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

The total surface area is SA = πr² + πrl, where r is the base radius and l is the slant height. The first term πr² is the circular base and πrl is the lateral (curved) surface.

How do I find the slant height from the perpendicular height?

Use the Pythagorean theorem: l = √(r² + h²), where r is the base radius and h is the perpendicular height from base to apex.

What is the difference between total and lateral surface area?

The lateral surface area (πrl) covers only the curved side of the cone, excluding the circular base. The total surface area adds the base circle (πr²) for the complete closed surface.

What units does this calculator support?

You can work in centimeters, meters, inches, or feet. The area results are displayed in the corresponding square units (cm², m², in², or ft²).

Can I enter slant height instead of perpendicular height?

Yes. Use the toggle to switch input mode. When slant height l is provided, the perpendicular height is derived as h = √(l² − r²), provided l > r.

Does this work for an open cone (no base)?

Yes. The lateral surface area result gives you the area of just the curved side without the base, which is what you need for an open cone.

Surface Area of a Cone Calculator

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

Enter the radius and height (or slant height) of a cone to instantly get the total and lateral surface area.

Cone Dimensions

Unit

Base Radius (r)

Height Input Mode

Perpendicular Height (h)

Formula Reference

Total Surface Area SA = πr² + πrl

Lateral Surface Area LSA = π · r · l

Base Area A = π · r²

Slant Height l = √(r² + h²)

Enter the radius and height, then click Calculate Surface Area.

Cone Diagram

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Summary

Enter the radius and height (or slant height) of a cone to instantly get the total and lateral surface area.

How it works

Enter the base radius of the cone.
Choose whether to provide the perpendicular height or the slant height.
Enter the chosen height value.
Select your preferred unit (cm, m, in, or ft).
Total surface area, lateral surface area, base area, and slant height are calculated instantly.
Use the Copy button to copy the total surface area to your clipboard.

Use cases

Calculate material needed to cover the surface of a conical roof or tent.
Estimate paint coverage for conical decorative objects.
Solve geometry homework on cone surface areas.
Determine wrapping material for cone-shaped party hats or packaging.
Compute heat-transfer area for conical nozzles in engineering.
Verify 3D model surface area during product design.
Calculate fabric required for funnel or cone-shaped filters.

Frequently Asked Questions

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