What is the angle between the hands of a clock at 4 O’clock?

Concept

The angle between the hour hand and the minute hand of a clock at any time can be found using the formula: Angle = |30H − 5.5M|, where H is the hour reading (1–12) and M is the minutes past the hour. This works because the hour hand moves 0.5° every minute (30° per hour), while the minute hand moves 6° every minute, so the minute hand gains 5.5° on the hour hand every minute.

Application

At exactly 4 O’clock, H = 4 and M = 0. Apply the formula step by step:

1. The hour hand’s position measured from the 12 mark is 30 × H = 30 × 4 = 120°.

2. The minute hand’s position measured from the 12 mark is 6 × M = 6 × 0 = 0°.

3. The angle between the two hands is the absolute difference: |120° − 0°| = 120°.

4. Since 120° is less than or equal to 180°, this is already the angle asked for, and no further adjustment (such as subtracting from 360°) is needed.

Cross-check

Using the clock face directly: the 12-hour dial is divided into 12 equal hour-marks, each 360°/12 = 30° apart. At 4 O’clock, the hour hand points exactly at the ‘4’ mark and the minute hand points exactly at the ‘12’ mark, so they are 4 hour-marks apart: 4 × 30° = 120°, matching the formula result.

Therefore, the angle between the hands of a clock at 4 O’clock is 120°.