Cone calculator
Find the volume, total surface area and slant height of a right circular cone from its base radius and perpendicular height.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Base radius | Enter the radius, which is half the diameter. |
| Perpendicular height | Enter perpendicular height using the definition in the method and example. |
Understanding your result
Read Volume (cubic units), Total surface area (square units), Slant height (units) in the units and model stated on this page. The formula V = πr²h/3 · S = πr(r + √(r² + h²)) 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
How much volume is inside a cone, and what area covers it?
Enter the radius and perpendicular height of a right circular cone. The results give its volume, area including the base, and slant height.
Common uses
- Estimate the volume of a conical shape.
- Calculate a cone’s surface area and slant height.
How it works
Slant height is √(r² + h²). Volume is one third of the volume of a cylinder with the same base and height. Total surface area includes the circular base and curved side. The perpendicular height is not the slant height.
Worked example
Radius 3 and height 4 give slant height 5, volume 12π ≈ 37.6991 and total surface area 24π ≈ 75.3982.