Cone Volume
Calculator
Results
- Volume
- 84.823001
- Slant height
- 9.486832
- Lateral surface area
- 89.411294
- Total surface area
- 117.685628
Results
| Volume | 84.823001 |
| Slant height | 9.486832 |
| Lateral surface area | 89.411294 |
| Total surface area | 117.685628 |
formula-map diagram
- Volume
- 84.823001
- Slant height
- 9.486832
- Lateral surface area
- 89.411294
- Total surface area
- 117.685628
Formula map
Formula
V = (π × r² × h) ÷ 3= 84.823001646924
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What inputs are required?+
The radius of the circular base and the height of the cone measured perpendicular from the base to the apex.
What is the formula and why is there a 1/3?+
Volume is (1/3)πr²h. The factor of 1/3 comes from the fact that a cone holds exactly one third of the volume of a cylinder with the same base and height — this is provable with calculus but was known geometrically well before that.
Is height the same as the slant length?+
No, height is the straight vertical distance from base to apex, not the slant height along the cone's surface. Using the slant height instead of the true height will overstate the volume.
How do I find the volume of a truncated cone (a frustum)?+
This calculator assumes a complete cone coming to a point. A frustum, which has both a top and bottom radius, needs a separate formula and is not covered here.
Why does a cone hold less than I'd guess compared to a cylinder?+
Visually a cone looks like it should hold about half a cylinder's volume, but it actually holds only a third, because volume tapers to zero at the apex rather than staying constant.