Angle = |30H − 5.5M|. At 3:30 that is 75°, not 90° — the hour hand has already drifted halfway to the 4.
The hour hand covers 30° an hour, so it moves 0.5° for every minute that passes. Leaving it parked on the hour mark is the classic error. The same 5.5° per minute closing speed answers every clock-hand question, including why the hands overlap 11 times in 12 hours rather than 12.
The formula gives the angle between the hands, which is not always the angle you want: it can exceed 180°, and the reflex angle is the one you see. It also assumes both hands sweep continuously — a clock with a stepping minute hand does not match it between ticks.
Estimate with the rule, then check it against the calculator that models it properly.
Open Clock Angle Calculator →