I am trying to find the correct formula to be able to systematically organize the rules for putting a golf ball on a green. There are normally the following types of putts

- Up hill

- Down hill

- Side slope

Also, each green is given a Stimp Meter reading to indicate the speed of the green. Stimp Meter is a 36 inch stick with V-shaped grooves. It will be raised to 20.5 degrees and a golf ball (1.62oz) is placed at the 30 inch mark and released down the grove. A Stimp Meter of 8 means the ball travels 8 ft (96 in) after it leaves the Stimp Meter.

Can someone please help me figure out the formula to calculate the distance the ball travels when the slope comes into the equation? Normally, the slopes could be ranged from 1 degree - 5 degrees.

Thank you all in advance!