Spherical Cap Volume
Calculator
Results
- Volume
- 435.634181
- Curved surface area
- 251.327412
- Cap base radius
- 8
Results
| Volume | 435.634181 |
| Curved surface area | 251.327412 |
| Cap base radius | 8 |
formula-map diagram
- Volume
- 435.634181
- Curved surface area
- 251.327412
- Cap base radius
- 8
Formula map
Formula
V = (π × h² ÷ 3) × (3R − h)= 435.63418129778
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
More in Advanced geometry
See all →Frequently asked questions
What is a spherical cap, and what inputs does its volume formula need?+
A spherical cap is the portion of a sphere cut off by a single plane, like the top of a dome. Its volume formula, V = (πh²/3)(3r − h), needs the cap's height (h), the vertical distance from the cutting plane to the top of the cap, and the sphere's full radius (r).
What happens to the formula when the cap height equals the sphere's full diameter?+
When h = 2r (the cap height equals the full diameter), the formula reduces exactly to the full sphere volume, V = (4/3)πr³. This confirms the cap formula is consistent with the whole-sphere formula as a limiting case.
Can I use this formula if I only know the cap's base radius instead of the sphere's full radius?+
Yes, but you'll need to first find the sphere's radius using the relationship between the base radius (a), cap height (h), and sphere radius (r): r = (a² + h²)/(2h). Once you have r, the standard cap volume formula applies directly.
Is a spherical cap the same thing as a hemisphere?+
A hemisphere is just a special case of a spherical cap where the height exactly equals the sphere's radius (h = r), cutting the sphere precisely through its center. For any other height value, the cap is either smaller or larger than exactly half the sphere.
Why is this formula useful for real objects like domes or contact lenses?+
Many real curved surfaces, architectural domes, lens shapes, or the top of a liquid meniscus, are geometrically spherical caps, so this formula directly gives their enclosed volume from simple height and radius measurements. It avoids needing calculus or integration for what would otherwise be a complex curved-surface volume problem.