A frustum is the portion of a cone remaining after its top is cut off by a plane parallel to the base. It has two circular faces (top and bottom) and a curved lateral surface connecting them.

What is the formula for the lateral surface area of a frustum?

The lateral surface area is LSA = π(R + r) × l, where R is the bottom radius, r is the top radius, and l is the slant height (the distance along the slanted surface).

What is the formula for the total surface area of a frustum?

The total surface area is TSA = π(R + r)l + πR² + πr². This adds the lateral surface to the areas of both circular bases.

How is slant height different from vertical height?

The slant height l is the distance along the sloped side of the frustum. The vertical height h is the perpendicular distance between the two bases. They relate by l = √(h² + (R − r)²).

What if the top radius equals zero?

When the top radius r = 0, the frustum becomes a complete cone. The formula reduces to the standard cone lateral surface area: πRl.

What if both radii are equal?

When R = r, the frustum is a cylinder. The lateral surface area becomes 2πRl (which equals 2πRh since l = h when radii are equal).

What units does this calculator support?

You can work in centimeters, meters, inches, or feet. All area results are shown in the corresponding square units.

Surface Area of a Frustum Calculator

Name: Surface Area of a Frustum Calculator
Availability: InStock
Author: Nham Vu

Enter the top radius, bottom radius, and slant height of a frustum to instantly get the lateral and total surface area.

Frustum Dimensions

Unit

Bottom Radius (R) — larger base

Top Radius (r) — smaller base

Slant Height (l)

Formula Reference

Lateral Surface Area LSA = π(R+r)l

Top Circle Area A₁ = π · r²

Bottom Circle Area A₂ = π · R²

Total Surface Area TSA = LSA + A₁ + A₂

Enter the dimensions, then click Calculate Surface Area.

Frustum Diagram

Copied!

Summary

Enter the top radius, bottom radius, and slant height of a frustum to instantly get the lateral and total surface area.

How it works

Enter the bottom (larger) radius of the frustum.
Enter the top (smaller) radius of the frustum.
Enter the slant height — the distance along the slanted side from edge to edge.
Select your preferred unit (cm, m, in, or ft).
The lateral surface area, both base areas, and total surface area are computed instantly.
Use the Copy button to copy the total surface area to your clipboard.

Use cases

Calculate material needed to cover a conical lampshade or bucket.
Estimate sheet metal required for a tapered pipe or duct section.
Solve geometry homework on frustum surface areas.
Determine fabric or wrapping for cone-frustum packaging.
Compute heat-transfer surface for tapered industrial vessels.
Verify 3D model surface area during product design.
Calculate paint coverage for conical storage tanks.
Find the net area of a truncated cone for pattern-making.

Frequently Asked Questions

Related tools

Surface Area Of Cone Volume Of Cone Surface Area Of Cylinder

Last updated: 2026-05-23 · Reviewed by Nham Vu