Calculate the angle between clock hands at any time. Animated clock face shows acute and reflex angles with degree/radian values.
Every clock face is a 360-degree protractor in disguise: the hour hand sweeps 30 degrees per hour, the minute hand 6 per minute, so the angle between them is subtraction plus one correction. Enter any time and this tool rotates both hands on an animated dial, then shows the two angles between them - the smaller arc and its reflex complement - in degrees and radians. The part most people get wrong is the hour hand, which never sits still: by 3:30 it has drifted 15 degrees past the 3, leaving 75 degrees between the hands, not the 90 the numerals suggest.
A concrete input and expected output from the current implementation.
Input
3:30
Expected output
75 degrees (5π/12 radians) for the smaller arc, 285 degrees (19π/12 radians) for the reflex arc, both drawn on the dial.
At 3:30 the minute hand points at 6 (180 degrees), while the hour hand has moved halfway from the 3 toward the 4, to 105 degrees (90 plus 15 degrees of drift). The difference is 75 degrees, and the reflex angle is 360 minus 75, or 285 degrees.
On a 12-hour dial the hour hand advances 30 degrees per hour (360/12) plus 0.5 degrees per minute, and the minute hand 6 degrees per minute (360/60). For H hours and M minutes the raw gap is 30H + 0.5M - 6M, or 30H - 5.5M degrees. The answer shown is that value folded into the smaller arc; the reflex angle is its complement to 360.
The dial draws the hands at their true positions rather than at the hour markers, so at half-past times the hour hand visibly sits between numerals. Both arcs between the hands are highlighted, and their degree and radian labels update as the time changes, so you can watch the smaller angle shrink and grow across a full hour.
Because the hour hand keeps moving. In the 30 minutes after 3:00 it advances 15 degrees (0.5 per minute) to sit halfway between the 3 and the 4, at 105 degrees on the dial, while the minute hand is at 180. The gap is 75 degrees. The hands form a right angle 44 times a day, but never at 3:30.
Eleven times per 12 hours, not twelve: the minute hand must close a 5.5-degree-per-minute relative gap, so each meeting comes 360/5.5, about 65 minutes and 27 seconds after the last. They coincide at 12:00, then roughly 1:05:27, 2:10:55, and 3:16:22, before repeating at 12:00.
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