Cone Frustum Calculator
What is the volume and surface area of a cone with its top cut off? Enter the values below to calculate the result.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Outer or sphere radius (length) | Enter the radius, which is half the diameter. |
| Radius (length) | Enter the radius, which is half the diameter. |
| Height (length) | Enter height in length; use the same basis as the other measurements. |
Understanding your result
Read volume (length^3), lateral (length^2), surface (length^2) in the units and model stated on this page. The formula l=hypot(h,R-r) · volume=pi*h*(R*R+R*r+r*r)/3 · lateral=pi*(R+r)*l · surface=lateral+pi*(R*R+r*r) defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Entering the diameter where the radius is requested.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
What is the volume and surface area of a cone with its top cut off?
What is the volume and surface area of a cone with its top cut off? Enter the values below to calculate the result.
Common uses
- What is the volume and surface area of a cone with its top cut off
How it works
l=hypot(h,R-r); volume=pi*h*(R*R+R*r+r*r)/3; lateral=pi*(R+r)*l; surface=lateral+pi*(R*R+r*r)
Worked example
Enter Outer or sphere radius: 3 length; Radius: 1 length; Height: 4 length. Results: volume: 54.45427266222308 length^3; lateral: 56.198517848325814 length^2; surface: 87.61444438422375 length^2.