# Lateral Area of a Cone Calculator

With Omni's lateral area of a cone calculator, you'll be able to determine the **lateral area of a right cone** in a blink of an eye!

Maybe you're wondering how to find the lateral area of a cone and even wondering if there's any difference between its **surface area** and **lateral area,** well, you just arrived at the right place!

If you like to learn about these and more, we invite you to keep reading and find:

- The lateral area formula of a cone;
- What is the difference between lateral area and surface area;
- How to find the lateral area of a cone using its diameter; and
- Is it true that the lateral of a cone is exactly 1/2 of the lateral surface area of a cylinder? 🤔

## What is the formula for the lateral area of a cone?

The **lateral surface area of a cone** is given by the expression:

`A_L = π x r x √(r² + h²)`

Or, in terms of the cone's slant:

`A_L = π x r x l`

Where:

`A_L`

-**Lateral surface area;**`r`

-**Radius**of the circular base of the cone;`h`

- Vertical**height**of the cone; and`l`

- Slant height.

## What is the difference between lateral area and surface area?

From the equation above, you might have noticed that the **lateral surface area** of a cone does not correspond to its **total surface area,** given by:

`A_T = π x r x √(r² + h²) + π x r²`

For any geometrical figure, the difference between these two areas is that the **lateral surface area** of a three-dimensional shape is the area that can be seen from a side-on view. This is, the sides of the shape, excluding its base and top. For the particular case of a cone, we'll only be excluding the base since this figure does not have a top.

The latter equation shows that the **total surface area** includes the **lateral area** `π x r x √(r² + h²)`

and the **area of the cone's circular base** `π x r²`

:

`A_T = Total area = Lateral area + base area`

`A_T = π x r x (√(r² + h²) + r) `

From here we can see that if the **total and base areas of a cone** are known, we could also determine its **lateral surface area** as the difference between these:

`A_L = Lateral area = Total area - base area`

Another option to calculate the **lateral area of a cone** is from its **volume and radius** or **volume and vertical height**. This means that if you know any of these, the lateral area of a cone calculator will be able to determine the lateral area of the cone 😉

## How do I find the lateral area of a cone?

To find the lateral area of a cone:

- Use the cone's lateral area formula,
`A_L = π x r x √(r² + h²)`

. - To employ this formula, you'll need to know the cone's radius and vertical height.
- With these two knowns, you can proceed to substitute the values and perform the required algebraic operation.

For example, if we had a cone of **radius r = 6 cm** and **height h = 10 cm,** we can determine its lateral area by:

- Using the formula
`A_L = π x r x √(r² + h²)`

. - Substitute the corresponding dimensions:
`A_L = 3.1416 x (6 cm) x √((6 cm)² + (10 cm)²)`

. - Finally, execute the required operations, and get the result:
`A_L = 219.8 cm²`

.

## More right circular cone calculators!

If you enjoyed the lateral area of a cone calculator, and want to learn more about right cone's geometrical properties, we invite you to visit other of our related tools:

## FAQ

### Is the lateral surface area of a cone exactly 1/2 the lateral area of a cylinder?

**True.** For a cone of slant "h" and a cylinder of height "h", both with the same radius "r", the lateral area of the cone is 1/2 the lateral area of the cylinder:

- The formulas for the lateral areas:
`A_L_cone = π x r x h`

and`A_L_cylinder = 2 x π x r x h`

. - From these,
`2 x A_L_cone = A_L_cylinder`

. - Thus,
`A_L_cone = A_L_cylinder/2`

. Indicating that a**cone's lateral area is 1/2 of the cylinder's.**

### How do I find the lateral area of a cone given its diameter?

To find the lateral of a cone given its diameter `D`

, follow these steps:

- Use the lateral area formula for a cone:
`A_L = π x r x √(r² + h²)`

. - Since the diameter
`D`

is equal to twice the radius of a circumference, employ the corresponding relationship:`r = D / 2`

. - By replacing this in the equation above:
`A_L = π x (D / 2) x √((D / 2)² + h²)`

. - Substitute the numeric values of diameter and height, perform the operations, and get the lateral area value.