Parallel Resistor CalculatorResistors in parallel & series
For resistors in parallel, the reciprocal of the total equals the sum of the reciprocals: 1/R = 1/R₁ + 1/R₂ + … For two resistors that simplifies to R = R₁R₂ ÷ (R₁ + R₂). In series they simply add. Enter up to six resistors to get the equivalent resistance, the current through each branch at a given voltage, or the resistor you need to reach a target value.
Formula verified against OpenStax — University Physics, Volume 2 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Resistor network
Leave unused resistors at 0. Units can be Ω, kΩ or MΩ per resistor.
Step-by-step working
What is parallel resistor?
Resistors in parallel are connected across the same two points, so each sees the same voltage and the current splits between them. The combined, or equivalent, resistance is always lower than any single resistor.
Parallel combinations show up everywhere: household outlets are wired in parallel, speaker cabinets combine drivers, and engineers parallel resistors to build precise or high-power values.
Quick answers
How do I calculate two resistors in parallel?
Use product over sum: R = R₁R₂ ÷ (R₁ + R₂). 220 Ω ∥ 330 Ω = 72,600 ÷ 550 = 132 Ω.
What happens to resistance when you add resistors in parallel?
It always goes down, because each new branch gives current another path. Two equal resistors in parallel halve the resistance.
How do I make a non-standard resistor value?
Combine standard parts. To get 75 Ω, put 100 Ω in parallel with 300 Ω, or 150 Ω ∥ 150 Ω. The Find missing resistor tab works out the partner value.
How is current divided in a parallel circuit?
Each branch carries I = V ÷ R, so the smallest resistor takes the most current. Check branch powers with the watt calculator to pick resistor ratings.
Parallel and series resistance formulas
n identical resistors in parallel give R ÷ n; in series, n × R.
| Symbol | Meaning | SI unit |
|---|---|---|
| Req | Equivalent resistance | Ω |
| Rᵢ | Individual resistances | Ω |
| V | Voltage across the network | V |
| I | Current | A |
How to calculate resistors in parallel
- Take the reciprocal of each resistance (1/R, in siemens).
- Add the reciprocals together.
- Take the reciprocal of the sum to get the equivalent resistance.
- Sanity-check: the answer must be smaller than the smallest resistor.
Worked example: 100 Ω, 220 Ω and 470 Ω in parallel
Three resistors (100 Ω, 220 Ω and 470 Ω) are connected in parallel across 12 V.
R = 1 ÷ 0.016673 = 59.98 Ω
I = 12 ÷ 59.98 = 200.1 mA
In series the same three add up to 790 Ω. To make 60 Ω from a 100 Ω resistor, parallel it with 1 ÷ (1/60 − 1/100) = 150 Ω.
Series vs parallel at a glance
| Property | Series | Parallel |
|---|---|---|
| Equivalent resistance | Sum of all R | Less than the smallest R |
| Current | Same through each | Splits between branches |
| Voltage | Splits (divider) | Same across each |
| One resistor fails open | Whole chain stops | Other branches still work |
Common mistakes to avoid
- Adding parallel resistors directly. 100 Ω ∥ 100 Ω is 50 Ω, not 200 Ω.
- Forgetting the last reciprocal. Σ1/R is a conductance in siemens; flip it back to ohms.
- Using the product-over-sum rule for three or more resistors at once. Apply it pairwise, or use reciprocals.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Parallel Resistor Calculator: frequently asked questions
1/Req = 1/R₁ + 1/R₂ + … For two resistors, Req = R₁R₂ ÷ (R₁ + R₂).
Yes. Each extra branch adds conductance, so the total resistance must fall below the smallest individual value.
Req = R₁ + R₂ + R₃ + … Series resistances simply add.
R ÷ n. Four 1 kΩ resistors in parallel give 250 Ω.
To make values not available as single parts, to share power dissipation between several resistors, or to provide redundancy.
References & sources
- OpenStax — University Physics, Volume 2 — Ch. 10.2, Resistors in Series and Parallel
- HyperPhysics, Georgia State University — resistor combinations
- OpenStax — College Physics 2e — Ch. 21.1, Resistors in Series and Parallel
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.