Surface Area Calculator

Surface Area Calculator The surface area of a solid is a measure of the total area occupied by the surface of an object. All of the objects addressed in this calculator are described in more detail on the Volume Calculator and Area Calculator pages.

Surface Area of a Triangular Prism Calculator

a = side length a
b = side length b = bottom triangle base b
c = side length c
h = height of prism
H = height of bottom triangle
V = volume
A_tot = total surface area = all sides
A_lat = lateral surface area = all rectangular sides
A_top = top surface area = top triangle
A_bot = bottom surface area = bottom triangle

A triangular prism is a geometric solid shape with a triangle as its base. It’s a three-sided prism where the base and top are equal triangles and the remaining 3 sides are rectangles.

Top Surface Area of a Triangular Prism Formula

Finds the area contained by the triangular surface at the top of the prism. This is the same area as the bottom surface area.

Bottom Surface Area of a Triangular Prism Formula

Finds the area contained by the triangular surface at the bottom of the prism. This is the same area as the top surface area.

Lateral Surface Area of a Triangular Prism Formula

Finds the total area contained by the three rectangular sides of the prism. You can think of the lateral surface area as the total surface area of the prism minus the two triangular areas at the top and bottom of the prism.

Total Surface Area of a Triangular Prism Formula

Finds the total area of all sides of a triangular prism. Total surface area of a prism includes the area of the top and bottom triangle sides of the prism, plus the area of all 3 rectangular sides.

Height of a Triangular Prism Formula in Terms of Volume

Finds the height of a triangular prism by solving the Volume Formula for height. Height, h, is calculated from volume, V, and side lengths a, b and c.

Height of a Triangular Prism Formula in Terms of Lateral Surface Area

Finds the height of a triangular prism by solving the Lateral Surface Area Formula for height. Height, h, is calculated from lateral surface area, A_lat, and side lengths a, b and c.

Sphere Surface Area Calculator

SA = 4πr²
where r is the radius

See also  547 in Words

SA = 4 × π × 0.325² = 1.327 in²

 

Cone Surface Area Calculator

A=πr(r+h2+r2)

base SA = πr²
lateral SA = πr√r² + h²
total SA = πr(r + √r² + h²)
where r is radius and h is height

lateral SA = π × 0.4√0.4² + 0.5² = 0.805 ft²

Circular Cone Formulas in terms of radius r and height h:
Volume of a cone:
V = (1/3)πr2h
Slant height of a cone:
s = √(r2 + h2)
Lateral surface area of a cone:
L = πrs = πr√(r2 + h2)
Base surface area of a cone (a circle):
B = πr2
Total surface area of a cone:
A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

 

Cube Surface Area Calculator

SA = 6a²
where a is edge length

SA = 6 × 4² = 96 in²

Surface Area of a Cylinder Calculator With Step

Surface Area of a Cylinder Formula A=2πrh+2πr2

base SA = 2πr²
lateral SA = 2πrh
total SA = 2πr(r + h) where r is radius and h is height

total SA = 2π × 3.5(3.5 + 5.5) = 197.920 ft²

Rectangular Tank

SA = 2lw + 2lh + 2wh
where l is length, w is width, and h is height

SA = (2 × 3 × 4) + (2 × 4 × 5) + (2 × 3 × 5) = 94 ft²

Capsule Surface Area Calculator

SA = 4πr² + 2πrh
where r is radius and h is height

SA = 4π × 0.05² + 2π × 0.05 × 0.5 = 0.188 in²

Spherical Cap Surface Area Calculator

spherical cap SA = 2πRh
base SA = πr²
Total solid sphere SA = 2πRh + πr²
where R is spherical cap radius, r is base radius, and h is height

SA = 2π × 0.80 × 0.53 = 2.664 ft²

Conical Frustum Surface Area Calculator

circular end SA = π(R² + r²)
lateral SA = π(R+r)√(R-r)² + h²
total SA = π(R² + r²) + π(R+r)√(R-r)² + h²
where R and r are radii of the ends, h is the height

total SA = π(1² + 0.3²) + π(1 + 0.3) √(1 – 0.3)² + 1.5² = 10.185 ft²

Ellipsoid

SA ≈ 4π ^1.6√(a^1.6b^1.6 + a^1.6c^1.6 + b^1.6c^1.6)/3
where a, b, and c are the axes of the ellipse

SA ≈ 4π ^1.6√(0.1^1.60.2^1.6 + 0.1^1.60.35^1.6 + 0.2^1.60.35^1.6)/3 = 0.562 in²

Square Pyramid

base SA = a²
lateral SA = 2a√(a/2)² + h²
total SA = a² + 2a√(a/2)² + h²

total SA = 3² + 2 × 3√(3/2)² + 5² = 40.321 ft²

Common Area Units

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by CC & CS