What this calculator does
The centroid of a rectangle, also called its geometric centre or centre of area, is the point where the shape would perfectly balance if it were a flat, uniform sheet. For a rectangle this is always the simplest possible case: the centroid sits exactly at the midpoint of both the width and the height, directly at the intersection of the two diagonals.
Knowing a shape's centroid matters in structural and mechanical engineering, where it is used as the reference point for calculating bending stresses, moments of inertia and load distribution. For more complex shapes the centroid can be far harder to find, but a rectangle's symmetry makes it a single, trivial calculation.
The formula
The centroid coordinates, measured from one corner of the rectangle, are simply half the width and half the height: (width ÷ 2, height ÷ 2). This is exactly where the two diagonals of the rectangle cross.
| Term | Meaning |
|---|---|
| Centroid | The geometric centre of a shape: the average position of every point in it, and the point at which a uniform flat shape balances. |
| Width and height | The two side lengths of the rectangle, measured at right angles to each other. |
The inputs explained
| Field | What to enter |
|---|---|
| Width (m) | The rectangle's width. |
| Height (m) | The rectangle's height. |
When to use it
Structural load calculations
The centroid of a rectangular cross-section (such as a beam or column) is the reference point used for calculating bending stress and moment of inertia in structural engineering.
Balancing a flat panel
A rectangular sign, panel or plate needs to be supported or lifted at its centroid to hang or balance evenly without tipping.
Building up a composite shape's centroid
When a more complex shape is broken down into rectangles for a composite-centroid calculation, each rectangle's own centroid (found here) is a required input to that larger calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Where is the centroid for common rectangle sizes?
A range of rectangle widths at a fixed height, showing how the centroid position shifts.
Questions
Is the centroid the same as the centre of mass?
For a flat shape of uniform, constant density, yes, the geometric centroid and the centre of mass are the same point. They can differ for a shape with varying density or thickness.
Why is a rectangle's centroid so simple to find?
Because a rectangle is symmetric about both its horizontal and vertical midlines, so the centroid falls exactly where those two midlines cross, without needing any integration or area-weighted averaging like more irregular shapes require.
Does the centroid change if the rectangle is rotated?
No. The centroid is a fixed point relative to the shape itself. Rotating the rectangle moves that point in space along with the shape, but its position relative to the rectangle's own corners and sides stays the same.
How is this used for a rectangular beam cross-section?
In beam design, the centroid marks the neutral axis reference point used when calculating bending stress and the second moment of area, both of which assume bending occurs about an axis through the centroid.
For the area and perimeter of the same rectangle, see the area of shapes calculator.