Metal Density and Spring Constant
Country: United Kingdom
Date: Spring 2013
Does the density of the metal in a spring effect the amount of force needed to compress it?
First of all, I assume that you are talking about comparing springs that
are identical.... same diameter of spring wire, same spring diameter,
same number of coils, same length, etc, and that the only difference
between them is the density of the metal used to make each spring.
In that case, the density of the metal used to make a spring has
nothing whatsoever to do with the force needed to compress the
The force required to compress a spring a specified distance is called
the "Spring Rate", and is expressed in pounds of force, per inch of
compression (or Kilograms per millimeter of compression in metric
terms). A spring that requires more force to compress a given distance
will have a higher Spring Rate.
The ONLY factors that influence the Spring Rate of a spring, are these
and only these:
1. The wire diameter of the wire used to make the spring
2. The diameter of the spring itself
3. The number of coils the spring has
4. The "Modulus of Rigidity" of the material used to make the spring.
You will notice that the density of the material used to make the spring
does not enter into the picture at all.
Items 1, 2, and 3, probably are no surprise to you.....
- Increase the diameter of the wire used to make the spring (without
changing anything else), and it becomes "stiffer" (harder to compress,
and therefore has a higher Spring Rate).
- Increase the diameter of the spring itself (without changing anything
else), and the spring will be less stiff (easier to compress, and
therefore will have a lower Spring Rate).
- Increase the number of coils that the spring has (without changing
anything else), and the spring will be less stiff.
The fourth factor, the "Modulus of Rigidity" is probably not familiar to
you. This is a characteristic unique to each type of metal or alloy, and
For example, the Modulus of Rigidity of steel (any kind of steel) is 11.5
million pounds per square inch (psi). The Modulus of Rigidity of brass
is 5.5 million psi.
So there are two things you can see from this. First, the density of the
metal used to make the spring is irrelevant. Second, you can see that
the TYPE of metal, or alloy, most certainly does affect the "stiffness"
(i.e. Spring Rate) of the spring.
If you compared two springs that were identical, except that one was
made of steel and the other was made of brass, the steel spring would
be much stiffer than the brass one, because the Modulus of Rigidity of
steel is about twice as high as that of brass. But importantly, the
density of the metal used to make the spring does into enter into the
picture at all.
Hope this helps you to understand a little about springs!
Thanks for the question. The density of the metal in a spring is not directly related to the ability to compress the spring. For instance, lead is really dense, but in the form of a spring, it compresses really easily. On the other hand, iron is less dense than lead and does not compress easily when it is made in the form of a spring. Density of the metal is only one factor that determines the ability of a metal spring to be compressed.
I hope this helps. Please let me know if you have more questions.
Click here to return to the Material Science Archives
Update: November 2011