Conical Frustum Angle Calculator

The Conical Frustum Angle Calculator is a tool that calculates the slant height, slant angle, and apex angle of a conical frustum based on its dimensions. A conical frustum is formed when the top portion of a cone is removed by a plane parallel to the base, leaving two circular bases. This calculator is essential for applications in engineering, manufacturing, and design, where precise dimensions and angles are critical.

Formula of Conical Frustum Angle Calculator

Step 1: Define the variables
R1 is the radius of the larger base
R2 is the radius of the smaller base
H is the height, which is the vertical distance between the two bases
L is the slant height, which is the distance along the side of the frustum
Theta is the slant angle or apex angle

Step 2: Calculate the slant height
The slant height is calculated using the Pythagorean theorem:
L = square root of ((R1 – R2)^2 + H^2)

Step 3: Calculate the slant angle
The slant angle is the angle between the slant height and the base plane:
Theta = arctan(H / (R1 – R2))

Step 4: Calculate the apex angle (optional)
The apex angle is twice the slant angle:
Apex angle = 2 * Theta

Table of Common Measurements

Example of Conical Frustum Angle Calculator

A conical frustum has the following dimensions:
R1 = 12 cm
R2 = 8 cm
H = 15 cm

Step 1: Calculate the slant height
L = square root of ((12 – 8)^2 + 15^2)
L = square root of 241 = 15.52 cm

Step 2: Calculate the slant angle
Theta = arctan(15 / (12 – 8))
Theta = arctan(15 / 4) ≈ 75.96°

Step 3: Calculate the apex angle
Apex angle = 2 * Theta
Apex angle = 2 * 75.96° ≈ 151.92°

Results:
Slant height: 15.52 cm
Slant angle: 75.96°
Apex angle: 151.92°

Most Common FAQs