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Feb 11, 2026
Enter Time
Smaller Angle
7.5°
Larger Angle
352.5°
How to Use This Calculator
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View detailed breakdowns and explanations below.
📘 Clock Angle Formula
The angle between clock hands at time H:M is:
$$ \theta = |30H + 0.5M - 6M| = |30H - 5.5M| $$
If θ > 180°, use 360° - θ for the smaller angle.
🧠 How It Works
- Minute hand: Moves 6° per minute (360°/60)
- Hour hand: Moves 30° per hour (360°/12) plus 0.5° per minute
- The hour hand moves continuously, not in discrete jumps
⚡ Special Times
- 3:00: 90° (right angle)
- 6:00: 180° (straight line)
- 12:00: 0° (hands overlap)
- Hands overlap: 11 times in 12 hours
✅ Key Takeaways
- The hands overlap exactly 11 times in 12 hours (not 12!)
- At 3:15, the angle is NOT 90° (it is 7.5°)
- The hour hand moves 0.5° per minute
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