Math Playground
Activities

Clocks & Angles

Where do the hands meet at 4:00? Geometry inside time.

A clock face is a circle: 360° divided into 12 hours. Each hour mark is 30°. Each minute is 6° (because 360 ÷ 60 = 6).

Drag the hands
121234567891011
3:00
24-hour: 03:00
3 o'clock

Clock-face geometry

  • The whole face is 360° split into 12 hours.
  • Each hour mark is 30° (360 ÷ 12).
  • Each minute is 6° (360 ÷ 60).
  • The hour hand also creeps 0.5° per minute — that's why 3:30 isn't exactly 90°.
Your turn

What angle is between the hands at 5:00?

At 6:00 the hands point opposite ways — 180°, a straight line. At 12:00 they overlap — 0°. At 3:00 and 9:00 you get a clean right angle.

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Angle between hands at 3:00

Hour hand at 3, minute hand at 12. That's 3 hours apart × 30° = 90°. A right angle.

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Angle at 4:00

4 hours × 30° = 120°. Obtuse.

At 6:00 the hands are 180° apart — a straight line. At 12:00 they overlap (0°).

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