How handicaps are calculated
Blame in on The R&A....
Calculating 9 hole handicaps is not hard. The issue is that The R&A have an incorrect par for The Hartington. They have it down as 31 for 9 (or 62 for 18). This makes England Golfs' app mis-calculate your playing handicap for 9 holes.
The formula used here is
Course Handicap = (Your handicap or handicap index / 2) x
(9-hole slope rating (87) / 113) + (9-hole Course Rating (30.4) - 9-hole par (32)
For your reference
Below are the sources for generating this calculator.