Enter two dependent variables into the calculator to determine the constant of proportionality.

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## Constant of Proportionality Formula

The following formula is used to calculate a constant of proportionality.

C = Y/X

- Where C is the constant of proportionality
- X is a variable directly dependent on Y
- Y is a variable directly dependent on X

## Constant of Proportionality Definition

A constant of proportionality is a value that directly relates two variables two one another.

## Constant of Proportionality Example

**How to calculate the constant of proportionality? **

**Example #1: **

In this example, the variables are inversely proportional. Let’s say we have X which we know is 5, and we have the constant of proportionality of 2. We can then find Y by rearranging the equation Y = X*C = 5*2 = 10.

The constant of proportionality can be used to calculate the missing variable.

**Example #2: **

In this example, we are going to calculate the constant of proportionality instead of using it to find a missing variable.

The values of x and y are given as 15 and 5 respectively. Using the formula above, the Constant of Proportionality is calculated to be C = Y/X = 5/15 = .333.

Now we want to calculate a new variable from this constant. We are given a variable Y of 10. To calculate the missing variable X, we re-arrange the equation to X=Y/C = 10/.333 = 30.33.

## 8 Things to Know About Constant of Proportionality

1.** Is the constant of proportionality the same as a** **slope? **

The terms slope and constant of proportionality are often used interchangeably. A typical linear equation is presented in the form y=a*x + b. In those cases, the variable a is considered the same as the constant of proportionality.

**2. Is the constant of proportionality the same as the** **unit rate? **

A unit rate is defined as a rate with a denominator of one. Since the constant of proportionality is used interchangeably with slope, it can also be used interchangeably with the unit rate in most cases.

This is because a slope is defined as the change in a variable Y with respect to X when X is simplified to 1.

**3. Is the constant of proportionality a fraction? **

The constant of proportionality is often displayed as a simplified fraction with a denominator of 1. For example, if we have values of Y=10 and X=5, the simplified fraction would be 10/5 = 2/1 = 2. In this example, the COP could be left as 10/5, which is, of course, a fraction, but simplifying the fraction to 2/1 simplifies further calculations using that COP.

**4. Can the constant of proportionality be negative?**

Whenever one of either of Y or X or negative, but not both, the constant of proportionality will also be negative. This is the same case as with a slope, which is clear if you have an understanding of basic graphs and linear lines.

**5. Does a constant of proportionality have units? **

The COP can have units if the problem or use requires it. For example, let’s say we are looking at a problem in which Y represents a weight, and X represents speed. In this scenario, Y would have units of kg or lbs and X would have units of m/s or ft/s. The subsequent units for the constant of proportionality would then be kg/(m/s).

Another example of this would be if Y represents force, and X represents mass. The units for Y would be Newtons (N) and the units for X would be kilograms (kg). This would yield units of Newtons per kilogram, N/kg, for the constant of proportionality.

**6. Can the constant of proportionality be a decimal?**

A constant of proportionality can be a fraction, and as a result, can be represented as a decimal, just like all fractions can.

For example, let’s say we have Y and X values of 1 and 2 respectively. This would yield a COP of 1/2. 1/2 can then be simplified to the decimal 0.5.

**7. What is the constant of proprotionality on a graph? **

On a graph, the constant of proportionality can be found by calculating the slope of the line on the graph. For example, if you have a line with the form y=2*x, the COP would be 2.

**8. How to find constant of proportionality on a table?**

Most tables are represented as individual cells with values when X and Y equal certain values. When these cells are equal to Y/X, the constant of proportionality is the value in that cell.