Clock — Hours and Minutes
Explore clock-hand angle problems: when the hands overlap, point at right angles, or line up in other ways. Touch and drag the clock to set the time directly.
Clock — Hours and Minutes
Classic clock problems ask when the hour and minute hands (and sometimes the second hand) line up in special ways. These puzzles develop intuition about angles, rates, and simple equations.
Key ideas
- Minute hand: moves 360° in 60 minutes → 6° per minute
- Hour hand: moves 360° in 12 hours → 0.5° per minute
- Overlap: when the two angles are equal
- Right angle: when the difference is 90° or 270°
Try it yourself
The interactive clock lets you click and drag to set the time. Watch how the angles change as you move the hands. Use the slider or ±1s / ±1m buttons for fine control.
Problems
Practice problems below let you find when the hands overlap during a given hour, or explore other configurations.
Set any time and see the hour, minute, and second hand angles. Use it to check your answers for angle problems or to find when the hands overlap.
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