Neutral Axis / Built-up Section Calculator
Enter rectangles in one shared coordinate system to calculate centroid and section properties. Not for structural certification.
Rectangle inputs
A QUICK WALKTHROUGH
How to use this tool
- Choose one length unit and use it for every dimension and coordinate.
- Add at least one non-overlapping rectangle using its lower-left corner, width, and height.
- Calculate the area centroid, centroidal moments of area, top/bottom section moduli, and radii of gyration.
Coordinate convention
Every rectangle is axis-aligned. Its x and y values locate the lower-left corner in one shared Cartesian coordinate system; x points right and y points up. Coordinates may be negative. All dimensions and coordinates must use the same length unit.
Composite-area calculation
The area centroid is the area-weighted average of rectangle centroids. Centroidal moments use each rectangle’s centroidal rectangle formula plus A·d² (parallel-axis theorem). Section moduli divide Ixx by the distances from the centroid to the top and bottom extreme y edges. Radii of gyration are √(I/A).
Scope and limits
Use distinct, non-overlapping rectangles to represent a uniform, solid 2D area. This calculator does not handle holes, negative areas, rotated shapes, shear center, warping, material variation, load cases, local buckling, code checks, or structural certification. Verify geometry and engineering decisions independently with a qualified professional.
Local calculation
Values are processed in this browser and are not a structural design approval or safety determination.
GOOD TO KNOW
Common questions
What is the reference axis?
The origin is the shared coordinate origin you choose. Each rectangle’s x,y values give its lower-left corner; the reported centroid is in that same coordinate system.
Can rectangles overlap or represent cutouts?
No. Overlap would double-count area, and cutouts require signed areas not supported here. Split the shape into non-overlapping positive rectangles.
Does this certify a structural member?
No. It reports geometric properties only and must not be used as structural certification or a substitute for applicable engineering review.