Bowl Segment Calculator — Spherical Cap Volume & Area
Enter the radius of the sphere and the depth of the bowl segment to instantly calculate the bowl's volume, curved surface area, base (opening) area and base radius.
Volume of the spherical cap (units³ matching your inputs)
- 1
3R − h
3 × 10 − 6 = 24 - 2
h²
6² = 36 - 3
Volume = π × h² × (3R − h) ÷ 3
π × 36 × 24 ÷ 3 = 904.7787Standard spherical-cap volume formula — when h = 2R the result equals 4πR³/3 (full sphere).
How does this calculator work?
A spherical bowl (spherical cap) of sphere radius R and depth h has volume V = π·h²·(3R−h)/3, curved surface 2π·R·h, and opening radius a = √(2Rh−h²). Enter R and h (same units) to get volume, areas and the base radius in those cubic/square units.
Formula
How this is calculated
A spherical cap (bowl segment) is the portion of a sphere cut off by a plane. You define it with two measurements: R, the radius of the original full sphere, and h, the depth (height) of the cap from the cutting plane to the top of the sphere. Because the cap is part of a sphere, its curved surface area is simply proportional to h — it equals 2π·R·h, the same formula as the lateral area of a cylinder with the same radius and height, which is a surprisingly elegant result.
The volume formula V = π·h²·(3R − h) / 3 can be derived by integrating circular cross-sections from the base of the cap to its apex. When h = R the cap is exactly a hemisphere (V = 2π·R³/3); when h = 2R it is the full sphere (V = 4π·R³/3). The base radius a = √(2Rh − h²) comes from the Pythagorean theorem applied to the sphere's cross-section at the cutting plane.
All results are in the cube (or square) of whatever unit you use for R and h — enter centimetres to get cm³ and cm², or metres to get m³ and m². There is no built-in unit conversion, so keep R and h in the same unit.
Frequently asked questions
A hemisphere is a special case where the cut passes exactly through the centre of the sphere (h = R). A spherical cap is the general case — h can be any depth from 0 to 2R (the full sphere). If h < R the cap is shallower than a hemisphere; if h > R it is deeper (more than half the sphere).
Let d = opening diameter (so a = d/2) and h = depth. From a² = 2Rh − h², solve for R: R = (a² + h²) / (2h). Enter this R along with h to get the volume and surface area.
Yes — enter R and h in centimetres to get volume in cm³; divide by 1,000 to convert to litres (1 L = 1,000 cm³). Enter in metres to get cubic metres; multiply by 1,000 for litres. Be aware that a real bowl is not a perfect sphere, so treat the result as an estimate.
TG we-Calculate Editorial Team. (2026). Bowl Segment Calculator — Spherical Cap Volume & Area [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bowl-segment-calculator
TG we-Calculate Editorial Team. "Bowl Segment Calculator — Spherical Cap Volume & Area." TG we-Calculate. 2026. https://we-calculate.com/calculator/bowl-segment-calculator.
TG we-Calculate Editorial Team, "Bowl Segment Calculator — Spherical Cap Volume & Area," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bowl-segment-calculator
@misc{wecalculate_bowl_segment_calculator, title = {Bowl Segment Calculator — Spherical Cap Volume & Area}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bowl-segment-calculator}}, year = {2026}, note = {TG we-Calculate} }
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