Right Circular Cone Calculator

Cone
Choose a Calculation:
r = m
h = m
Units*:
Significant Figures:

Answer:

r = m
h = m
s = m
V = m3
L = m2
B = m2
A = m2

Cone Shape

Cone Diagram with h = height and r = radius and s = slant height

r = radius
h = height
s = slant height
V = volume
L = lateral surface area
B = base surface area
A = total surface area
π = pi = 3.14159
√ = square root

About this Calculator

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, ft2 or ft3.  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 mm3, L in mm2, B in mm2 and A in mm2.

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)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))

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 = √(s2 - r2)
  • 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) / (πr2)
  • 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 = √(s2 - r2)
  • 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 - (πr2)] / (πr)
    • h = √(s2 - r2)
  • 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 = √(s2 - h2)
  • 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 = √(s2 - r2)

References

Weisstein, Eric W. "Cone." From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/Cone.html

 

 

Cite this content, page or calculator as:

Furey, Edward "Cone Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.