# Cone Calculator

## Cone Shape

r = radius

h = height

s = slant height

V = volume

L = lateral surface area

B = base surface area

A = total surface area

π = pi = 3.1415926535898

√ = square root

## Calculator Use

This online calculator will calculate the various properties of a right circular cone given any 2 known variables. The term "circular" clarifies this shape as a pyramid with a circular cross section. The term "right" means that the vertex of the cone is centered above the base. Using the term "cone" by itself often commonly means a right circular cone.

**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, ft^{2} or ft^{3}. For example, if you are starting with mm and you know r and h in mm, your calculations will result with s in mm, V in mm^{3}, L in mm^{2}, B in mm^{2} and A in mm^{2}.

Below are the standard formulas for a cone. Calculations are based on algebraic manipulation of these standard formulas.

## Circular Cone Formulas in terms of radius r and height h:

- Volume of a cone:
- V = (1/3)πr
^{2}h

- V = (1/3)πr
- Slant height of a cone:
- s = √(r
^{2}+ h^{2})

- s = √(r
- Lateral surface area of a cone:
- L = πrs =
πr√(r
^{2}+ h^{2})

- L = πrs =
πr√(r
- Base surface area of a cone (a circle):
- B = πr
^{2}

- B = πr
- Total surface area of a cone:
- A = L + B = πrs + πr
^{2}= πr(s + r) = πr(r + √(r^{2}+ h^{2}))

- A = L + B = πrs + πr

### Circular Cone Calculations:

Use the following additional formulas along with the formulas above.

- Given radius and height calculate the slant height, volume, lateral surface area and total surface area.

Given r, h find s, V, L, A- use the formulas above

- Given radius and slant height calculate the height, volume, lateral surface area and total surface area.

Given r, s find h, V, L, A- h = √(s
^{2}- r^{2})

- h = √(s
- Given radius and volume calculate the height, slant height, lateral surface area and total surface area.

Given r, V find h, s, L, A- h = (3 * v) / (πr
^{2})

- h = (3 * v) / (πr
- Given radius and lateral surface area calculate the height, slant height, volume and total surface area.

Given r, L find h, s, V, A- s = L / (πr)
- h = √(s
^{2}- r^{2})

- Given radius and total surface area calculate the height, slant height, volume and lateral surface area.

Given r, A find h, s, V, L- s = [A - (πr
^{2})] / (πr) - h = √(s
^{2}- r^{2})

- s = [A - (πr
- Given height and slant height calculate the radius, volume, lateral surface area and total surface area.

Given h, s find r, V, L, A- r = √(s
^{2}- h^{2})

- r = √(s
- Given height and volume calculate the radius, slant height, lateral surface area and total surface area.

Given h, V find r, s, L, A- r = √[ (3 * v) / (π * h) ]

- Given slant height and lateral surface area calculate the radius, height, volume, and total surface area.

Given s, L find r, h, V, A- r = L / (π * s)
- h = √(s
^{2}- r^{2})

## References

Weisstein, Eric W. "Cone." From *MathWorld*--A Wolfram Web Resource.

http://mathworld.wolfram.com/Cone.html