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Geometry & Practical Projects

Cone Volume Calculator

Calculate a cone’s volume, slant height and total surface area from its radius and height.

Your inputs

Results

Volume

37.699112 m³

Slant height
5 m
Total surface area
75.398224 m²
In litres
37,699.1118 L

✓Exact calculation — rounded only for display

What this calculator does

Cones describe funnels, piles of sand or gravel, and conical roofs. Find the volume, the sloping side length and the surface area from the radius and height.

Formula and method

Volume = ⅓ π r² h; Slant height l = √(r² + h²); Surface area = π r (r + l)

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Length unit: Metres
  • Base radius: 3
  • Height: 4

Results

  • Volume: 37.699112 m³
  • Slant height: 5 m
  • Total surface area: 75.398224 m²
  • In litres: 37,699.1118 L

How to read the results

A cone holds one-third of the cylinder with the same base and height.

Assumptions and limitations

  • Use one length unit consistently; areas are in square units and volumes in cubic units of that length.

Quantities and costs are planning estimates. Add sensible allowances, and check with suppliers, carriers or professionals before buying, shipping or building.

Questions

How do I estimate a gravel pile?

Treat it as a cone using the base radius and the pile height.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
2 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy