# Height of a Cone Calculator

The height of a cone calculator will help you **find the height of any cone given just two parameters**.

Here you will learn:

- How to find the height of a cone given its
**volume**and**radius**. - How to find the height of a cone without its volume, knowing its
**radius**and**slant height**.

Is the radius of a cone proportional to its height? Keep reading to learn the answer to that question and read on some cone height examples!

## Cone definition

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**.

## Height of a cone formula

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

And given, again, its radius and volume ($V$):

Let's see when to apply each next.

## How to find the height of a cone without knowing its volume?

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

**Write down**the**radius**and**slant height**dimensions.**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.

**That's it**!

## How to find the height of a cone given its volume?

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

**Write down**the**radius**and**volume**.**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.

**It's as simple as that**!

## Examples using the height of a cone calculator

### Example 1: Find the height given radius and slant height

Let's say we want to find the height of a cone with radius $r = 5\ \text{cm}$ and slant height $l = 8\ \text{cm}$. 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 $20\ \text{cm}$ radius cone is $V = 1\ \text{L} = 1000\ \text{cm³}$.

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

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## FAQ

### Is the radius of a cone proportional to its height?

**No**. The radius of a cone and the cone's height are independent of each other if there are no fixed variables (for example, the cone's volume). However, the height of a cone and radius are directly proportional to its slant height dimension.

### What's the height of a 10 cm radius and 15 cm slant height cone?

**5√5 = 11.18**. To find the height of a `10 cm`

radius and `15 cm`

slant height cone, you need to input those parameters in the height of a cone formula `h = √(l² - r²)`

where:

`l`

is the cone's slant height; and`r`

is the radius.