The formula here is for Very Fast Greens
y = mx + b
y= HIT
M=constant (9.3966)
x = variable which for this equation is slope of green = rise or drop divided by distance to hole.
b is a constant = 0.8450 (essentially the factor for a flat green where x = 0).
say 10 ft to hole 2 inches uphill so the math
variable x = 2 inches divided by (10 ft * 12 inches/foot) = 0.01667
HIT = 10 * ( 9.3966 * 0.01667 + 0.8450 ) + 1.0 feet (for uphill)
HIT = 11.016 feet
another
30 feet uphill 6 inches (same slope of green as previous example )
HIT = 30 * ( 9.3966 * 0.01667 + 0.8450 ) + 1.0 = 31.05 feet
50 feet uphill 21 inches ( x = 21/(12*50) = 0.035 so
HIT = 50 * ( 9.3966 * 0.035 + 0.8450 ) + 1.0 = 59.69 ft
DOWNHILL
10 ft down 1 inch (variable has to be multiplied by -1 as it is downhill)
HIT = 10 * ( ( -1 ) * ( 9.3966 * 0.01667 + 0.8450 ) = 6.884 feet
30 ft down 6 inches
HIT = 30 * ((-1) * (9.3966 * 0.016667 + 0.845 ) = 20.651 feet
50 ft down hill 21 inches
HIT = 50 * ((-1) * 9.3966 * 0.035 +0.845 ) = 25.806 feet
I hope this clarifies. you will have to fudge for certain courses but this formula will be within 2 feet of length of putt (probably closer). It won't help you read the curve however. add 1-2 % of a putt if there is a LARGE curve.
KZ