Surface Area Calculator

Square Pyramid Shape

h = height
s = slant height
a = side length
e = lateral edge length
r = a/2
V = volume
S_tot = total surface area
S_lat = lateral surface area
S_bot = bottom surface area

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Pyramid 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

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