# Free Moment of Inertia Calculator

## Calculate the section properties, second moment of area and section modulus for steel beams and columns.

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
Radius of Gyration x-x: mm
Radius of Gyration y-y: mm
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.

## How is the moment of intertia or second moment of area calculated?

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.
##### Extra information:
What's this calculator used for?
This a free tool for Civil Engineers to calculate the geometrical properties of different shapes needed for structural analysis calculations. Calculate the section properties of custom beam and column section. Generate results to calculate the moment of inertia, elastic section modulus and radius of gyration for a profile. This tool use the parallel axis thereom to determine the neutral axis for the combined shape and then detemine section properties for a composite section.