**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?

**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

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**

### Cone Surface Area Calculator

A=πr(r+h2+r2)

base SA = πr^{2}

lateral SA = πr√r^{2} + h^{2}

total SA = πr(r + √r^{2} + h^{2})

where **r** is radius and **h** is height

lateral SA = π × 0.4√0.4^{2} + 0.5^{2} = 0.805 ft^{2}

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 = 6a^{2}

where **a** is edge length

SA = 6 × 4^{2} = 96 in^{2}

## Surface Area of a Cylinder Calculator With Step

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

base SA = 2πr^{2}

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 ft^{2}

### 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 ft^{2}

### Capsule Surface Area Calculator

SA = 4πr^{2} + 2πrh

where **r** is radius and **h** is height

SA = 4π × 0.05^{2} + 2π × 0.05 × 0.5 = 0.188 in^{2}

### Spherical Cap Surface Area Calculator

spherical cap SA = 2πRh

base SA = πr^{2}

Total solid sphere SA = 2πRh + πr^{2}

where **R** is spherical cap radius, **r** is base radius, and **h** is height

SA = 2π × 0.80 × 0.53 = 2.664 ft^{2}

### Conical Frustum Surface Area Calculator

circular end SA = π(R^{2} + r^{2})

lateral SA = π(R+r)√(R-r)^{2} + h^{2}

total SA = π(R^{2} + r^{2}) + π(R+r)√(R-r)^{2} + h^{2}

where **R** and **r** are radii of the ends, **h** is the height

total SA = π(1^{2} + 0.3^{2}) + π(1 + 0.3) √(1 – 0.3)^{2} + 1.5^{2} = 10.185 ft^{2}

### Ellipsoid

SA ≈ 4π ^{1.6}√(a^{1.6}b^{1.6} + a^{1.6}c^{1.6} + b^{1.6}c^{1.6})/3

where **a**, **b**, and **c** are the axes of the ellipse

SA ≈ 4π ^{1.6}√(0.1^{1.6}0.2^{1.6} + 0.1^{1.6}0.35^{1.6} + 0.2^{1.6}0.35^{1.6})/3 = 0.562 in^{2}

### Square Pyramid

base SA = a^{2}

lateral SA = 2a√(a/2)^{2} + h^{2}

total SA = a^{2} + 2a√(a/2)^{2} + h^{2}

total SA = 3^{2} + 2 × 3√(3/2)^{2} + 5^{2} = 40.321 ft^{2}

### Common Area Units

Unit | meter^{2} |

kilometer^{2} |
1,000,000 |

centimeter^{2} |
0.0001 |

millimeter^{2} |
0.000001 |

micrometer^{2} |
0.000000000001 |

hectare | 10,000 |

mile^{2} |
2,589,990 |

yard^{2} |
0.83613 |

foot^{2} |
0.092903 |

inch^{2} |
0.000645 |

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by CC & CS

### What is normal body surface area?