Academics · Study Skills · Math

Unfold the shape,
add up every
face.

Choose a shape and type its measurements. The calculator gives the surface area and the volume, puts your numbers into the formula, and lists each face of the net so you can see where every square unit comes from.

Find the surface areaWhat you get

The surface area calculator

The worked example: how much paper a soup can’s label and lids take. Nothing you type leaves this browser.

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What you get

Academics · Study SkillsFree

What you finish with
The surface area, side area and volume of the solid, the formula with your numbers, and a face-by-face table of its net. It prints as a summary and downloads as a spreadsheet.
Who it is for
Middle school math students, families helping with geometry homework, and math teachers and tutors.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Six shapes, any unit. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The Study Skills space in Caveat Academics.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Say what the solid is and choose its shape.
  2. Type the unit and the measurements the shape asks for.
  3. Read the surface area, then the face-by-face table.
  4. Compare the side area with the total to see what the top and bottom add.
  5. Print the summary or download the spreadsheet.

Find the surface area

How surface area is worked out

The area of the net, face by face.

The worked example: a soup can, opened into its netTwo circles72.63 cm²2 × π × 3.4²The label213.63 cm²2π × 3.4 around × 10 tallSurface area286.26 cm²circles + labelThe worked example: a soup can, opened into its netTwo circles72.63 cm²2 × π × 3.4²The label213.63 cm²2π × 3.4 around × 10 tallSurface area286.26 cm²circles + label
Unroll a cylinder and it becomes two circles and a rectangle; the rectangle’s width is the distance around the circle.

Nets

Surface area is the total area of every surface of a solid: what it would take to wrap it. Cut a solid along its edges and fold it flat and you get its net, a set of flat shapes whose areas add up to the surface area. A box opens into six rectangles, a cylinder into two circles and a rectangle, a pyramid into a square and four triangles.

Curved shapes

A cone’s side uses the slant height, the distance along the surface from the tip to the edge, which the Pythagorean theorem gives from the radius and the height. A sphere cannot be flattened without stretching, but its area is exactly four times the area of its widest circle, a result Archimedes proved.

Sources

  1. Common Core State Standards for Mathematics, Grade 6, 6.G.A.4 (nets and surface area) and Grade 7, 7.G.B.6 (area, volume and surface area of solids).
  2. Common Core State Standards for Mathematics, Grade 8, 8.G.C.9 (volume of cones, cylinders and spheres).
  3. OpenStax. Prealgebra 2e (2020), section 9.6, Solve Geometry Applications: Volume and Surface Area (openstax.org).
  4. NIST Digital Library of Mathematical Functions, the constant π (dlmf.nist.gov).

The worked example uses round measurements. Your figures stay in this browser. Support: team@caveatacademic.com.