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Geometry

Annulus Calculator

Annulus area and dimensions. Free online Annulus Calculator. Calculate annulus online — fast, accurate, mobile-friendly, no signup needed.

Area
263.893783

Derivation

  1. ├── 01GivenR = 10, r = 4
  2. ├── 02Formulaπ × (t²-a²)
  3. └── 03Compute Area263.893783
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§01What is

Understanding the Annulus Calculator

The Annulus Calculator computes Area from 2 inputs: outer radius, inner radius. Annulus area and dimensions.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Annulus Calculator sits in that toolkit — it annulus area and dimensions. 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

π × (t²-a²)

Where

R
Outer radius
r
Inner radius
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Outer radius = 10, Inner radius = 4.

  1. 01Start by noting the input — Outer radius: 10.
  2. 02Start by noting the input — Inner radius: 4.
  3. 03Substitute these values into the formula: π × (t²-a²)
  4. 04Compute Area: the calculator returns 263.894.
  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 Annulus 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

Outer radius halved

R = 5 (from 10)

Keep every other input at its default and halve the outer radius. See how area responds.

  1. 01New Outer radius: 5
  2. 02Baseline Area: 263.894
  3. 03New Area: 28.2743
  4. 04Area decreases by 89.3% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Outer radius doubled

R = 20 (from 10)

Keep every other input at its default and double the outer radius. See how area responds.

  1. 01New Outer radius: 20
  2. 02Baseline Area: 263.894
  3. 03New Area: 1206.37
  4. 04Area increases by 357.1% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Inner radius halved

r = 2 (from 4)

Keep every other input at its default and halve the inner radius. See how area responds.

  1. 01New Inner radius: 2
  2. 02Baseline Area: 263.894
  3. 03New Area: 301.593
  4. 04Area increases by 14.3% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Inner radius doubled

r = 8 (from 4)

Keep every other input at its default and double the inner radius. See how area responds.

  1. 01New Inner radius: 8
  2. 02Baseline Area: 263.894
  3. 03New Area: 113.097
  4. 04Area decreases by 57.1% → 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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