Dimensional Analysis Calculator

Formula

To calculate the ratio between two quantities:

\[ R = \frac{\frac{Q1}{\text{GCD}}}{\frac{Q2}{\text{GCD}}} \]

Where:

\(R\) is the ratio of quantity 1 to quantity 2
\(Q1\) is quantity 1
\(Q2\) is quantity 2
\(\text{GCD}\) is the greatest common divisor of \(Q1\) and \(Q2\)

What is Dimensional Analysis?

Dimensional analysis is a method to analyze the relationship between different physical quantities by identifying their dimensions (units). It helps in simplifying problems and checking the consistency of equations. The calculator above determines the ratio of two quantities by simplifying them using their greatest common divisor (GCD).

Example Calculation 1

Let's assume the following values:

Quantity 1 (Q1) = 20
Quantity 2 (Q2) = 15

Step 1: Calculate the GCD of 20 and 15, which is 5.

Step 2: Use the formula:

\[ R = \frac{\frac{20}{5}}{\frac{15}{5}} = \frac{4}{3} = 1.33 \]

The ratio of Quantity 1 to Quantity 2 is 1.33.

Example Calculation 2

Let's assume the following values:

Quantity 1 (Q1) = 50
Quantity 2 (Q2) = 25

Step 1: Calculate the GCD of 50 and 25, which is 25.

Step 2: Use the formula:

\[ R = \frac{\frac{50}{25}}{\frac{25}{25}} = \frac{2}{1} = 2.00 \]

The ratio of Quantity 1 to Quantity 2 is 2.00.