About the Spherical Cap Calculator
A spherical cap is the piece you get when a plane slices off the top of a sphere, like a dome or a bowl. It is described by the radius of the full sphere and the height of the cap. This calculator gives the volume, the curved surface area, the radius of the flat base and the total area including the base. Type the sphere radius and the height of the cap and the spherical cap volume appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Spherical Cap Calculator
- 1Enter the sphere radius and the height of the cap.
- 2Pick the units or options from the menus if the spherical cap volume tool offers them.
- 3Read the spherical cap volume in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the spherical cap volume
Architects and builders use it for domes and vaulted roofs, tank designers for dished ends, and cooks for the portion of a bowl that is full. Opticians and photographers meet the same shape in lenses.
If you know the base radius and the height instead of the sphere radius, use R = (a² + h²) ÷ (2h) to find R first. The tool needs the sphere radius so it can use the simple formulas.
How the spherical cap volume is worked out
Volume = π × h² × (3R − h) ÷ 3. Curved area = 2π × R × h. Base radius = √(h × (2R − h)). A cap of height 4 cut from a sphere of radius 10 has a volume of 435.63, a curved area of 251.33 and a base radius of 8. With the flat base added the surface is 452.39. When the height is 20, the whole sphere, the volume is 4,188.79.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Volume, curved and total area
- Base radius shown
- Whole sphere is allowed
Mistakes to avoid with spherical cap volume
The height must not be more than the diameter of the sphere. A common slip is to use the radius of the base where the sphere radius belongs. The curved area is the same as that of a cylinder wrapped round the sphere with the same height, a handy fact from Archimedes.
On phone and computer
On a phone, type into the boxes one after another and read the spherical cap volume underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the spherical cap volume move. The spherical cap calculator works the same on both. A cap is a slice of a sphere, so Sphere Calculator gives the whole ball. Cone Calculator is useful for similar shapes, and Volume Calculator and Surface Area Calculator cover other solids.
Features
- Height at most the diameter
- Find R from the base if needed
- Archimedes' area rule
- Clear messages when the spherical cap volume inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate spherical cap volume?
Volume = π × h² × (3R − h) ÷ 3. Curved area = 2π × R × h. Base radius = √(h × (2R − h)). A cap of height 4 cut from a sphere of radius 10 has a volume of 435.63, a curved area of 251.33 and a base radius of 8. With the flat base added the surface is 452.39. When the height is 20, the whole sphere, the volume is 4,188.79.
What is the formula for spherical cap volume?
Volume = π × h² × (3R − h) ÷ 3. Curved area = 2π × R × h. Base radius = √(h × (2R − h)). The spherical cap calculator applies it exactly and rounds only the displayed answer to six significant figures.
How do I find R from the base and height?
R = (a² + h²) ÷ (2 × h), where a is the base radius and h the height.
Is a hemisphere a spherical cap?
Yes, the case where the height equals the radius. The volume is then two thirds of π × R³.
What is the curved area used for?
It is the area of the dome surface, useful for painting, roofing or cladding.
Is this spherical cap calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.