# 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.

### What is the formula for the surface area?

We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

## 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
Atot = total surface area = all sides
Alat = lateral surface area = all rectangular sides
Atop = top surface area = top triangle
Abot = 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.

Atop=14(a+b+c)(b+ca)(c+ab)(a+bc)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√Atop=14(a+b+c)(b+c−a)(c+a−b)(a+b−c)

### 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.

Abot=14(a+b+c)(b+ca)(c+ab)(a+bc)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√Abot=14(a+b+c)(b+c−a)(c+a−b)(a+b−c)

### 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.

Alat=h(a+b+c)Alat=h(a+b+c)

### 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.

Atot=Atop+Abot+AlatAtot=Atop+Abot+Alat

### 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.

h=4V(a+b+c)(b+ca)(c+ab)(a+bc)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√h=4V(a+b+c)(b+c−a)(c+a−b)(a+b−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, Alat, and side lengths a, b and c.

h=Alat(a+b+c)

Sphere Surface Area Calculator

### 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 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√(a1.6b1.6 + a1.6c1.6 + b1.6c1.6)/3
where ab, and c are the axes of the ellipse

SA ≈ 4π 1.6√(0.11.60.21.6 + 0.11.60.351.6 + 0.21.60.351.6)/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

 Unit meter2 kilometer2 1,000,000 centimeter2 0.0001 millimeter2 0.000001 micrometer2 0.000000000001 hectare 10,000 mile2 2,589,990 yard2 0.83613 foot2 0.092903 inch2 0.000645

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by CC & CS

### What is normal body surface area?

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