KEVOS® MAKEOS · Geometry
Prismoidal Formula Volume
What is the volume of this prism, pyramid, frustum or earthwork from its end and middle sections?
Volume of any prismoid — prism, pyramid, frustum of a pyramid or cone, and approximately other tapering bodies — from the areas of the two ends and the middle section by the prismoidal formula, with helpers for rectangular and circular ends.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Sections given as | choice | How the sections are described. |
| Height (distance between ends) | mm | Perpendicular distance between the two end sections. |
| Area of end 1 | mm² | Area of one end. |
| Area of the middle section | mm² | Area of the section halfway between the ends (measured, not averaged). |
| Area of end 2 | mm² | Area of the other end. |
| End 1 length (rectangular) | mm | Length of the rectangular end 1. |
| End 1 width (rectangular) | mm | Width of end 1. |
| End 2 length (rectangular) | mm | Length of end 2. |
| End 2 width (rectangular) | mm | Width of end 2. |
| End 1 diameter (circular) | mm | Diameter of circular end 1. |
| End 2 diameter (circular) | mm | Diameter of circular end 2. |
Method and formulas
- V = h (A₁ + 4A_m + A₂) ÷ 6.
- For straight-sided bodies the middle section has the average linear dimensions of the ends; the formula is then exact for prisms, pyramids and frustums.
- Example: rectangular ends 600 × 400 and 300 × 200 mm, 500 mm apart, enclose 70 L.
Limitations
- Exact for bodies whose section area varies as a quadratic along the height; approximate for others.
- Ends must be parallel.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the volume of a hopper, chute or tapered tank
- Estimate the volume of a casting or forging blank between two sections
- Calculate cut-and-fill or stockpile volumes
Who it is for
- Design engineers
- Estimators
- Toolmakers
What you get
- Volume
- End and middle areas used
- Volume in litres
Interpreting the result
- For irregular bodies, measure the middle section rather than averaging the ends.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 66. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
