Cone Frustum Calculator
Find the volume, slant height, lateral area and total surface area of a truncated cone from its two radii and height.
units
units
units
Capacity of the truncated cone
- 1
Radius term (R² + R·r + r²)
5² + 5 × 3 + 3² = 49Weighted average of the two circular faces. - 2
Volume
π × 8 ÷ 3 × 49 = 410.50
How does this calculator work?
For a truncated cone with bottom radius R, top radius r and height h: slant height l = √((R − r)² + h²), volume V = (π·h/3)(R² + R·r + r²), lateral area = π(R + r)l, and total surface = lateral + πR² + πr². Enter the three measurements to get every value at once.
Formula
How this is calculated
A conical frustum is what remains when the tip of a cone is sliced off parallel to its base, leaving a bottom radius R, a smaller top radius r, and a vertical height h between the two circular faces. Enter all three values in any consistent length unit; results follow in those units (areas squared, volume cubed).
The slant height is the diagonal distance along the sloped side, found with the Pythagorean theorem from the radius difference and the height: l = √((R − r)² + h²). The volume averages the two end circles in a weighted way, V = (π·h/3)(R² + R·r + r²), which reduces to the standard cone volume when r = 0 and to a cylinder when R = r. The curved (lateral) surface is π(R + r)l, and adding the two flat circular faces πR² and πr² gives the total surface area.
Inputs must be non-negative and the height must be positive; a zero or negative height returns no result. Setting r = R yields a cylinder, and r = 0 collapses the shape into a full cone. The bar chart compares the three surface contributions so you can see how much of the total comes from the side versus each face.
Frequently asked questions
It is a cone with the top cut off by a plane parallel to the base, leaving two parallel circular faces of different radii joined by a sloped side — the shape of a typical bucket or lampshade.
The height h is the straight vertical distance between the two circular faces, while the slant height l is measured along the sloped surface and is always longer: l = √((R − r)² + h²).
Yes. Total surface = lateral area + bottom circle (πR²) + top circle (πr²). For an open bucket you would omit the top face and use lateral + πR² instead.
Also known as
TG we-Calculate Editorial Team. (2026). Cone Frustum Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cone-frustum-calculator
TG we-Calculate Editorial Team. "Cone Frustum Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/cone-frustum-calculator.
TG we-Calculate Editorial Team, "Cone Frustum Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cone-frustum-calculator
@misc{wecalculate_cone_frustum_calculator, title = {Cone Frustum Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cone-frustum-calculator}}, year = {2026}, note = {TG we-Calculate} }
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