Calculate simplified ratios, solve proportions, find unit rates, and convert drawing scales with fractions, decimals, and custom units.

Numbers may be decimals, fractions (3/4), or mixed numbers (2 1/3). A:B compares A to B. Unit ratios do not convert incompatible dimensions.

Unit Ratio Formula

The following formula is used to calculate the Unit Ratio. 

UR = Q1 / Q2
  • Where UR is the unit rate in first-unit quantities per one second-unit quantity; Q2 must be nonzero
  • Q1 is the quantity of the first unit 
  • Q2 is the quantity of the second unit 

To calculate a unit rate, divide the first quantity by the second or reference quantity. A simplified ratio expresses the same relationship with reduced integer terms: 8:10 becomes 4:5, while the unit rate is 8/10 = 0.8. Convert quantities to compatible units before forming a dimensionless ratio.

How to Calculate Unit Ratio?

The following example problems outline how to calculate Unit Ratio.

Example Problem #1:

  1. First, determine the quantity of the first unit.
    • The quantity of the first unit is given as 5.
  2. Next, determine the quantity of the second unit.
    • The quantity of the second unit is provided as 7.
  3. Finally, calculate the Unit Ratio using the equation above: 

UR = Q1 / Q2

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

UR = Q1 / Q2 = 5/7 ≈ 0.7142857143 first units per second unit.

Example Problem #2: 

For this problem, the variables required are provided below:

quantity of first unit = 8

quantity of second unit = 10

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

UR = Q1 / Q2 = ?