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Surface Area of Cone Calculator

Calculate the total surface area of a cone instantly. Enter the radius and height to find the slant height, curved surface area, base area, and total surface area.

Calculate Your Cone Surface Area

Enter the measurements below for an instant calculation.

Total Surface Area

0 square units
Slant Height 0
Lateral Surface Area 0
Base Area 0

Surface Area of a Cone Formula

The total surface area of a cone includes the circular base and the curved outer surface. The calculation uses the radius of the base and the slant height of the cone.

Total Surface Area Formula
A = πr(r + l)

In this formula, r is the radius of the circular base and l is the slant height.

How Does the Calculator Work?

This Surface Area of Cone Calculator automatically performs each step needed to calculate the complete surface area. You only need to enter the radius and vertical height.

1

Enter Radius

Enter the radius of the circular base of your cone.

2

Enter Height

Enter the perpendicular vertical height of the cone.

3

Get Results

Instantly receive the slant height and complete surface area calculation.

How Is Slant Height Calculated?

The slant height is calculated using the radius and vertical height of the cone.

Slant Height Formula
l = √(r² + h²)

Understanding the Surface Area of a Cone

A cone is a three-dimensional shape with a circular base and a pointed top known as the vertex. Its total surface area consists of the curved outer surface and the circular base.

Surface area calculations are useful when estimating materials for cone-shaped objects. They are commonly used in mathematics, education, engineering, architecture, manufacturing, and construction projects.

Frequently Asked Questions

What is the formula for the surface area of a cone?
The total surface area formula is A = πr(r + l), where r is the radius and l is the slant height.
Does total surface area include the base?
Yes. The total surface area includes both the curved surface and the circular base.
How is the slant height calculated?
The slant height is calculated with the formula l = √(r² + h²).
What units are used for surface area?
Surface area is measured in square units such as cm², m², ft², or in².
Can I use decimal numbers?
Yes. The calculator accepts both whole numbers and decimal values.