Math

Cone Volume Calculator

Estimate cone volume, filled volume, and slant height.

Inputs

Adjust the assumptions to match your scenario. Results update instantly.

RadiusRadius of the circular base of the cone.HeightVertical height of the cone from base center to the tip.Fill percentPercentage of the cone volume considered filled or occupied.

Results

Primary outputs and comparison insights are built from the current inputs.

Full volume

167.55

Total volume of the cone from the selected radius and height.

Filled volume

100.53

Volume occupied after applying the selected fill percentage.

Slant height

10.77

Slanted edge length from the cone tip to the base edge.

How this calculator works

The Cone Volume Calculator helps you estimate full cone volume, partial fill volume, and slant height from a simple radius and height input. Enter radius, height, and fill percent to estimate full volume, filled volume, and slant height. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision.

Quick guide

Jump straight to the section you need, then return to the calculator.

Inputs Outputs Assumptions Tips Formulas Examples Reference table Visual breakdown References

Inputs

Radius of the circular base of the cone.
Vertical height of the cone from base center to the tip.
Percentage of the cone volume considered filled or occupied.

Outputs

Total volume of the cone from the selected radius and height.
Volume occupied after applying the selected fill percentage.
Slanted edge length from the cone tip to the base edge.

Assumptions

The cone is treated as a right circular cone with one flat circular base.
Fill percent is modeled as a direct share of total volume for quick planning.

Tips

Keep radius and height in the same unit so the outputs stay coherent.
Use the slant height when you need material length along the side of the cone, not only capacity.

Formula guide

Use these formulas to audit the output or explain it to someone else.

2 formulas

Volume = pi * radius^2 * height / 3

Slant Height = sqrt(radius^2 + height^2)

Usage examples

Review a ready-made scenario, copy it, then tweak inputs to match your case.

Example

3 inputs3 outputs

Conical hopper estimate

Inputs

Example input Radius: 5
Example input Height: 14
Example input Fill percent: 70%

Outputs

Example result Full volume: 366.52
Example result Filled volume: 256.56
Example result Slant height: 14.87

Conical volume estimates are easier to use when you compare total capacity with the realistic fill level you expect in practice.

Cone volume by height

5 of 5 rows

Height	Full volume	Slant height
6	100.53	7.21
8	134.04	8.94
10	167.55	10.77
12	201.06	12.65
14	234.57	14.56

Cone volume depends heavily on height, so compare a shorter case with a taller case before you translate the result into material or capacity planning.

Cone volume sensitivity

Highest: 14 (234.57)Lowest: 6 (100.53)

Sort

HeightFull volume

Focus point

100.53

Position

#1 of 5

Original order

Share of total

12%

Total: 837.76

PositiveNegative

Cone volume depends heavily on height, so compare a shorter case with a taller case before you translate the result into material or capacity planning.

References

Cone geometry formulas for volume and slant height
Capacity planning with conical shapes

FAQ

Common questions

What does the Cone Volume Calculator do?

What inputs do I need?

Typical inputs include Radius of the circular base of the cone., Vertical height of the cone from base center to the tip., Percentage of the cone volume considered filled or occupied..

How are the results calculated?

We follow the formulas and assumptions outlined in the "How this calculator works" section. You will see outputs like Total volume of the cone from the selected radius and height., Volume occupied after applying the selected fill percentage., Slanted edge length from the cone tip to the base edge..