How to Calculate Cross Section Area

Updated April 17, 2017

Slice through any three-dimensional object and you produce a two-dimensional, internal view of the object. When slicing or sectioning at exactly 90 degrees to the primary axis of the object, a cross section is created. Cross sections of symmetrical objects are typically simple geometric shapes like circles and rectangles. The area of the cross section is a function of the dimensions of the two-dimensional view. Measurement of these dimensions provides the data required to calculate the object's cross-sectional area.

Identify the axis of symmetry for the object. For example, the axis of symmetry for a cylinder is the imaginary line directed down the middle and extending the length of the cylinder.

Imagine a plane oriented perpendicular to the symmetry axis slicing through the object. The intersection of the plane with the object forms a two-dimensional projection on the plane.

Identify the geometric shape formed by the projection of the object on the cross-sectional plane. For example, the cross section of a sphere or a cylinder is a circle, while the cross section of a cube will be a square.

Measure the dimensions of the geometric shape using the ruler. For example, for a circular shape, measure the radius. If the shape is rectangular, measure the width and length of the rectangle.

Calculate the cross-sectional area by determining the area of the geometric shape. For a rectangle, multiply adjacent side lengths using this formula: area = length x width. For a circle, the area = (3.14) x radius x radius. For example, the cross-sectional area of a wire with a radius of 0.1 inch is: area = (3.14) x (0.1) x (0.1) = 0.0314 inches squared.

Things You'll Need

  • Ruler
  • Calculator
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About the Author

Pearl Lewis has authored scientific papers for journals such as "Physica Status Solidi," "Materials Science and Engineering" and "Thin Solid Films" since 1994. She also writes an education blog entitled Simple Science in Everyday Life. She holds a doctorate from University of Port Elizabeth.