Resistors in Series & Parallel Calculator

How to use the resistors in series & parallel calculator

Enter up to three resistor values (Ω, kΩ or MΩ). You get the total for both a series and a parallel connection. For just two resistors, set R3 to a very large value such as 1e12 Ω.

Resistors in series & parallel formulas

Series: R = R₁ + R₂ + R₃
Parallel: 1/R = 1/R₁ + 1/R₂ + 1/R₃

Worked example

100 Ω, 220 Ω and 470 Ω:

• Series = 790 Ω
• Parallel = 1 ÷ (1/100 + 1/220 + 1/470) = 60.0 Ω

Quick rules

• Two equal resistors in parallel → half the value (2 × 1 kΩ = 500 Ω).
• n equal resistors in parallel → R ÷ n.
• Parallel total is always smaller than the smallest single resistor.

Two resistors in parallel: shortcut

For two resistors, the parallel value is the product over the sum:

R = R₁ × R₂ ÷ (R₁ + R₂)

100 Ω and 220 Ω in parallel = 22,000 ÷ 320 = 68.75 Ω.

Making a value you do not have

Target	Combination	Result
50 Ω	Two 100 Ω in parallel	50 Ω
150 Ω	100 Ω + 47 Ω in series	147 Ω
330 Ω	220 Ω + 100 Ω + 10 Ω in series	330 Ω
4.7 kΩ	10 kΩ ∥ 8.2 kΩ (close)	4.51 kΩ

Voltage divider

Two resistors in series divide a voltage:

V_out = V_in × R₂ ÷ (R₁ + R₂)

With 12 V, R₁ = 10 kΩ and R₂ = 4.7 kΩ, V_out = 3.84 V. Dividers are used to scale sensor and battery voltages to a microcontroller’s input range. See the voltage divider calculator.

Current in parallel branches

In parallel, current splits in inverse proportion to resistance. With 100 Ω and 220 Ω across 12 V, the branches carry 120 mA and 54.5 mA, totalling 174.5 mA.

Colour codes

Four-band resistors: two digit bands, a multiplier and a tolerance. Brown-black-red-gold is 1, 0, ×100 = 1,000 Ω (1 kΩ) ±5%.

Standard values (E12 series)

10 · 12 · 15 · 18 · 22 · 27 · 33 · 39 · 47 · 56 · 68 · 82 (× 1, 10, 100, 1k …)

Frequently asked questions

How do resistors add in series?

Simply add them — R = R1 + R2 + R3. The same current flows through each one.

How do resistors combine in parallel?

Add the reciprocals — 1/R = 1/R1 + 1/R2 + 1/R3. The total is always less than the smallest resistor.

What about only two resistors in parallel?

Use R = (R1 × R2) ÷ (R1 + R2). For two equal resistors, the result is half of one.

Is the parallel resistance always smaller?

Yes. The total resistance of parallel resistors is always less than the smallest one.

What is the total of 10 kΩ resistors in series?

In series they add: three 10 kΩ resistors make 30 kΩ.

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