Enter the physical quantities of two different measurements into the calculator to determine the dimensional analysis. The dimensional analysis is the ratio of one number to another.

## Dimensional Analysis Formula

The following formula is used to perform dimensional analysis.

R = Q1/GCD : Q2/GCD

- Where R is the ratio of quantity 1 to 2
- Q1 is quantity 1
- Q2 is quantity 2
- GCD is the greated common denominator of Q1 and Q2

It’s important to note that in this formula the units for each quantity should be the same. The calculator above will convert the units on its own.

## Dimensional Analysis Example

**How to calculate dimensional analysis? **

First, determine the first quantity. For this example, quantity 1 is equal to 20m.

Next, determine the second quantity. In this case, the second quantity is 100cm.

Next, convert both units to equal units so the proper ratio can be determined. For this problem, we can convert the 100cm into meters by dividing 100.

So 100/100 = 1 m.

Next, determine the greatest common denominator of both quantities. The GCD of 1 and 20 is 1.

Next, divide both numbers by the GCD. In this case, since the GCD is 1, the quantities don’t change.

Finally, present the dimensional analysis as a ratio.

R = 20:1