Cone Slant Height

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Cone Slant Height Calculation:

  •  r =

    Radius of the circular base of the cone

  •  i =

    Height along outer slanted portion of cone from point on circumference to tip

  •  h =

    Height from the base of the cone to the tip

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Cone Slant Height Formula

Cone height, from center of base to tip, can be calculated with the radius and slant height using Pythagorean theorem. If a cone to sliced exactly in half the cut face will be a triangle where the slant height of the cone forms the hypotenuse, finding the height then works like any other right angle triangle.

h = √(i2 - r2)

Cone Slant Height Variables

The height of a cone can be calculated if the slant height and radius of the circular base are known.

Slant Height (i)
The straight line length from a point on the cone circumference to the tip.
Radius (r)
Radius of the circular base of the cone in linear units.
Height (h)
Length from the center of the circular base to the tip of the cone at a right angle.

Cone Slant Height Solution

How do we find the height of a cone where the slant height is 5 and the radius is 3?

  • h = √(i2 - r2)
  • substitute in the known values, note the formula is the same as Pythagorean theorem if we are given the hypotenuse and base, which we are given under the names "slant height" and "radius", respectively
  • h = √(52 - 32)
  • Find the height of a cone with a slant height of 5 and radius of 3
  • h = √(25 - 9)
  • Square the slant height and radius
  • h = √16
  • Subtract the squared radius from the squared slant height
  • h = 4
  • Take the square root
  • 4

The height of a cone with slant height 5 and radius 3 is 4 linear units.

Cone Slant Height Example

Find the height of a cone with a radius of 4 and a slant height of 11.

  • h = √(i2 - r2)
  • h = √(112 - 42)
  • h = √(121 - 16)
  • h = √105
  • 10.247

The height of a cone with a slant height of 11 and radius of 4 is approximately 10.247, rounding to three decimal places.

Want to calculate the volume of a cone with known volume?

Cone Height Calculator