In economics there are things such as "fixed" and "variable" costs. In math there are "fixed" and "variable" slopes. Is there a single word that's best to describe both of the terms at once? I've come up with measurability, gradient, and quantifiability, but I don't feel super comfortable with any of them. An example in Economics would be "The ____ of the cost is fixed."
You said in a comment under the question:
Variability works, and it's most likely the one I'll accept, but it is definitely odd to say "The variability of the temperature is variable".
The easiest thing to do is pick a synonym that also sounds natural—and which doesn't reuse the base words fixed or variable.
I suggest changeability. From the adjective changeable:
: capable of change: such as
a : able or apt to vary
// changeable weather
b : subject to change : ALTERABLE
// changeable plans
While still slightly odd, it suggests the following in your sentences:
The changeability of the cost is fixed.
🠆 The cost cannot be changed.
The changeability of the temperature is variable.
🠆 The temperature can change.
Note that in all cases, however, the meaning is slightly different than you intend.
If the variability of the temperature is variable, it could mean that the amount of variation can change. For instance, temperatures that used to vary between 20 degrees now vary between 40 degrees: the amount of variability has increased.
Similarly, the same could be said for the amount of changeability.
Whether it sounds odd or not, whatever word you use to come up with an abstract is going to be open to some level of ambiguity.
Therefore, it's best to simply say:
The cost is fixed.
The temperature is variable.
Or if you're thinking of a table with headings (for example), just use Fixed or Variable as the heading instead of a different word that tries to encompass both things.
the type or main characteristic (of something) [Cambridge]
The nature of this cost is fixed.
You might prefer to say "The cost is fixed" or "The cost is variable"
Otherwise it seems like you want to talk about "variability".