Cross-Sectional Area Calculator

The cross-sectional area is the area of the face you would see if you sliced straight through an object at a right angle to its length. Cut a pencil in half and look at the flat circle: that circle is the cross-section. It turns up everywhere in engineering and physics, because so many things depend on it. Stress is force divided by cross-sectional area. The current a wire can carry scales with it. The flow through a pipe depends on it. Get the area wrong and every number downstream is wrong too.

For a solid round rod or wire, the area is the familiar circle: pi times the radius squared, or equivalently pi divided by 4 times the diameter squared. A rectangular bar is just width times height. A square is the side squared. The one that catches people out is the hollow tube or pipe. Its cross-section is a ring, not a disc, so you take the area of the outer circle and subtract the area of the hollow bore. The metal that is left, the wall, is the load-bearing part, which is why a fat-looking pipe with a thin wall can be surprisingly weak.

Units matter more here than almost anywhere, because area scales with the square of length. Double the diameter and the area quadruples. Mix up millimetres and centimetres and you are off by a factor of 100, not 10. This calculator keeps you honest by taking your dimensions in whichever unit you pick and then reporting the answer in square millimetres, square centimetres, and square inches at once, so you can drop the right one straight into the next formula. Choose the shape, enter the dimensions, and for a tube you also get the bore area and the wall area broken out separately.