The Conical Frustum Angle Calculator is a valuable tool designed to determine the slant angle of a truncated cone. This angle is important in many fields such as engineering, design, and architecture, especially when working with funnels, silos, and other frustum-shaped structures. With this tool, all you need are the radii and height to calculate the angle with precision.
Formula
To calculate the slant angle (θ) of a conical frustum, use this formula:
θ = arctangent of (R₁ − R₂) divided by height h, then multiply the result by (180 divided by π) to convert it to degrees.
How to use
Enter the larger radius (R₁), the smaller radius (R₂), and the vertical height (h) into the calculator. After filling in the values, click the “Calculate” button. The calculator will instantly provide the slant angle θ in degrees.
Example
If R₁ is 12, R₂ is 8, and the height is 10, the calculation becomes:
θ = atan((12 – 8) / 10) × (180 / π) = atan(0.4) × (180 / π) ≈ 21.80 degrees
FAQs
1. What is a conical frustum?
A conical frustum is a cone with the top part removed by a cut parallel to its base.
2. What does the angle in this calculator represent?
It represents the angle between the slanted side of the frustum and its vertical axis.
3. Can I use different units like inches or centimeters?
Yes, just make sure all inputs are in the same unit system.
4. What happens if both radii are equal?
The shape becomes a cylinder and the angle will be zero.
5. What if the height is zero?
The calculator will show “Invalid input” because height cannot be zero.
6. Can this tool help with real-world construction?
Yes, it’s perfect for engineers, metal workers, and designers who need accurate slant angles.
7. Is the input height vertical or slant height?
It must be the vertical height between the two circular bases.
8. Can I enter decimal values?
Yes, decimal values are fully supported for precision.
9. What if I enter a negative radius?
Negative values are invalid and will return an error.
10. Does this calculator work on phones?
Yes, it works on any modern browser including mobile devices.
11. Is the result in degrees or radians?
The result is shown in degrees.
12. What kind of shapes use conical frustums?
Funnels, hoppers, cups, and silos are common examples.
13. Can I save or print the result?
You can copy the result or take a screenshot for your records.
14. Can I embed this calculator on my site?
Yes, just copy and paste the HTML and JavaScript into your webpage.
15. Does it need an internet connection?
No, once the page is loaded, it works entirely offline.
16. Is this tool accurate?
Yes, it uses JavaScript’s Math library for precise calculations.
17. Can I reset the form?
You can manually clear the fields or reload the page.
18. Is it suitable for educational use?
Absolutely, it’s great for teaching geometry and trigonometry.
19. Can it calculate the slant height too?
No, this version only calculates the angle. You’d need a separate tool for slant height.
20. Who uses conical frustum calculations?
Engineers, designers, teachers, and students often use these calculations for various projects.
Conclusion
The Conical Frustum Angle Calculator simplifies a common geometric problem into a quick and easy solution. Whether you’re building components, designing structures, or teaching geometry, this tool gives you accurate angle measurements in seconds. No more manual formulas—just input, click, and calculate.