Inertia formulas

formulaire

1. Useful Moment of Inertia Formulas

Note: In the table below, the overbar indicates the moment of inertia is taken about an axis that
passes through the centroid, denoted as ‘C’. Parallel axis theorems are:

2
AdII
xx
 2
AdII
yy
 yxAII
xyxy

Here, A is the area of the shape, d is the distance from the centroidal axis to the desired parallel
axis, and yx are the x and y distances of the centroid from the origin of the desired coordinate
frame.

Rectangle:
3
12
1
bhI
x

3
3
1
bhI
x
 hbI
y
3
12
1


hbI
y
3
3
1
 0
yx
I
Area = bh
Triangle:
3
36
1
bhI
x


3
12
1
bhI
x 72
)2(
2
hsbb
I
xy


bhArea
2
1

Circle:
4
4
1
rII
yx 
0
yx
I
2
rArea

Semi-circle:
4
8
1
rII
yx

4
'
9
8
8
rI
x 







 0
yx
I
2
2
r
Area


Ellipse:
3
4
1
abI
x
baI
y
3
4
1
 0
yx
I
abArea


C
r
y
x
a
b
C
r
y
x
4r/3π
x`
C
r
y
x
b
h
x
x`
C
h/3
s
y
x
y`
x`
b
h
C
b/2
h/2