Enter the resistance value for each resistor below:
Enter the resistance value for each resistor below:
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:
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:
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:
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:
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:
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.
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.
| Colour | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | ×1 Ω | — |
| Brown | 1 | ×10 Ω | ±1% |
| Red | 2 | ×100 Ω | ±2% |
| Orange | 3 | ×1 kΩ | — |
| Yellow | 4 | ×10 kΩ | — |
| Green | 5 | ×100 kΩ | ±0.5% |
| Blue | 6 | ×1 MΩ | ±0.25% |
| Violet | 7 | ×10 MΩ | ±0.1% |
| Grey | 8 | — | ±0.05% |
| White | 9 | — | — |
| 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
Last updated: March 2026