Cone Frustum Calculator
Find a right circular cone frustum’s volume, slant height and surface areas from two radii and vertical height. Mix input units and compare volume equivalents.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
The radius changes linearly along perpendicular height. Integrating the circular cross-sections gives πh(R²+Rr+r²)/3. The Pythagorean theorem gives slant height, and unfolding the side gives lateral area π(R+r)s.
V=πh(R²+Rr+r²)/3; s=√[h²+(R−r)²]; A_side=π(R+r)s; A_closed=A_side+πR²+πr²
Worked example
Radii 5 cm and 3 cm with height 8 cm give volume 392π/3 ≈410.501440 cm³, or 0.410501440 L. Slant height is √68≈8.24621125 cm.
Assumptions and input details
The circular ends must be parallel and coaxial, with height measured perpendicular to the ends. Radius means half the diameter. Either radius may be zero for the cone limit; equal radii give the cylinder limit. At least one radius and height must be positive. Surface totals explicitly distinguish open sides from two closed ends. Internal dimensions give an ideal capacity; wall thickness, rounded edges, fill level and material deformation are not modelled. This is not an oblique cone or a pyramid frustum.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
The 36 volume definitions distinguish US liquid, US dry and Imperial measures. Cups carry an explicit definition. Japanese shō is 2401/1331 L and a gō is one tenth of it; the explicitly labelled 180 mL rice cup is separate.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · UK Imperial definitions · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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