# Surface Area of a Spherical Cap Calculator

## Spherical Cap Shape

R = sphere radius

a = cap base radius

h = height of cap

V = volume

S_{cur} = curved surface area

π = pi = 3.14159

√ = square root

## Calculator Use

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

**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 r and h in mm, your calculations will result with V in mm^{3} and S in mm^{2}.

Below are the standard formulas for surface area.

## Surface Area Formulas:

## Capsule Surface Area

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

- 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 Surface Area

- 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 Surface Area

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

- 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 Surface Area

- 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 Surface Area

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

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

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

## Top Surface Area of a Triangular Prism Formula

\[ A_{top} = \dfrac{1}{4} \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]\[ A_{top} = \dfrac{1}{4} \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]## Bottom Surface Area of a Triangular Prism Formula

\[ A_{bot} = \dfrac{1}{4} \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)} \]\[ A_{bot} = \dfrac{1}{4} \sqrt{\begin{aligned}(a+&b+c)(b+c-a)\\&\times(c+a-b)(a+b-c)\end{aligned}} \]## Lateral Surface Area of a Triangular Prism Formula

\[ A_{lat} = h (a+b+c) \]## Total Surface Area of a Triangular Prism Formula

\[ A_{tot} = A_{top} + A_{bot} + A_{lat} \]

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

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

Last updated: October 4, 2023