Cross-Sectional Area Calculator

The cross-sectional area of a solid circular section is A = pi times r squared, where r is the radius (half the diameter). For example, a steel rod with diameter 50 mm has radius 25 mm, so A = pi times 625 = 1963.5 mm². This formula applies to solid shafts, rods, and any circular cross-section with no hollow interior.

For a hollow circular section (pipe or annulus), A = pi times (R squared minus r squared), where R is the outer radius and r is the inner radius. Equivalently, A = pi divided by 4 times (D squared minus d squared), where D is the outer diameter and d is the inner diameter. Example: a pipe with outer diameter 100 mm and inner diameter 80 mm has A = pi times (50 squared minus 40 squared) = pi times 900 = 2827.4 mm².

I-beam cross-sectional area = 2 times (flange width times flange thickness) plus (web height times web thickness), where web height = total height minus 2 times flange thickness. For an I-beam with flange width 150 mm, total height 300 mm, flange thickness 15 mm, and web thickness 10 mm: web height = 300 minus 30 = 270 mm, area = 2 times 150 times 15 plus 270 times 10 = 4500 plus 2700 = 7200 mm².

The cross-sectional area of a rectangular section is A = width times height (A = b times h). This is the simplest case and applies to square sections when b equals h. Example: a wooden joist 50 mm wide and 200 mm deep has A = 50 times 200 = 10 000 mm², which is 10 cm² or 100 cm².

Cross-sectional area determines the axial stress in a member under load. Stress = Force divided by Area (sigma = F/A). A larger cross-section carries more load at the same stress level, or the same load at lower stress. It also governs electrical resistance in conductors (R = rho times L divided by A) and fluid flow capacity in pipes.

Cross-sectional area is the area of a flat slice through an object, measured perpendicular to an axis. It is a 2D area in square units. Surface area is the total area of all outer surfaces of a 3D object, also in square units but representing the outer skin. A cylinder of radius r and length L has cross-sectional area pi r squared and total surface area 2 pi r squared plus 2 pi r L.

Increasing wall thickness by a small amount dt increases the cross-sectional area by approximately pi times D times dt, where D is the mean diameter. Doubling the wall thickness roughly doubles the cross-sectional area if the wall is thin relative to the diameter. For thick-walled pipes, use the exact formula A = pi times (R squared minus r squared).

The calculator is unit-agnostic. Enter any consistent unit (mm, cm, m, inches, feet) and the area result is in the square of that unit. For example, if you enter dimensions in millimetres, the area is in mm². There is no automatic unit conversion, so all inputs must be in the same unit system.

An I-beam with flange width 150 mm, total height 300 mm, flange thickness 15 mm, and web thickness 10 mm has area 7200 mm². A solid rectangle of the same envelope (150 times 300) would have area 45 000 mm². The I-beam uses only 16% of the solid rectangle's material but achieves most of its bending stiffness because the flanges are placed far from the neutral axis where bending stress is highest.

Yes. The hollow circle mode computes annular cross-sectional area A = pi times (R squared minus r squared) for any annular section: pipe flanges, hollow shafts, tubular columns, bearing rings, and pressure vessel walls. Enter the outer and inner diameters to get the metal cross-section area and wall thickness instantly.

To convert mm² to cm², divide by 100. To convert mm² to m², divide by 1 000 000. To convert cm² to m², divide by 10 000. For example, 7200 mm² equals 72 cm² equals 0.0072 m². To convert square inches to square centimetres, multiply by 6.4516.

A circle encloses the maximum area for a given perimeter. This is the isoperimetric property of the circle. Among rectangular sections, a square (equal width and height) maximises area for a given perimeter. This is why circular pipes are preferred for pressure vessels and why square sections appear in columns where efficiency matters.