Constant of Proportionality Calculator

Created by Wei Bin Loo
Reviewed by Anna Szczepanek, PhD and Adena Benn
Last updated: Nov 22, 2022

With this constant of proportionality calculator, we aim to help you to calculate the ratio that relates two dependable given values. The constant of proportionality enables you to understand how the dependent variable changes with the independent variable.

We have written this article to help you understand the following:

  • What the constant of proportionality is and
  • How to find the constant of proportionality.

We will also demonstrate some constant of proportionality examples to help you understand the concept. Let us start with the definition of the constant of proportionality.

What is constant of proportionality? Definition

The constant of proportionality is the ratio that measures the changes of the dependent variable with the changes of the independent variable. The higher the constant of proportionality, the more the dependent variable changes with the independent variable.

The constant of proportionality is the unit rate of a linear relationship. In a graph, the constant of proportionality is also called the slope or the gradient. It is defined as the m within the y = mx + c relationship. Check out our slope calculator and gradient calculator to understand these concepts in linear regression.

The constant of proportionality is usually expressed as a fraction or decimal. This is because we calculate the constant of proportionality by dividing the dependent variable by the independent variable. We will talk about this in detail in the next section.

How to find the constant of proportionality? Constant of proportionality equation

To understand the calculation of the constant of proportionality, let's look at the constant of proportionality example below:

  • Relationship: linear;
  • Independent variable, X: 10; and
  • Dependent variable, Y: 20.

You can compute the constant of proportionality in three steps:

  1. Determine the independent variable, X

    The first step is to determine the independent variable, X. This is the variable that is not dependent on other variables. In this example, the X is 10.

  2. Determine the dependent variable, Y

    Next, let's look at the dependent variable, Y. This is the variable that is dependent on the independent variables. The dependent variable for this example is 20.

  3. Calculate the constant of proportionality constant of proportionality = Y / X

    The last step is to calculate the metric using the constant of proportionality equation below:

    constant of proportionality = Y / X.

    For this example, the constant of proportionality is 20 / 10 = 2.

FAQ

What is the constant of proportionality if the two variables are the same?

The constant of proportionality will be 1. You can calculate it by dividing the dependent variable by the independent variable.

Can the constant of proportionality be negative?

Yes, the constant of proportionality can be negative. The constant of proportionality will be negative when exactly one of the variables is negative.

How can I calculate the constant of proportionality?

You can calculate the constant of proportionality in three steps:

  1. Determine the independent variable, X.
  2. Determine the dependent variable, Y.
  3. Apply the constant of proportionality formula: constant of proportionality = Y / X.

Is the constant of proportionality the same as a slope?

Yes, in most cases, the constant of proportionality is the same as a slope. They represent the rate of change between the independent and dependent variables.

Wei Bin Loo
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Constant of proportionality
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