How to find perimeter ratio

Author: Calculator Academy Team

Last Updated: October 30, 2022

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Enter the total perimeter length (in) and the total area (in^2) into the Perimeter Ratio Calculator. The calculator will evaluate and display the Perimeter Ratio. 

Perimeter Ratio Formula

The following formula is used to calculate the Perimeter Ratio. 

• Where PRR is the Perimeter Ratio (1/in)
• PL is the total perimeter length (in) 
• TA is the total area (in^2) 

To calculate the perimeter ratio, divide the perimeter length by the total area.

How to Calculate Perimeter Ratio?

The following example problems outline how to calculate Perimeter Ratio.

Example Problem #1:

1. First, determine the total perimeter length (in). 
   • The total perimeter length (in) is given as: 50.
2. Next, determine the total area (in^2). 
   • The total area (in^2) is provided as: 600.
3. Finally, calculate the Perimeter Ratio using the equation above: 

PRR = PL / TA

The values given above are inserted into the equation below and the solution is calculated:

PRR = 50 / 600 = .0833 (1/in)

Example Problem #2: 

For this problem, the variables required are provided below:

total perimeter length (in) = 70

total area (in^2) = 800

Test your knowledge using the equation and check your answer with the calculator above.

PRR = PL / TA = ?

1 Expert Answer

Meredith D. answered • 07/09/20

Tutor with Extensive Special Needs Experience

a) The ratio of perimeters is the same as the scale factor for any similar polygons.

For instance, if the sides of one triangle are 4, 4, and 4 (assuming the triangle is equilateral) and the sides of the similar triangle are 5, 5, and 5, the perimeter of the first triangle is 12 and the perimeter of the second triangle is 15. A 12/15 ratio can be simplified to 4/5.

b) The ratio of areas is the square of the scale factor for similar polygons.

The reason that we must square the scale factor is because area is found by multiplying the base and height of the triangle. If both the base and the height are at a 4/5 ratio, the areas are at a 16/25 ratio. For instance, in a right triangle with base 4 and height 8, the area is 4*8 / 2 = 16 and in a right triangle with base 5 and height 10, the area is 5 * 10 / 2 = 25.

Both of these problems could be done with more "messy" numbers and still give you the same ratio in the end. Try it with any numbers at a 4/5 ratio that you like and see how it turns out.

Updated October 26, 2020

By Josh Infiesto

The perimeter of a shape is the measure of the length of a shape around its outermost extremities. The area of a shape is the amount of two-dimensional space that it covers. The ratio of the perimeter to the area of a shape is simply the perimeter divided by the area. This is easily calculated.

Find the radius of your circle. This is the distance from the center to the outer edge.

Calculate the perimeter or circumference of the circle. This can be done using the equation

C=2\pi r

Calculate the area of the circle. This can be done using the equation

\text{Area}=\pi r^2

where r is the radius of the circle.

Divide the perimeter by the area to obtain the ration of perimeter to area.

Find the length and width of the rectangle. This will be the measurement of one of the long sides and one of the short sides.

Calculate the perimeter using the formula

2(b+w)=P

where b is the base and w is the width.

Calculate the area using the formula

A=bw

where b is the base and w is the width.

Divide the perimeter by the area to obtain the ration of the perimeter to the area.

Tips

• There are an infinite variety of shapes. If you don't know the formulas for a shape, get creative and try breaking it down into smaller rectangles.