Geratriz do Cone
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
ℓ = √(r²+h²)
About this calculator
The cone generator calculator determines the length of the slant height (ℓ) of a right cone, which is the distance from the apex to a point on the base edge. The formula used is ℓ = √(r² + h²), where r is the base radius and h is the cone height. This relationship comes from the Pythagorean theorem applied to the right triangle formed by the height, radius, and slant height.
To use the calculator, enter the base radius and height of the cone in any unit of measurement (e.g., centimeters or meters). The result will be displayed in the same unit. This tool is useful for geometry students, engineers, architects, and designers who need to calculate cone dimensions in projects or problems.
Examples of use include calculating the amount of material needed to make a paper cone, determining the length of a cut line in a metal cone, or solving math exercises. It is important to remember that the formula only applies to right cones (with the apex aligned with the center of the base).
Cautions: ensure that the radius and height values are in the same unit. If the cone is oblique, the slant height is not constant and this formula does not apply. Also, note that the slant height is always greater than both the height and the radius, as it is the hypotenuse of the triangle.
Frequently asked questions
What is the slant height of a cone?
The slant height of a cone is the straight line from the apex to the edge of the base. In a right cone, all slant heights are equal.
How do I calculate the slant height of a cone?
Use the formula ℓ = √(r² + h²), where r is the base radius and h is the height. Simply enter the values into the calculator.
Does the formula work for any cone?
No, the formula ℓ = √(r² + h²) is valid only for right cones. For oblique cones, the slant height varies and the calculation is more complex.
Do I need to use the same unit for radius and height?
Yes, the radius and height must be in the same unit for the result to be meaningful.
What is the difference between slant height and height?
The height is the perpendicular distance from the apex to the center of the base. The slant height is the inclined distance from the apex to the base edge, always larger than the height.