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Physics

Series Resistors

R = R₁ + R₂. Free online Series Resistors. Calculate series resistors online — fast, accurate, mobile-friendly, no signup needed.

R_total = R₁ + R₂ + … + Rₙ.
R total
30

Derivation

  1. ├── 01GivenR1 = 10, R2 = 20
  2. ├── 02Formulae.R1+e.R2
  3. ├── 03Substitutee.10+e.20
  4. └── 04Compute R total30
Did you know?

Georg Simon Ohm published V = I·R in 1827 but was dismissed by German universities for 15 years before his work was accepted.

§01What is

Understanding the Series Resistors

The Series Resistors computes R total from 2 inputs: r₁, r₂. R = R₁ + R₂.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Series Resistors sits in that toolkit — it R = R₁ + R₂. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

e.R1+e.R2

Where

R1
R₁
R2
R₂
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: R₁ = 10, R₂ = 20.

  1. 01Start by noting the input — R₁: 10.
  2. 02Start by noting the input — R₂: 20.
  3. 03Substitute these values into the formula: e.R1+e.R2
  4. 04Compute R total: the calculator returns 30.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Series Resistors Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

R₁ halved

R1 = 5 (from 10)

Keep every other input at its default and halve the r₁. See how r total responds.

  1. 01New R₁: 5
  2. 02Baseline R total: 30
  3. 03New R total: 25
  4. 04R total decreases by 16.7% → use this sensitivity to plan for real-world variation.
02 · PATTERN

R₁ doubled

R1 = 20 (from 10)

Keep every other input at its default and double the r₁. See how r total responds.

  1. 01New R₁: 20
  2. 02Baseline R total: 30
  3. 03New R total: 40
  4. 04R total increases by 33.3% → use this sensitivity to plan for real-world variation.
03 · PATTERN

R₂ halved

R2 = 10 (from 20)

Keep every other input at its default and halve the r₂. See how r total responds.

  1. 01New R₂: 10
  2. 02Baseline R total: 30
  3. 03New R total: 20
  4. 04R total decreases by 33.3% → use this sensitivity to plan for real-world variation.
04 · PATTERN

R₂ doubled

R2 = 40 (from 20)

Keep every other input at its default and double the r₂. See how r total responds.

  1. 01New R₂: 40
  2. 02Baseline R total: 30
  3. 03New R total: 50
  4. 04R total increases by 66.7% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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