Math

Clock Angle Calculator

Find the angle between clock hands.

Calculated Output

Angle between hands (°) 7.5

Formula: |30·hour − 5.5·minute|, then take the smaller side

Step-by-Step Breakdown

1. Values used:

2. Hour = 3

3. Minute = 15

5. Angle between hands = 7.5°

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The math behind it

Hour hand: 30° per hour + 0.5° per minute. Minute hand: 6° per minute. Take the difference, then the smaller of it and 360 − it.

3:15 → 7.5°.

Why not 0° at 3:15?

The hour hand has moved a quarter past 3, so it's slightly ahead of the 3.