Clock angle formula
Hour hand = 30 × H + 0.5 × M
Minute hand = 6 × M
Angle = |30 × H − 5.5 × M|, and if over 180°, use 360° − angle
Worked example
At 9:45, the hour hand is at 30 × 9 + 0.5 × 45 = 292.5° and the minute hand is at 6 × 45 = 270°. The difference is 22.5°, the smaller angle. The larger angle is 337.5°.
Clock angles at common times
| Time | Angle | Time | Angle |
|---|
| 12:00 | 0° | 3:30 | 75° |
| 1:00 | 30° | 4:20 | 10° |
| 2:00 | 60° | 6:00 | 180° |
| 3:00 | 90° | 7:20 | 100° |
| 3:15 | 7.5° | 9:45 | 22.5° |
| 12:30 | 165° | 11:59 | 5.5° |
Working with other angles? Try the trigonometry calculator or the triangle calculator.
Last reviewed October 2026.
Frequently asked questions
How do you find the angle between clock hands?
Use the formula angle = |30 × H − 5.5 × M|, where H is the hour (1–12) and M is the minutes. If the answer is more than 180°, subtract it from 360° to get the smaller angle. At 3:15 the angle is |90 − 82.5| = 7.5°.
Why 30 and 5.5?
The hour hand moves 360° in 12 hours, which is 30° per hour or 0.5° per minute. The minute hand moves 360° in 60 minutes, which is 6° per minute. The difference in speed is 6 − 0.5 = 5.5° per minute.
Why isn't 3:15 a 0° angle?
Because the hour hand keeps moving. At 3:15 it has moved a quarter of the way from 3 towards 4, which is 7.5°, so the hands are 7.5° apart.
How often do the hands overlap?
The hands line up 11 times every 12 hours, about every 65 minutes 27 seconds, for example at 12:00, about 1:05:27 and about 2:10:55.
Can I include seconds?
Yes. Enter seconds and the calculator moves both hands slightly to match, which makes a small difference to the angle.