Diameter of a Cone Calculator

Created by Jack Bowater
Reviewed by Komal Rafay
Last updated: May 09, 2022

Understanding the properties of a cone can be difficult at the best of times, which is where this diameter of a cone calculator comes into its own! No matter the variables you have - height, surface area, volume of a cone - your diameter won't be far away. We also explain how to calculate the diameter of a cone and the diameter of a cone formula in case you wish to perform the work by hand.

Diameter of a cone formula

The diameter of a cone equation depends on a number of things, mainly which variables you have to hand. To illustrate this properly, we will go through them all one-by-one. To start with, we have the diameter of a cone from height and slant height:

d=2×l2h2d = 2 \times \sqrt{l^2-h^2}

where:

  • ll - Slant height;
  • hh - Height; and
  • dd - Diameter.

This one is quite simple to remember as it relies on using Pythagoreas' theorem to find the radius of the base, then doubling it. Our next formula is to find the diameter of a cone from its volume and height:

d=2×3×Vπ×hd = 2 \times \sqrt{\frac{3 \times V}{\pi \times h}}

where:

  • VV - Volume.

As you can see, while this formula might not be too difficult to remember, its quite difficult to calculate accurately due to requiring both π\pi and a square root. That's why we made the diameter of a cone calculator! We now come to a few questions regarding area. First, we use the lateral area and slant height of a cone:

d=2×ALπ×ld = 2 \times \frac{A_L}{\pi \times l}

where:

  • ALA_L - Lateral area.

Then we use the base area of a cone to find the diameter:

d=2×ABπd = 2 \times \sqrt{\frac{A_B}{\pi}}

where:

  • ALA_L - Base area.

Now, if we have just the whole surface area of a cone and its slant height, we can find its diameter, although we have to solve the following quadratic equation:

0=πr2+πlrA0 = \pi r^2 + \pi l r - A

where:

  • r - Radius; and
  • A - Surface area.

You must then take the positive root and let d=2rd = 2r get your answer. That's a lot of work, so just use our diameter of a cone calculator instead!

How do I find the diameter of a cone?

To use the height and volume of a cone to find diameter:

  1. Multiply the volume of the cone by 3.
  2. Divide the resultant number by pi times the height.
  3. Find the square root of the result of the above division.
  4. Double the result of Step 3 to get the diameter.

Our other cone calculators.

While this diameter of a cone calculator answers "How to calculate the diameter of a cone?" in full, you may wish to explore other topics around the topic. In that case, please check out our other relevant tools:

FAQ

How do I find the volume of a cone from its diameter?

To find the volume of a cone from its diameter:

  1. Square the diameter.
  2. Multiply this square by pi and the height of the cone.
  3. Divide the result by 12 to get your cone volume.
Jack Bowater
Diagram of a right circular cone.
Height (h)
in
Slant height (l)
in
Radius (r)
in
Diameter (2r)
in
Other information
Surface area (A)
in²
Volume (V)
cu in
Lateral surface area (A_L)
in²
Base area (A_B)
in²
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