Calculate a round cake’s surface area from its diameter and height, including the top-and-side icing area, or scale a recipe or size a pan for servings.

Model a round cake as a closed cylinder. Total surface area includes top, bottom and side; top-and-side icing area is shown separately.

Output unit only; input quantities retain their own units.

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Cake Surface Area Formula

The following formula gives the total surface area of a closed cylindrical cake for a given radius and height, including the top, bottom and side.

A = 2ฯ€r(r + h)

Variables:

  • A is the surface area of the cake
  • ฯ€ is the constant pi (approximately 3.14159)
  • r is the radius of the cake
  • h is the height of the cake

To calculate the surface area of the cake, multiply 2 by pi, then multiply by the radius, and finally multiply by the sum of the radius and height.

What is a Cake Surface Area?

The total surface area includes the top, bottom and side of an ideal cylindrical cake. For usual top-and-side coverage, exclude the bottom: the area is ฯ€rยฒ + 2ฯ€rh, shown separately in the calculator. Area alone does not determine icing quantity; thickness, decoration and waste also matter. Use consistent length units and corresponding square units.

How to Calculate Cake Surface Area?

The following steps outline how to calculate the Cake Surface Area.

  1. First, measure the radius (r) of the cake.
  2. Next, measure the height (h) of the cake.
  3. Use the formula A = 2ฯ€r(r + h) to calculate the surface area.
  4. Insert the values of radius and height into the formula and calculate the result.
  5. Choose Total cake surface area in the calculator and enter the diameter (or radius) and height. Reverse solve choices find radius or height from total area.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Radius (r) = 10 cm

Height (h) = 5 cm. Total surface area = 300ฯ€ โ‰ˆ 942.48 cmยฒ; top-and-side area = 200ฯ€ โ‰ˆ 628.32 cmยฒ.