What is the difference between a parameter and a variable?

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SUMMARY

The discussion clarifies the distinction between parameters and variables in mathematical and physical contexts. Parameters, such as g=9.8 m/s² and c=300,000 km/s, are fixed values that define the conditions of a model, while variables represent values that can change within that model. For instance, in the quadratic function f(x) = ax² + bx + c, the coefficients a, b, and c are treated as parameters, whereas x is the variable that changes. This differentiation is crucial for understanding how models operate.

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  • Knowledge of fixed versus variable values in mathematical modeling
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arroy_0205
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It seems (to me) that parameters are also kind of variables in descriptions of physics. I am confused what makes a parameter different from a variable. Can anybody please explain this?
 
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Hi there,

From my point of view, here are a few parameters: g=9.8m/s2, c= 300'000km/s.

Variables are the values that you are trying to find in any model. The model bases itself on different fixed values, or parameters.

Cheers
 
From a mathematical point of view, a parameter is a variable that is meant to stay fixed in a certain application. For example, in middle or high school you studied the three-parameter family of functions

f(x) = ax^2 + bx + c.

While the three numbers a, b, c are variables, you want to think of them as fixed and let only x vary. To distinguish the roles of a,b,c on the one side and x on the other, we refer to a,b,c as parameters.
 

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