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Physics

Parallel Resistors

1/R = 1/R₁ + 1/R₂. Free online Parallel Resistors. Calculate parallel resistors online — fast, accurate, mobile-friendly, no signup needed.

1/R_total = 1/R₁ + 1/R₂ + … + 1/Rₙ.
R total
6.666667

Derivation

  1. ├── 01GivenR1 = 10, R2 = 20
  2. ├── 02Formula1 / (1 / e.R1+1 / e.R2)
  3. ├── 03Substitute1 / (1 / e.10+1 / e.20)
  4. └── 04Compute R total6.666667
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 Parallel Resistors

The Parallel Resistors computes R total from 2 inputs: r₁ (ω), r₂ (ω). 1/R = 1/R₁ + 1/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 Parallel Resistors sits in that toolkit — it 1/R = 1/R₁ + 1/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

1 / (1 / e.R1+1 / e.R2)

Where

R1
R₁ (Ω)
R2
R₂ (Ω)
§03Practical Example

Step-by-step walkthrough

Scenario

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

  1. 01Start by noting the input — R₁ (Ω): 10.
  2. 02Start by noting the input — R₂ (Ω): 20.
  3. 03Substitute these values into the formula: 1 / (1 / e.R1+1 / e.R2)
  4. 04Compute R total: the calculator returns 6.66667.
  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 Parallel 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 (Ω) halved

R1 = 5 (from 10)

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

  1. 01New R₁ (Ω): 5
  2. 02Baseline R total: 6.66667
  3. 03New R total: 4
  4. 04R total decreases by 40% → use this sensitivity to plan for real-world variation.
02 · PATTERN

R₁ (Ω) doubled

R1 = 20 (from 10)

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

  1. 01New R₁ (Ω): 20
  2. 02Baseline R total: 6.66667
  3. 03New R total: 10
  4. 04R total increases by 50% → use this sensitivity to plan for real-world variation.
03 · PATTERN

R₂ (Ω) halved

R2 = 10 (from 20)

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

  1. 01New R₂ (Ω): 10
  2. 02Baseline R total: 6.66667
  3. 03New R total: 5
  4. 04R total decreases by 25% → use this sensitivity to plan for real-world variation.
04 · PATTERN

R₂ (Ω) doubled

R2 = 40 (from 20)

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

  1. 01New R₂ (Ω): 40
  2. 02Baseline R total: 6.66667
  3. 03New R total: 8
  4. 04R total increases by 20% → 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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