# Free Moment of Inertia Calculator

## Calculate the moment of inertia of an I beam. Calculate the centroid, centre of mass and area of an irregular shape.

Center (x) mm
Center (y) mm
H mm
W mm
##### Section profile controls
Section selected:
##### Section property results
Area cm2
Moment of intertia x-x cm4
Moment of intertia y-y cm4
Elastic Section Modulus x-x: cm3
Elastic Section Modulus y-y: cm3
Shape Complexity:
Area Percent Error: %
##### Detailed section dimensions
Section depth mm
Section width mm
Web thickness mm
Flange thickness mm
Mass per m kg/m

## What is the second moment of area?

• The second moment of area (otherwise known as the moment of inertia), is a measure of the 'efficiency' of a cross-section to resist bending, caused by applied forces.

## What is the moment of inertia?

• The moment of inertia (otherwise known as the second moment of area), is a measure of the 'efficiency' of a cross-section to resist bending, caused by applied forces.

## What’s the difference between moment of inertia and second moment of area?

• There is no difference between the second moment of area and the moment of intertia, the terms can be used interchangeably.

## What is the centroid of a shape?

• The centroid of a shape (otherwise known as the centre of gravity) is the geometric centre of the object and if the shape possesses an axis of symmetry this is where the axis will be located.

## How is the centroid of a shape calculated?

• The centroid of a complex shape can be calculated using hand calculation methods, by using the Method of Geometric Decomposition. To find the centroid, the individual centroids of each component shape are determined, the idividual centroid are then multiplied by the area of the correponding shape and summed. This summed value is then divided by the total area of all combined component shapes to give the centroid.

## What’s the difference between the centroid of a shape and the centre of gravity?

• There is no difference between the centroid of a shape and the centre of gravity, the terms can be used interchangeably.

## What is the radius of gyration?

• The radius of gyration of a shape is the distance between the shapes axis of rotation and the shapes centre of gravity.

## How is the radius of gyration calculated?

• The radius of gyration is calculated using the formula
• k = sqrt ( I / A)
• Where I is the second moment of area of a shape and A is the area.

## What is the section modulus?

• The section modulus (otherwise known as the first moment of area) is a parameter which measures a section strength in bending. This can either be the elastic section modulus which considers the strength of the beam up to elastic yielding or the plastic section modulus which considers strength up to plastic yielding.

## What is the moment of inertia?

• The moment of inertia (otherwise known as second moment of area) is a a measure of a shapes resistance to angular acceleration.

## What is the second moment of area?

• The second moment of area (otherwise known as moment of inertia) is a a measure of a shapes resistance to angular acceleration.

## Moment of inertia equation

The moment of inertia can be calculated by hand for the most common shapes:
• Rectangle: (bh^3)/12
• >Circle: (pi * r^4)/4
• Triangle: (bh^3)/12
• If the shape is more complex then the moment of inertia can be calculated using the parallel axis thereom. The parallel axis thereom is used to seperate the shape into a number of simpler shapes. An axis is fixed and then the second moment of area of each shape is calculated and summed to the area multiplied by the distance between the fixed axis and the shape centroid squared.

## Calculating the moment of inertia of an I beam

The moment of inertia of I beam can be calculated by used the inertia equations for a rectangle (bh^3)/12 for each component of the I beam. A method known as parallel axis thereom is then used to calculate the combined second moment of area about the centroid of the section. The parallel axis thereom works by considering the offset distance of the centroid of each rectangle from the centroid of the composite section and then summing the results.

## What are the moment of inertia units?

The units for moment of inertia are kg·m2.

## What is the oment of inertia?

The oment of inertia is common mispelling of moment of intertia. The moment of inertia is a measure of the 'efficiency' of a cross-section to resist bending, caused by applied forces.

## What is the mass moment of inertia?

The mass moment of intertia is equivalent to the moment of intertia. The terms mass moment of intertia and moment of inertia can be used interchangeably.
What's this calculator used for?
This is a free calculator explaining how to calculate the moment of inertia of an I beam. This calculator uses the inertia formula and in particular the moment of inertia formula for a rectangle to calculate section properties. Create a custom shape to use this calculator as an irregular shape area calculator. Calculate the neutral axis and centroid for a an I beam or an irregular section. The section modulus is calculated and output as part of this calculation.
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