Clock angle calculator
The hour hand moves half a degree a minute and the minute hand six. The gap between them closes and opens on a 65 5/11 minute cycle.
Angle between the hands
58.5000degrees
- Reflex angle
- 301.5000 degrees
- Hour hand from 12
- 103.5000 degrees
- Minute hand from 12
- 162.0000 degrees
Show the working
- Hour = 3
- Minute = 27
- Hour hand from 12 = mod(3, 12) * 30 + 27 * 0.5 = 103.5
- Minute hand from 12 = 27 * 6 = 162
- raw = abs(103.5 - 162) = 58.5
- Angle between the hands = min(58.5, 360 - 58.5) = 58.5
- Reflex angle = 360 - 58.5 = 301.5
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- hour hand = 30 x (hour mod 12) + 0.5 x minutes
- minute hand = 6 x minutes
- angle = the smaller of the difference and 360 minus it