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Surface Area Calculator

Surface area is the total area of the outside of a solid — what you would paint, wrap or cover. Choose a shape and enter its dimensions to get the total, split into the side (lateral) area and the area of the base or bases.

Quick examples

Vertical height, not the slant height.

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Total surface area52 ft²
Side (lateral) area
40 ft²
Area of the base(s)
12 ft²
Formula used
Surface area = 2 × (lw + lh + wh)
Sides vs bases
  • Side area
  • Bases

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      Formula

      Box: 2 × (lw + lh + wh)
      Cube: 6 × side²
      Cylinder: 2πr × height + 2πr²
      Sphere: 4 × π × r²
      Cone: π × r × slant height + πr², where slant height = √(r² + height²)
      Square pyramid: side² + 2 × side × slant height, where slant height = √(height² + (side ÷ 2)²)

      How to use it

      1. Choose the shape.
      2. Enter the dimensions. For cones and pyramids use the vertical height; the slant height is worked out for you.
      3. Read the total, or use the side area alone if the ends are open — a pipe, a label, a lampshade.

      Worked examples

      A 2 × 3 × 4 ft box: 52 ft² in total (4.83 m²), 40 ft² of it on the four sides

      Total surface area
      52 ft²
      Side (lateral) area
      40 ft²
      Area of the base(s)
      12 ft²

      A cylinder 1 m in radius and 3 m tall

      Total surface area
      25.13 m²
      Side (lateral) area
      18.85 m²
      Area of the base(s)
      6.28 m²

      A cone with a 3 m radius and 4 m height (slant height 5 m)

      Total surface area
      75.4 m²
      Side (lateral) area
      47.12 m²
      Area of the base(s)
      28.27 m²

      A square pyramid with a 6 m base and 4 m height

      Total surface area
      96 m²
      Side (lateral) area
      60 m²
      Area of the base(s)
      36 m²

      Lateral versus total

      The lateral area leaves out the flat ends. A can’s label covers only the lateral area; the metal needed for the whole can is the total. For an open-top container, add the lateral area and half the base figure shown for a cylinder or box.

      Questions people ask

      What is the surface area of a cube with 3 ft sides?

      6 × 3² = 54 square feet.

      What is the surface area of a cylinder with radius 2 and height 5?

      The side is 2π × 2 × 5 = 62.83 and the two ends are 2π × 2² = 25.13, for a total of 87.96 square units.

      Does a sphere have a base area?

      No. A sphere is one continuous curved surface, so its whole area, 4πr², is shown as the side area and the base is zero.

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