Series and parallel resistor calculator

Series & Parallel Resistor Calculator
S
Series Resistor Calculator
Rtotal = R1 + R2 + R3 + …
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Enter the resistance value for each resistor below:

Total Series Resistance
Ω
Step-by-step
Find Missing Resistor
Enter a target total resistance and leave one resistor field empty — the calculator will solve for the missing value.
Missing Resistor Value
Series Circuit — Resistors Connected End to End
P
Parallel Resistor Calculator
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …
Open CalculatorClose Calculator

Enter the resistance value for each resistor below:

Total Parallel Resistance
Ω
Step-by-step
Find Missing Resistor
Enter a target total resistance and leave one resistor field empty — the calculator will solve for the missing value.
Missing Resistor Value
Parallel Circuit — Resistors Connected Side by Side

What Is a Series & Parallel Resistor Calculator?

A resistor calculator takes two or more resistor values and returns the total resistance of the circuit — whether those resistors are connected in series or in parallel. Enter your numbers, and the calculator handles the formula, unit conversions, and arithmetic so you can focus on circuit design.

How resistors are connected determines how the overall resistance combines into a single equivalent value. The two core configurations — series and parallel — each follow a different formula, covered below. Understanding both is essential for anyone working with Ohm’s law.

Series Resistors — How to Calculate Total Resistance

The Series Resistor Formula

When resistors are connected in series, current flows through each resistor along a single path. The total resistance is simply the sum of every individual resistor value:

R_total = R1 + R2 + R3 + …

The equivalent resistance of a series circuit is always larger than the biggest single resistor in the chain. Each component you add increases the overall resistance.

Series Resistors — Worked Example

Three resistors are connected end to end: R1 = 100 Ω, R2 = 220 Ω, R3 = 470 Ω. Because resistors in series add, the equivalent resistance is:

R_total = 100 + 220 + 470 = 790 Ω

In a series circuit the voltage drop across each resistor is proportional to its resistance value, while the current through the single path stays the same. Resistors connected in this way are useful for voltage dividers.

Voltage Drop Across Each Resistor in Series

If a 12 V source drives the 790 Ω circuit above, the current is I = 12 / 790 ≈ 0.0152 A. The voltage drop across the second resistor (220 Ω) is V = 0.0152 × 220 ≈ 3.34 V. For calculating voltage loss over long cable runs, our Voltage Drop Calculator handles this automatically.

Parallel Resistor Calculator — Formula and Examples

The Parallel Resistor Formula

When resistors are connected in parallel, every resistor shares the same two nodes — the voltage across each resistor is identical, but the current splits among available paths. The parallel resistance formula uses reciprocals:

1 / R_total = 1 / R1 + 1 / R2 + 1 / R3 + …

The equivalent parallel resistance is always lower than the resistance of the smallest individual resistor.

Two Resistors in Parallel — Shortcut

When exactly two resistors are connected in parallel, use the product-over-sum shortcut:

R_total = (R1 × R2) / (R1 + R2)

Example: R1 = 1 kΩ, R2 = 2.2 kΩ. R_total = (1000 × 2200) / (1000 + 2200) = 687.5 Ω — lower than the smallest resistor, confirming the total resistance must be lower than any single branch.

Parallel Resistors — Larger Network Example

Four resistors connected in parallel: 100 Ω, 220 Ω, 330 Ω, 470 Ω:

1/R_total = 1/100 + 1/220 + 1/330 + 1/470 = 0.019703
R_total ≈ 50.75 Ω

The equivalent resistance is ~50.75 Ω — well below the smallest resistor. Adding resistors in parallel reduces the overall resistance while each branch carries current proportional to the inverse of its resistance value.

Current Through Each Resistor in Parallel

With 10 V across the network, the current through the 100 Ω resistor is 0.1 A; through the 470 Ω resistor, ≈ 0.0213 A. The sum of all branch currents equals the total entering the node. For understanding how current divides, see our Current Divider Calculator.

Parallel Resistors Explained

Series and Parallel Resistance — Combined Circuits

Resistor Networks with Mixed Connections

Most electronic circuits combine both series and parallel connections. To find the total, identify sub-groups that are purely series or parallel, calculate the equivalent resistance of each, substitute back, and repeat until you reach a single value.

Example: R1 = 200 Ω in series with a parallel pair of R2 = 300 Ω and R3 = 600 Ω. Parallel first: (300 × 600) / (300 + 600) = 200 Ω. Total: R_total = 200 + 200 = 400 Ω.

Series or Parallel — How to Tell the Difference

Resistors are connected in series when one leads directly into the next with no branching. Resistors connected in parallel share the same pair of nodes at both ends. Trace the current path: one route = series; multiple routes = parallel. Choosing the wrong formula gives an incorrect result, so identification matters.

Series and Parallel Circuits Explained

How to Use the Calculator

Select series or parallel, choose the number of resistors from the dropdown or click “Add Resistor”, and enter each resistor value. Each field supports Ω, kΩ, and MΩ — the calculator handles conversions automatically. Results update in real time with a step-by-step breakdown showing your actual numbers in the formula.

The “Find Missing Resistor” section lets you work backwards: enter a target total resistance, leave one field empty, and the tool solves for the unknown value. Remove any resistor with the × button — remaining values are preserved and renumbered automatically.

Tip: If you don’t know your resistor values, use our Resistor Colour Code Calculator to decode the coloured bands before entering values here.

Resistor Colour Code — Reading Resistance Values

Through-hole resistors use coloured bands on the body to indicate the resistance value in ohms. A standard resistor typically has four or five bands: significant digits, a multiplier, and a tolerance band.

ColourDigitMultiplierTolerance
Black0×1 Ω
Brown1×10 Ω±1%
Red2×100 Ω±2%
Orange3×1 kΩ
Yellow4×10 kΩ
Green5×100 kΩ±0.5%
Blue6×1 MΩ±0.25%
Violet7×10 MΩ±0.1%
Grey8±0.05%
White9
Gold×0.1 Ω±5%
Silver×0.01 Ω±10%

Example: brown, black, red, gold = 1-0 × 100 = 1,000 Ω (1 kΩ), ±5% tolerance. Once you decode the resistor colour code and know each value, plug the numbers into the calculator above to find the total resistance.

Practical Tips for Circuit Design with Resistors

When to Add Resistors in Parallel vs. Series

Add resistors in series to increase total resistance — useful for limiting current or building voltage dividers. Add resistors in parallel to decrease the overall resistance or distribute current so no single component is overloaded. Parallel configurations dominate power distribution because adding more paths always lowers the equivalent resistance.

Combining Standard Resistor Values

Resistors come in preferred values (E12, E24, E96), so the exact resistance you need may not exist as a single component. Combine two or more values in parallel or series to hit any target. Need 750 Ω? Connect 1 kΩ and 3 kΩ in parallel: (1000 × 3000) / (1000 + 3000) = 750 Ω. The calculator lets you explore combinations instantly.

Power Dissipation in Resistor Networks

When current flows through a resistor, it dissipates power as heat. Make sure each resistor’s power rating exceeds the actual power it will handle. Use our Electrical Power Calculator to check: P = I² × R for each resistor in the network.

Frequently Asked Questions

How do I calculate the total resistance of resistors in series?
Sum all individual resistor values: R_total = R1 + R2 + R3 + … . The result is always larger than the largest single resistor. Enter your values into the series calculator above to find the total resistance instantly.
How do I calculate resistance in parallel?
Use 1/R_total = 1/R1 + 1/R2 + 1/R3 + … , then invert the sum. The equivalent parallel resistance is always lower than the smallest individual resistor. The parallel calculator above handles up to ten resistors at once.
Why is parallel resistance always smaller than the smallest resistor?
Each resistor in a parallel circuit gives current another path. More paths mean less overall opposition, so the total resistance must be lower than any single branch.
What happens to the voltage across each resistor in parallel?
It stays the same — equal to the source voltage across the shared nodes. Only the current divides, with each branch drawing current inversely proportional to its resistance.
Can I mix series and parallel resistors in one calculation?
Yes. Break the circuit into purely series or parallel sub-groups, calculate the equivalent resistance of each, then combine. Repeat until you have a single equivalent resistance.
How do I find a missing resistor value?
In series: R_unknown = R_total − (sum of known resistors). In parallel the algebra is trickier, but the “Find Missing Resistor” feature above solves it — enter known values, set your target total, leave one field empty, and the tool returns the missing resistance.
What is the product-over-sum shortcut for two parallel resistors?
When exactly two resistors are in parallel, use R_total = (R1 × R2) / (R1 + R2). This avoids the reciprocal formula and gives the same result. It only works for two resistors — for three or more, use the full reciprocal formula.
How do I read resistor values from the colour bands?
Each coloured band represents a digit or multiplier. Read bands from left to right: the first two (or three) bands give the significant digits, the next band is the multiplier, and the last band indicates tolerance. Use our Resistor Colour Code Calculator for a quick lookup.

Last updated: March 2026