What is the difference between a parameter and a variable?

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Parameters in physics are fixed values that define specific characteristics of a model, such as gravitational acceleration (g=9.8 m/s²) and the speed of light (c=300,000 km/s). In contrast, variables represent values that can change within the model, typically the outcomes being calculated. Parameters remain constant during analysis, allowing only the variable to change, which helps clarify the relationship being studied. For instance, in the quadratic function f(x) = ax² + bx + c, a, b, and c are treated as parameters while x is the variable. Understanding this distinction is crucial for accurately interpreting mathematical and physical models.
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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 paramater 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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