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Constant of Proportionality Calculator

Enter the values for the variables (X and Y) to find the constant of proportionality with steps.

k = y / x

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Constant of Proportionality Calculator:

Use this calculator to calculate the constant of proportionality (K) for the given dependent (X) and independent (Y) variables. A tool helps you to find the constant value that defines the proportional relationship.

What is the Constant of Proportionality?

“The constant value of the ratio between two proportional quantities”

Two quantities are said to be in relation to proportionality when their multiplier is constant. These include:

Direct Proportion: 

Two quantities are known as direct proportional if these decrease or increase at the same rate. 

The equation for the direct proportionality is:

y = kx

Example: The cost per item (y) is directly proportional to the number of items(x) purchased and is generally expressed as y ∝ x 

Inverse Proportion: 

The relation between two quantities in which one increases in proportion as the other decreases. 

The equation for the indirect proportionality is:

y = k/x

Example: The speed of a moving car (y) inversely varies as the time taken (x) to cover a certain distance and is generally expressed as y ∝ 1/x

Constant of Proportionality Formula:

A proportional relationship between two quantities x and y which has a constant of proportionality k is indicated by the constant of proportionality equation given as under:

y = k * x

To find the constant K, the mathematical equation expresses this relationship as:

k = y/x

Where:

  • k = constant proportionality
  • y = dependent variable
  • x = independent variable

How To Find The Constant of Proportionality?

  • Determine the two variables that are proportional to each other
  • Divide the value of one variable by the other for each pair
  • Ensure the result of the division is the same for all pairs. This consistent value is the constant of proportionality

Example # 01

What is the constant of proportionality if y=20 x=5, and y ∝ x?

Solution:

As we know y varies directly proportionally with x. We can write the equation of the proportionality constant as y = kx.

Substitute the given values of x and y, and solve for 

20 = k (5)

k = 20 ÷ 5 = 4

Therefore, the constant of proportionality is 8.

Example # 02

What is a constant of proportionality for direct and indirect variation initial value = 17 units, constant of proportionality k = 6?

Solution:

Constant of Proportionality, y = k / x

= 6 / 17 

= 0.352

Therefore, the constant of proportionality is 0.352.

FAQs:

Is proportion a type of ratio?

Yes, since a proportion is an equation or equality of the two ratios (y/x) and we can write proportions to calculate equivalent ratios between two unknown quantities.

Can there be two constants of proportionality?

When two variables or quantities are directly or indirectly proportional to each other, then their relationship can be expressed as y = kx or k =y/x. Where k determines how the two variables or quantities are related to one another. You can calculate the value of k (proportionality constant) by subjecting this online constant of proportionality calculator.

Is mass a constant of proportionality?

No, mass is not a proportionality constant. Mass or weight is a universal constant. It is measured in Kilograms and grams

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