Clock Angle Calculator
Enter a time to find the angle between the hour and minute hands.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Hour hand = 30° × hour + 0.5° × minute
- Minute hand = 6° × minute
- Angle = the difference, and the smaller angle is the lesser of that and 360° minus it
For the arithmetic of time, see the time to decimal calculator.
Worked example
At 9:15:
- Hour hand = 270° + 7.5° = 277.5°
- Minute hand = 90°
- Difference = 187.5°, so the smaller angle is 172.5°
Why your number may differ
Some puzzles want the larger angle or give a clock that tells a different time. The calculator shows both angles.
Frequently asked questions
How is the angle between the clock hands found?
The minute hand moves 6° a minute and the hour hand 0.5° a minute. The angle is the difference between their positions measured from 12.
Why is it 90° at 3:00?
At 3:00 the minute hand points at 12 (0°) and the hour hand points at 3 (90°).
Why is the angle at 12:30 not 180°?
By 12:30 the hour hand has moved halfway to 1, to 15°, so the angle with the minute hand at 180° is 165°.