Clock Angle Calculator
The clock angle calculator helps you find the angle between clock hands. ⏰
Angle between the hands7.5°the smaller of the two angles
Larger angle352.5°
Hour hand97.5° from 12
Minute hand90° from 12
Hands overlapping?No
How the hands move
| Minute hand | 360° in 60 min = 6° per minute |
| Hour hand | 360° in 12 h = 0.5° per minute |
| Relative speed | 5.5° per minute |
| Hands align every | 360 ÷ 5.5 ≈ 65.45 minutes |
The rule
hour hand 0.5°/min, minute hand 6°/min
The hour hand keeps moving
The usual mistake is to place the hour hand exactly on its number. At 3:15 it has already crept a quarter of the way towards 4, so the angle is 7.5° rather than 0°. The minute hand gains 5.5° per minute on the hour hand, which is why they align every 65 5/11 minutes rather than every hour.
Degrees and radians
A full turn is 360° or 2π radians, so:
radians = degrees × π/180 and degrees = radians × 180/π
Degrees are convenient because 360 divides so many ways. Radians are the natural choice in mathematics because arc length becomes simply rθ and the calculus of sine and cosine comes out clean — derivatives pick up stray factors of π/180 in degrees.
Names worth knowing
- Acute — under 90°. Right — exactly 90°. Obtuse — between 90° and 180°.
- Straight — 180°. Reflex — over 180°.
- Complementary pairs add to 90°; supplementary pairs add to 180°.