Clock Hand Angle
Angle between the hour and minute hands of an analog clock.
Formula
Variables
Example
3:15 ⇒ |30×3 − 5.5×15| = 7.5°
How it works
On an analog clock, the minute hand moves 6° each minute because it makes 360° in 60 minutes, while the hour hand moves 30° each hour and also creeps forward 0.5° each minute. The formula compares their positions from 12 o'clock and takes the absolute difference, giving the smaller angle between the two hands.
When to use it
Use this when you need the angle between clock hands in geometry or word problems involving analog clocks. It is also useful in timing puzzles, exams, and situations that ask for the separation of the hour and minute hands at a specific time.
Worked example, step by step
Find the angle at 7:20. H = 7, M = 20 θ = |30H - 5.5M| θ = |30×7 - 5.5×20| θ = |210 - 110| θ = |100| θ = 100°
Common mistakes to avoid
- Using H as a 12-hour clock value without reducing it to 0–11 when needed
- Forgetting that the hour hand moves a little each minute, not just once per hour
- Giving the reflex angle instead of the smaller angle between the hands
Did You Know?
The two hands line up only 22 times every 12 hours — never exactly at 6:30, as many people guess.
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