Frustum Cone Area
Calculate total surface area of a conical frustum using top radius, bottom radius, and slant height. Get lateral, top, and base area results for 3D geometry.
About This Calculator
A conical frustum (truncated cone) is a three-dimensional shape formed by cutting off the top of a right circular cone with a plane parallel to its base. This shape is ubiquitous in everyday objects including buckets, drinking cups, flower pots, funnels, and tapered architectural columns. Our frustum cone area calculator computes the lateral, top, base, and total surface areas from just three input measurements.
The calculator applies the standard frustum surface area formulas: lateral area A_l = \u03c0(r + R)l, top circular area A_t = \u03c0r\u00b2, base area A_b = \u03c0R\u00b2, and total area A = A_l + A_t + A_b. Here r is the top radius, R is the bottom radius, and l is the slant height measured along the sloping lateral surface between the edges of the two circular faces.
This tool serves students studying solid geometry, manufacturers calculating material requirements for tapered products, DIY enthusiasts planning craft projects with conical frustum shapes, and engineers designing or analyzing truncated conical components. The calculator features shareable URL parameters for easy saving and collaboration.
Frequently Asked Questions
What is the formula for frustum cone surface area?
The total surface area of a conical frustum is A = \u03c0(r + R)l + \u03c0r\u00b2 + \u03c0R\u00b2, where r is the top radius, R is the bottom radius, and l is the slant height. The lateral surface area is \u03c0(r + R)l, the top area is \u03c0r\u00b2, and the base area is \u03c0R\u00b2.
What is the difference between a frustum and a truncated cone?
A frustum and a truncated cone describe the same geometric shape: a cone with its top cut off by a plane parallel to its base. The term frustum is the technical geometric name (from Latin meaning piece or fragment), while truncated cone is the more descriptive everyday term. They are used interchangeably.
How do I find slant height if I only have vertical height?
If you have the vertical height (h), top radius (r), and bottom radius (R), calculate the slant height using l = \u221a(h\u00b2 + (R - r)\u00b2). This is derived from the Pythagorean theorem, where the difference in radii forms the base of a right triangle and the vertical height forms the perpendicular side.
What units does the frustum area calculator support?
The calculator accepts any linear unit (cm, m, in, ft). Ensure all three inputs (top radius, bottom radius, and slant height) use the same unit. Area results are returned in the corresponding square units. For example, cm inputs give cm\u00b2 results, and inch inputs give in\u00b2 results.
Where are frustum area calculations used in practice?
Frustum area calculations are used in manufacturing buckets and pails (estimating material needed), designing tapered containers and funnels, calculating paint or coating requirements for conical frustum surfaces, architectural design of truncated columns, and engineering analysis of tapered structural components.
Is this frustum cone area calculator free?
Yes, this calculator is completely free with no registration. Use it for unlimited calculations and share results via URL for academic, professional, and personal projects.