`r_x = r_z = sqrt( (3r^2 +4 h^2) /12)`

Enter a value for all fields

The Radius of Gyration of a Cylinder about the x-axis calculator computes the Radius of Gyration, r_x, of a cylinder about the specified axis (x-axis) as defined in the picture.

INSTRUCTIONS: Choose the preferred units and enter the following:

• (R) This is the radius of the solid cylinder
• (h)  This is height of the solid cylinder

Radius of Gyration: The radius of gyration is returned in meters.  However, this can be automatically converted to other length units via the pull-down menu.

Related Calculators:

• Radius of Gyration of a Cylinder about the y-axis

General Information

The radius of gyration is a general measure of the distribution of an object's mass.  The radius of gyration about an axis, `r_"axis"`, is computed as the root mean square of the distances of the object's component parts from the specified axis. The radius of gyration is related to the mass moment of inertia: `r_"axis" = sqrt(I_"axis"/m)` where m is the mass of the object and `I_"axis"` is the mass moment of inertia about the same specified axis. ¹

Related Cylinder Calculator Functions:

1. Cylinder (solid) - Radius of Gyration about y-axis
2. Cylinder - Mass Moment of Inertia About z-axis
3. Compute the Lateral Surface Area (sides) of the cylinder based on height and radius.
4. Compute the Total Surface Area of a cylinder including the sides, top and bottom.
5. Compute the Volume of a cylinder based on cylinder height and radius
6. Compute the Height of a cylinder based on the volume and radius.
7. Compute the Radius of a cylinder based on the volume and height.
8. Compute the Mass or Weight of a cylinder as a function of the volume and mean density of the substance of the cylinder.  
9. Compute the Density of a cylinder.
10. Compute the Lateral Surface Area of a Slanted cylinder.
11. Compute the Volume of a Slanted cylinder.
12. Compute the Weight or Mass of a Slanted cylinder.
13. Compute the moment of inertia of a cylinder shaped object based around the central axis
14. Compute the moment of inertia of a  cylinder shaped object around the end of the cylinder
15. Compute the moment of inertia of a  cylinder shaped object perpendicular to the central axis.
16. Look up the mean density of common substances (useful in calculating the mass/weight and the moments of inertia)

1. ^ Fundamentals of Engineering. 8th edition, 2nd Revision.  National Council of Examiners for Engineering and Surveying (NCEES) - 2001. ISBN 978-1-932613-59-9.  pg 61