Radius of a Cone Calculator

Created by Komal Rafay
Reviewed by Gabriela Diaz
Last updated: Jun 02, 2022

Are you stuck in a geometric problem and need the assistance of a radius of a cone calculator? You have come to the right place.
Our radius of a cone calculator will help you determine the radius of a cone using various dimensions and formulas of a cone.
You will also get to learn:

  • How to calculate the radius of a cone?; and
  • The radius of a cone formula.

The radius of a cone calculator

The radius of a cone calculator is an efficient and time-saving tool. It calculates the radius of a cone, primarily using the height and slant height of a cone. The other dimensions that use the radius or height are surface area, volume, lateral surface area, and base area. Thus these dimensions can be used to estimate the radius of a cone as well.

The tool is simple to use. All you have to do is:

  1. Input the height of the cone.
  2. Input the slant height of the cone. You have the option to choose different units of measuring heights as well. The default is centimeters (cm).
  3. The result is the radius of the right circular cone along with the other dimensions.

If you have the surface area of the cone and want to determine the radius, you may enter the surface area and the slant height, and the result would be the radius along with all the other dimensions of the cone.
Similarly, there are other dimensions present in the calculator that can be used to figure out the radius of a cone.
Continue reading, and you will understand how to use all of the other formulas.

The radius of a cone formula

The radius of a cone formula is simple, but there are multiple ways to calculate the radius of a cone.

  • Using height and slant height

    r=l2h2\large{r = \sqrt{l^2 - h^2}}

    where:

    • rr - Radius;

    • ll - Slant height; and

    • hh - Height.

    This is the simplest of all the other radius of cone formulas. It is also the primary formula used in our tool.

  • Using volume
    The next formula is to find radius of the cone using its volume and height. It looks like:
    r=3×Vπ×h\large{r = \sqrt{\frac{3 \times V}{\pi \times h}}}

    where:

    • VV - Volume.

    If you decide to use the volume to determine the radius, you may input the volume and height of the cone in the tool, and the result is the radius in centimeters.

  • Using lateral area
    The radius of a cone plays a role in determining the lateral area, so when you shuffle the formula, you can obtain the radius given the lateral area of the cone.

    r=ALπ×l\large{r = \frac{A_L}{\pi \times l}}

    • ALA_L - Lateral area.
  • Using base area
    The radius of a cone can also be calculated using the base area. The formula looks something like this:

    r=ABπ\large{r = \frac {A_B}{\pi}}

    where:

    • ABA_B - Base area.
  • Using surface area
    You might have the total surface area of the cone, so you have the formula in the form of a quadratic equation:
    πr2+πrlA=0\large{\pi r^2 + \pi r l - A = 0}

    where:

    • AA - Surface area.

So, if you were wondering how to calculate the radius of a cone, now you have the answer and so many options to calculate it, with the best option being to use the radius of the cone calculator, we made it just for you.

Is the radius of a cone proportional to its height?

No, the height and radius of a cone are not proportional to each other.
When we need to use both the height and radius of a cone to determine any other cone dimension, it is when the radius and height are interrelated. Other than that, the radius and height of a cone do not depend on each other, and you may not be able to predict one based on the other.

For instance, to determine the volume, slant height, lateral area, and surface area, you need the radius and height.

Cone dimension amazingness

The radius of a cone is one of the many dimensions of a cone, check out some other of our tools to get to know more about each of them.

FAQ

How can I calculate the radius of a cone?

The simplest formula to calculate the radius of a cone is:
r = √(l² - h²)

where:

  • r - Radius;
  • l - Slant height; and
  • h - Height.

So, to calculate the radius:

  1. Square the lateral height.
  2. Square the height.
  3. Subtract height squared from lateral height squared.
  4. Find the square root of the result from step three.
  5. The result is the radius of the cone.

What is the radius of a cone with base area of 34 cm²?

The radius is 3.29 cm if a cone has a base area of 34 cm².
The formula to determine the radius of a cone with known base area is:
r = AB / π

where:

  • AB - Base area;
  • π - Constant with value 3.14159; and
  • r - Radius.

So, to determine the radius from the base area:

  1. Divide the base area by pi.
  2. The result is the radius of the cone.
Komal Rafay
Diagram of a right circular cone.
Height (h)
in
Slant height (l)
in
Radius (r)
in
Other dimensions
Surface area (A)
in²
Volume (V)
cu in
Lateral surface area (A_L)
in²
Base area (A_B)
in²
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