by the same factor scales the result by that factor. Combining values hits the nominal value but does not shrink the tolerance, so if accuracy matters choose tighter-tolerance resistors.

Examples in the field

• RS-485 termination: with a device's built-in 120 Ω terminator and an external 120 Ω both on at the same end, that end is 120 ∥ 120 = 60 Ω. Correct termination, one at each end of the line, also measures 60 Ω across A-B (power off), so check the reading together with the number of devices and their built-in termination settings.
• 4–20 mA input resistor: without a 250 Ω part, use four 1 kΩ in parallel (250 Ω) or the E24 values 120 Ω + 130 Ω in series.
• LED current-limiting resistor: R = (supply − Vf) ÷ current. At 24 V, Vf 2 V and 10 mA that is 2.2 kΩ dissipating 0.22 W, over ten times the LED's 20 mW. A 1/4 W part leaves almost no margin, so use a higher rating or split it into two in series.

4k7 and 2M2 notation

Schematics and parts lists often put the unit letter where the decimal point goes: 4k7 (4.7 kΩ), 2M2 (2.2 MΩ), 0R47 (0.47 Ω). PortDock's resistor calculator reads this notation directly.

In PortDock

• «Parallel & Series Resistor Calculator» web tool: series and parallel totals, current share and currents, the partner value, and E12/E24/E96 pairs by error.
• «LED Resistor Calculator» web tool: supply, Vf, current and LEDs in series → resistor and power, current with a standard value.
• «Voltage Divider Calculator» web tool: standard R1/R2 pairs for a ratio, with load and tolerance.

Published 2026-10-23