Cone, frustum, and prism volumes
The volume of a cone, frustum, or prism from its dimensions, or of a conical pile from its base and an angle of repose you enter with its source.
Experimental: not yet fully verified. How results are checked
The volume is 5,026.55 ft³, or 186.17 yd³.
- Volume, cubic yards
- Height
Provenance
- Computed by
- survey.earthwork.solid-volume 1.0.0, core 0.1.0
- Model
- Cone πr²h/3; frustum πh(R² + Rr + r²)/3; prism A·h; a conical pile's height r·tan(angle of repose)
- Accuracy
- Exact for the shape; real piles are rarely perfect cones
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Cone πr²h/3; frustum πh(R² + Rr + r²)/3; prism A·h; a conical pile's height r·tan(angle of repose)
Accuracy: Exact for the shape; real piles are rarely perfect cones
Worked example: A cone 20 ft in radius and 12 ft high. Source: πr²h/3 = 5,026.55 ft³. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Height
- 12 ft
- Base radius
- 20 ft
- Shape
- cone
You get
- Volume
- 5,026.55 ft³
- Volume, cubic yards
- 186.17 yd³
- Height
- 12 ft
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapter 26 (volumes: TIN-based volumes and volumes of solids).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.