Math
Cone
Calculate cone volume, slant height, lateral area, and closed surface area from radius and perpendicular height.
Calculators / Math / Cone frustum
Cone frustum calculator
Calculate the volume of a truncated cone and distinguish its sloping lateral area from the total area including both circular ends.
On this page
Volume87.96units³
Lateral area67.96units²
Surface area130.79units²
Calculator controls
How to calculate
Calculate the volume of a truncated cone and distinguish its sloping lateral area from the total area including both circular ends.
Volume = pi*h*(R^2+R*r+r^2)/3 units³; Lateral area = pi*(R+r)*sqrt(h^2+(R-r)^2) units²; Surface area = pi*(R+r)*sqrt(h^2+(R-r)^2)+pi*(R^2+r^2) units²
Worked example
Lower radius: 4; Upper radius: 2; Perpendicular height: 3.
Volume: 87.96 units³; Lateral area: 67.96 units²; Surface area: 130.79 units².
Assumptions and limits
Calculate the volume of a truncated cone and distinguish its sloping lateral area from the total area including both circular ends. Use the same length unit throughout. Angles marked degrees use degrees. Results describe ideal geometric shapes.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate the volume of a truncated cone and distinguish its sloping lateral area from the total area including both circular ends.
When this tool is useful
Volume = pi*h*(R^2+R*r+r^2)/3 units³; Lateral area = pi*(R+r)*sqrt(h^2+(R-r)^2) units²; Surface area = pi*(R+r)*sqrt(h^2+(R-r)^2)+pi*(R^2+r^2) units²
Understanding your inputs
| Input | What to enter |
|---|---|
| Lower radius | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Upper radius | Enter a number of at least 0 and no more than 1000000000000. |
| Perpendicular height | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Calculate the volume of a truncated cone and distinguish its sloping lateral area from the total area including both circular ends. Use the same length unit throughout. Angles marked degrees use degrees. Results describe ideal geometric shapes.
How is the result calculated?
Volume = pi*h*(R^2+R*r+r^2)/3 units³; Lateral area = pi*(R+r)*sqrt(h^2+(R-r)^2) units²; Surface area = pi*(R+r)*sqrt(h^2+(R-r)^2)+pi*(R^2+r^2) units²