Calculating your cap volume is straightforward once you know the Spherical Cap Volume 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 Spherical Cap Volume Calculator.
What is Spherical Cap Volume?
The Spherical Cap Volume calculation tells you your cap volume from a few simple inputs. The figure you are solving for here is the cap volume.
The Spherical Cap Volume formula
The core formula is:
Cap volume = 3.141592653589793 × Cap height (h) ^ 2 × (3 × Sphere radius (R) - Cap height (h)) ÷ 3Here is what each input means:
- Sphere radius (R) — a value measured in units. Example: 5 units.
- Cap height (h) — a value measured in units. Example: 2 units.
How to calculate it step by step
- Write down the sphere radius (r) (for example, 5 units).
- Write down the cap height (h) (for example, 2 units).
- Apply the formula above to get your cap volume.
- Double-check the result with the Spherical Cap Volume Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Sphere radius (R) | 5 units |
| Cap height (h) | 2 units |
| Cap volume | 54.4543 |
With sphere radius (r) of 5 units and cap height (h) of 2 units, the cap volume works out to 54.4543.
Example 2
With sphere radius (r) of 10 units and cap height (h) of 2 units, the cap volume works out to 117.2861.
| Result | Value |
|---|---|
| Cap volume | 117.2861 |
Example 3
With sphere radius (r) of 2.5 units and cap height (h) of 2 units, the cap volume works out to 23.0383.
| Result | Value |
|---|---|
| Cap volume | 23.0383 |
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 Spherical Cap Volume Calculator does it instantly, for free, with the formula and a worked example built in.
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