Enter the distance from A to C, the distance from B to D, and the distance from B to C into the Cross Ratio Calculator. The calculator will evaluate and display the Cross Ratio. 

Cross Ratio Formula

The following formula is used to calculate the Cross Ratio. 

CR = (AC*BD) / ( BC * AD)

  • Where CR is the Cross Ratio
  • AC is the distance from A to C 
  • BD is the distance from B to D 
  • BC is the distance from B to C 
  • AD is the distance from A to D

How to Calculate Cross Ratio?

The following example problems outline how to calculate Cross Ratio.

Example Problem #1

  1. First, determine the distance from A to C.
    • The distance from A to C is calculated to be : 4.
  2. Next, determine the distance from B to D. 
    • The distance from B to D is measured to be: 6.
  3. Next, determine the distance from B to C. 
    • The distance from B to C is found to be: 7.
  4. Next, determine the distance from A to D.
    • The distance from A to D is found to be: 10.
  5. Finally, calculate the Cross Ratio using the formula above: 

CR = (AC*BD) / ( BC * AD)

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

CR = (4*6) / ( 7 * 10) = .3428 ( )


Example Problem #2

The variables required for this problem are provided below:

distance from A to C = 8

distance from B to D = 9

distance from B to C = 10

distance from A to D = 4

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

CR = (AC*BD) / ( BC * AD) = ( )