** Variable vs Parameter
**

Variable and parameter are two terms widely used in mathematics and physics. These two are commonly misunderstood as the same entity. A variable is an entity that changes with respect to another entity. A parameter is an entity which is used to connect variables. The concepts of variable and parameter are very important in fields such as mathematics, physics, statistics, analysis and any other field that has usages of mathematics. In this article, we are going to discuss what variable and parameter are, their definitions, the similarities between variable and parameter, the applications of variable and parameter, some common usages of variable and parameter, and finally the difference between variable and parameter.

**Variable**

A variable is an entity which changes in a given system. Consider a simple example of a moving particle through space. In such a case, entities such as time, distance travelled by the particle, the direction of travelling are called variables.

There are two main types of variables in a given experiment. These are known as independent variables and dependent variables. Independent variables are the variables which are changed or which are naturally unchangeable. In a simple example, if the strain of a rubber band is measured while changing the stress of the band, Strain is the dependent variable and stress is the independent variable. The dependence is applied when the dependent variable is dependent on the independent variable.

Variables can also be categorized as discrete variables and continuous variables. This classification is mostly used in mathematics and statistics. Problems can be categorized depending on the number of variables. The number of variables is very important in fields such as differential equations and optimization.

**Parameter**

A parameter is an entity that is used to connect or unify two or more variables of an equation. The parameters may or may not have the same dimensions as the variables. Consider the equation x2+y2=1. In this equation, x and y are variables. This equation represents a circle of unit radius with the center at the origin of the coordinate system. The parametric form of this equation is x = cos (w) and y = sin (w) where w changes from 0 to 2π. Any point on the circle can be given using the single value of w instead of the two x and y values of the equation. The problem becomes relatively easy as it has only one parameter to analyze rather than the two variables.

**V****ariable vs Parameter**

- A variable is a real world value with a measureable quantity whereas a parameter is an entity that we may or may not be able to measure.

- The same set of variables can have different parameters to describe the system.

- A system, which requires multiple numbers of variables to describe, can be described with a lesser number of parameters.

katie knight says

thanks for explaining ^^

Gary says

You make some good points, but , re a single parameter and its value uniquely determining a point, the same is the case for the circle: once you know its x coordinate, you also automatically know its y coordinate, as y depends uniquely on x.