How the angle is calculated
The minute hand moves 6° per minute (360° ÷ 60). The hour hand moves 30° per hour (360° ÷ 12) plus 0.5° for every minute, because it creeps forward as the minutes pass. The angle between the hands is the difference between the two positions; when that difference is more than 180°, the smaller angle is 360° minus it. The reflex angle is the larger of the two arcs.
Worked example: 3:00
At 3:00 the minute hand points to 12 (0°) and the hour hand points to 3 (90°). The difference is 90°, so the angle between the hands is exactly 90° — a right angle. The reflex angle is 360° − 90° = 270°.
Frequently asked questions
What is the angle between the clock hands at 3:15?
At 3:15 the minute hand is at 90° and the hour hand has crept to 97.5° (90° + 15 × 0.5°), so the angle between them is 7.5°.
When are the clock hands exactly opposite?
They form a straight 180° line at 6:00. Because the two hands realign every 12/11 hours, a 180° angle also recurs roughly every 65 minutes throughout the day.
Does AM or PM change the angle?
No. The angle depends only on the hour within a 12-hour cycle and the minutes, so 3:00 AM and 3:00 PM both give 90°.