Spherical Cap Calculator

What Is a Spherical Cap Calculator?

A spherical cap is the dome-shaped piece you get when you slice off the top of a sphere with a single flat cut — like the top of a scoop of ice cream or a contact lens. This calculator finds the cap's volume, curved surface area, and the radius of its flat circular base from the original sphere's radius and the cap's height.

How to Use This Spherical Cap Calculator

1. Measure the radius R of the full sphere the cap was cut from.
2. Measure the height h of the cap (from the flat cut to the top of the dome).
3. Enter both values above and click Calculate to get the volume, curved surface area, and base radius.

Formula

• Volume = (π × h² / 3) × (3R − h)
• Curved Surface Area = 2 × π × R × h
• Base Radius a = √(h × (2R − h))

Worked Example

A dome-shaped roof is cut from a sphere of radius 10 m, with the dome standing 3 m tall. Volume = (π × 3² / 3) × (30 − 3) ≈ 254.47 m³. Curved Surface Area = 2π(10)(3) ≈ 188.50 m². Base Radius = √(3 × 17) ≈ 7.14 m.