Online Calculators

# Surface Area of a Conical Frustum Calculator

Surface Area Calculator
total surface area
Stot =
lateral surface area
Slat =
top surface area
Stop =
bottom surface area
Sbot =

## Conical Frustum Shape

h = height
s = slant height
V = volume
Stot = total surface area
Slat = lateral surface area
Stop = top surface area
Sbot = bottom surface area
π = pi = 3.14159
√ = square root

Calculate more with
Conical Frustum Calculator

## 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, ft2 or ft3. For example, if you are starting with mm and you know r and h in mm, your calculations will result with V in mm3 and S in mm2.

Below are the standard formulas for surface area.

## Surface Area Formulas:

### Capsule Surface Area

• Volume = πr2((4/3)r + a)
• Surface Area = 2πr(2r + a)

### Circular Cone Surface Area

• Volume = (1/3)πr2h
• Lateral Surface Area = πrs = πr√(r2 + h2)
• Base Surface Area = πr2
• Total Surface Area
= L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

### Circular Cylinder Surface Area

• Volume = πr2h
• Top Surface Area = πr2
• Bottom Surface Area = πr2
• Total Surface Area
= L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

### Conical Frustum Surface Area

• Volume = (1/3)πh (r12 + r22 + (r1 * r2))
• Lateral Surface Area
= π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2)
• Top Surface Area = πr12
• Base Surface Area = πr22
• Total Surface Area
= π(r12 + r22 + (r1 * r2) * s)
= π[ r12 + r22 + (r1 * r2) * √((r1 - r2)2 + h2) ]

### Cube Surface Area

• Volume = a3
• Surface Area = 6a2

### Hemisphere Surface Area

• Volume = (2/3)πr3
• Curved Surface Area = 2πr2
• Base Surface Area = πr2
• Total Surface Area= (2πr2) + (πr2) = 3πr2

### Pyramid Surface Area

• Volume = (1/3)a2h
• Lateral Surface Area = a√(a2 + 4h2)
• Base Surface Area = a2
• Total Surface Area
= L + B = a2 + a√(a2 + 4h2))
= a(a + √(a2 + 4h2))

### Rectangular Prism Surface Area

• Volume = lwh
• Surface Area = 2(lw + lh + wh)

### Sphere Surface Area

• Volume = (4/3)πr3
• Surface Area = 4πr2

### Spherical Cap Surface Area

• Volume = (1/3)πh2(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 Conical Frustum Calculator" at https://www.calculatorsoup.com/calculators/geometry-solids/surfacearea.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: October 4, 2023