Clock Hands

The time is quarter past three. What is the angle between the hour and minute hands at 3:15?

Answer

The angle is 7.5 degrees.

At 3 o’clock, the hour hand will be at 90 degrees. At 4 o’clock, the hour hand will be at 120 degrees. In other words, for every hour, the hour hand moves by 30 degrees. And every time the minute hand makes one full round, the hour hand moves by 0.5 degrees (1/60 minutes x 30 degrees).

At 3:15, the hour hand will have moved by 7.5 degrees (15/60 minutes x 30 degrees) and the minute hand will be at 90 degrees, perfectly horizontal pointing at number 3.

At 3:15, the hour hand will be at 97.5 degrees and the minute hand will be at 90 degrees. The difference is 7.5 degrees.