Calculate the missing top radius, bottom radius, height, or angle of a conical frustum using three known values and unit selections.
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Conical Frustum Angle Formula
The following formula is used to calculate the angle of a conical frustum for given dimensions.
θ = atan((R₁ - R₂) / h) * (180 / π)
Variables:
- θ is the angle in degrees
- R₁ is the top radius
- R₂ is the bottom radius
- h is the height of the frustum
To calculate the angle of a conical frustum, subtract the bottom radius from the top radius, divide by the height, and then take the arctangent of the result. Multiply by 180/π to convert from radians to degrees.
What is a Conical Frustum?
A conical frustum is a portion of a cone that lies between two parallel planes cutting the cone. It has a circular top and bottom with different radii, and a height that is the perpendicular distance between the two parallel planes. Conical frustums are commonly found in various engineering and architectural applications, such as in the design of funnels, towers, and other structures that require a tapered shape.
How to Calculate Conical Frustum Angle?
The following steps outline how to calculate the angle of a conical frustum.
- First, determine the top radius (R₁).
- Next, determine the bottom radius (R₂).
- Next, determine the height (h).
- Finally, calculate the angle using the formula θ = atan((R₁ – R₂) / h) * (180 / π).
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Top Radius (R₁) = 5
Bottom Radius (R₂) = 3
Height (h) = 4
