# Volume of a Spherical Cap Calculator

## Spherical Cap Shape

R = sphere radius

a = cap base radius

h = height of cap

V = volume

S = surface area

π = pi = 3.14159

√ = square root

## Calculator Use

Online calculator to calculate the volume of geometric solids including a capsule, cone, frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere and spherical cap.

**Units:** Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft^{2} or ft^{3}. For example, if you are starting with mm and you know a and h in mm, your calculations will result with V in mm^{3}.

Below are the standard formulas for volume.

## Volume Formulas:

## Capsule Volume

- Volume = πr
^{2}((4/3)r + a)- Surface Area = 2πr(2r + a)
## Circular Cone Volume & Surface Area

- Volume = (1/3)πr
^{2}h- Lateral Surface Area = πrs = πr√(r
^{2}+ h^{2})- Base Surface Area = πr
^{2}- Total Surface Area

= L + B = πrs + πr^{2}= πr(s + r) = πr(r + √(r^{2}+ h^{2}))## Circular Cylinder Volume

- Volume = πr
^{2}h- Top Surface Area = πr
^{2}- Bottom Surface Area = πr
^{2}- Total Surface Area

= L + T + B = 2πrh + 2(πr^{2}) = 2πr(h+r)## Conical Frustum Volume

- Volume = (1/3)πh (r
_{1}^{2}+ r_{2}^{2}+ (r_{1}* r_{2}))- Lateral Surface Area

= π(r_{1}+ r_{2})s = π(r_{1}+ r_{2})√((r_{1}- r_{2})^{2}+ h^{2})- Top Surface Area = πr
_{1}^{2}- Base Surface Area = πr
_{2}^{2}- Total Surface Area

= π(r_{1}^{2}+ r_{2}^{2}+ (r_{1}* r_{2}) * s)

= π[ r_{1}^{2}+ r_{2}^{2}+ (r_{1}* r_{2}) * √((r_{1}- r_{2})^{2}+ h^{2}) ]## Cube Volume

- Volume = a
^{3}- Surface Area = 6a
^{2}## Hemisphere Volume

- Volume = (2/3)πr
^{3}- Curved Surface Area = 2πr
^{2}- Base Surface Area = πr
^{2}- Total Surface Area= (2πr
^{2}) + (πr^{2}) = 3πr^{2}## Pyramid Volume

- Volume = (1/3)a
^{2}h- Lateral Surface Area = a√(a
^{2}+ 4h^{2})- Base Surface Area = a
^{2}- Total Surface Area

= L + B = a^{2}+ a√(a^{2}+ 4h^{2}))

= a(a + √(a^{2}+ 4h^{2}))## Rectangular Prism Volume

- Volume = lwh
- Surface Area = 2(lw + lh + wh)
## Sphere Volume

- Volume = (4/3)πr
^{3}- Surface Area = 4πr
^{2}## Spherical Cap Volume

- Volume = (1/3)πh
^{2}(3R - h)- Surface Area = 2πRh
## Triangular Prism Volume

\[ V = \dfrac{1}{4}h \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]

**Cite this content, page or calculator as:**

Furey, Edward "Volume of a Spherical Cap Calculator" at https://www.calculatorsoup.com/calculators/geometry-solids/volume.php from CalculatorSoup,
*https://www.calculatorsoup.com* - Online Calculators

Last updated: April 21, 2020