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Free online moment of inertia calculator and centroid calculator. This calculator will find area moment of inertia for a user defined area and also calculate the centroid for that area shape.

This calculator is a versatile calculator and is programmed to find  area moment of inertia and centroid for any user defined shape.

Find moment of inertia for I section, rectangle, circle, triangle and various different shapes. The area moment of inertia can be found about an axis which is at origin or about an axis defined by the user. Moment of inertia for I section can be built using 3 rectangles, and similarly many shapes can be built using basic shapes.

Find the tutorial for this calculator in this video.


Embedded OneDrive Excel Workbook Example

How to use calculator:

Solved Example for reference

Moment of inertia online calculator example 1

Let us calculate the area MOI of this shape about XX and YY axis which are at a distance of 30mm and 40mm respectively from origin.

It should be noted here that the equation for XX axis is y=30mm and equation for YY axis is x=40mm.

STEP 1: Divide in simple shapes


The given shape can be divided into 5 simpler shapes namely i) Rectangle ii) Right angled triangle iii) Circle iv) Semi circle v) Quarter circle.

It should be noted that 2 right angled triangles, circle, semi circle and quarter circle are to be subtracted from rectangle, and hence they will be assigned with a ‘Subtract’ option in calculator and rectangle with a ‘Add’ option.

STEP 2: Select Units and define axis.

From the dropdown menu kindly choose the units for your calculations.

MOI Axis info

The axis about which moment of inertia and centroid is to be found has to be defined here. If you want to find about origin then keep x=0 and y=0.

STEP 3: Adding Shapes


moi rec1
moi rec2

A rectangle has to be defined from its base point, which is the bottom left point of rectangle. The width ‘B’ and height ‘H’ is defined from this base point.

In this example the base point co ordinate for rectangle are (0,0) and B=90mm, H=120mm.

Also the shapes that you add can be seen in the graph at bottom of calculator.

The red line indicates the axis about which area moment of inertia will be calculated

Moment of inertia formula for rectangle is bh(^3)/12 about centroidal axis, and about base it is b(h^3)/3.

Right Angled Triangle

R triangle
r triangle 2

A right angled triangle is also defined from its base point as shown in diagram. Width ‘B’ and height ‘H’ can be positive or negative depending on the type of right angled triangle.

The shape can be seen formed simultaneously in the graph, with objects being subtracted shown in dotted lines.

Moment of inertia formula for triangle is bh(^3)/36 about centroidal axis.

The equation for moment of inertia about base is bh(^3)/12.


circ graph1

A circle is defined by co ordinates of its centre and the radius of the circle.

Moment of inertia formula for circle is given as pi*R(^4)/4.

Semi Circle

Semi circle 1

A semi circle is described by the co ordinates of its centre, and the radius.

Another important term to define semi circle is the quadrant in which it lies, the attached diagram may be referred for the purpose.

The equation for moment of inertia is given as pi*R(^4)/8

Quarter Circle


The quarter circle should be defined by the co ordinates of its centre and the radius of quarter circle.

Another important term to define quarter circle is the quadrant in which it lies.

The equation for moment of inertia is given as pi*R(^4)/16.



The results will display the calculations for the axis defined by the user.

The calculations are also done about centroidal axis.

Centroid for the defined shape is also calculated.

Centroid calculator will also calculate the centroid from the defined axis, if centroid is to be calculated from origin x=0 and y=0 should be set in the first step.

One of the important features is changing the units of the result, as seen in the image you can change the units of the result and it will appropriately calculate results for the new units.

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