Calculating your ring area is straightforward once you know the Annulus (Ring) formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Annulus (Ring) Calculator.
What is Annulus (Ring)?
The Annulus (Ring) calculation tells you your ring area from a few simple inputs. The figure you are solving for here is the ring area.
The Annulus (Ring) formula
The core formula is:
Ring area = 3.141592653589793 × (Outer radius (R) ^ 2 - Inner radius (r) ^ 2)Here is what each input means:
- Outer radius (R) — a value measured in units. Example: 8 units.
- Inner radius (r) — a value measured in units. Example: 5 units.
How to calculate it step by step
- Write down the outer radius (r) (for example, 8 units).
- Write down the inner radius (r) (for example, 5 units).
- Apply the formula above to get your ring area.
- Double-check the result with the Annulus (Ring) Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Outer radius (R) | 8 units |
| Inner radius (r) | 5 units |
| Ring area | 122.5221 |
| Ring width | 3.0000 |
With outer radius (r) of 8 units and inner radius (r) of 5 units, the ring area works out to 122.5221.
Example 2
With outer radius (r) of 16 units and inner radius (r) of 5 units, the ring area works out to 725.7079.
| Result | Value |
|---|---|
| Ring area | 725.7079 |
| Ring width | 11.0000 |
Example 3
With outer radius (r) of 4 units and inner radius (r) of 5 units, the ring area works out to -28.2743.
| Result | Value |
|---|---|
| Ring area | -28.2743 |
| Ring width | -1.0000 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Annulus (Ring) Calculator does it instantly, for free, with the formula and a worked example built in.
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