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Cone Surface Area Calculator

Work out cone surface area instantly with clear inputs, formula shown and shareable results.

About Cone Surface Area Calculator

The curved surface of a cone unrolls into a circular sector of radius l, giving lateral area πrl. Adding the circular base gives πr² + πrl = πr(r + l).

Formulas

Lateral area

A = πrl, l = √(r² + h²)

Total area

S = πr(r + l)

Worked example

With the default values below, Cone Surface Area Calculator returns Total surface area of 113.0973. Change any input above and every figure here is recalculated in your browser.

Inputs used

Base radiusminimum 0
4
Perpendicular heightminimum 0
3

Results

Total surface area
113.0973
Curved (lateral) area
62.8319
Base area
50.2655
Slant height
5.0000

Step by step

  1. 1Values used
  2. 2Lateral area
  3. 3Total area
  4. 4Total surface area= 113.0973
  5. 5Curved (lateral) area= 62.8319
  6. 6Base area= 50.2655
  7. 7Slant height= 5.0000

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Radius 4, height 3?

Slant height is 5, so lateral area is 20π and total area 36π ≈ 113.097336 square units.

Which height goes in the formula?

The lateral area uses the slant height l; only the volume uses the perpendicular height h.

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Cone Surface Area Calculator – Calculate Total surface area