Height of a Cone Calculator

A cone is a three-dimensional shape with a circular base, and a single vertex called the apex. This is the most intuitive cone to picture in your head (such as traffic cones or ice-creams).

The height of a cone calculator works with cones where its apex is located directly above its base center. These are called right circular cones. Cones with apex not above its base center are called oblique cones.

There are two different formulas to find the height of a cone. Given its radius (rr) and slant height (ll):

And given, again, its radius and volume (VV):

Let's see when to apply each next.

To find the height of a cone without knowing its volume:

1. Write down the radius and slant height dimensions.
2. Input them in the height of a cone formula: h = √(l² - r²) where:
   • l is the slant height;
   • r is the radius; and
   • h is the resulting height.
3. That's it!

To find the height of a cone given its radius and volume:

1. Write down the radius and volume.
2. Input them in the height of a cone formula for volume: h = 3 × V/(π × r²) where:
   • V is the cone's volume;
   • r is the radius; and
   • h is the resulting height.
3. It's as simple as that!

Example 1: Find the height given radius and slant height

Let's say we want to find the height of a cone with radius r=5 cmr=5 cm and slant height l=8 cml=8 cm. Then we use the height of a cone formula without volume:

Example 2 Find the height given radius and volume

Now, let's assume the volume of a 20 cm20 cm radius cone is V = 1\ \text{L} = 1000\ \text{cm^3}V=1 L=1000 cm³.

Looking at the formula from the previous section, we know that the height will be equal to:

Be sure to check our other calculators similar to the height of a cone calculator!

• Right circular cone
• Radius of a cone
• Lateral area of a cone
• Slant height of a cone, and
• Diameter of a cone.