What is Clock Hands?
Clock hand questions ask you to work out where clock hands point after rotations, or to calculate angles between hands at given times. They combine time-telling skills with rotation and angle knowledge.
Remember: a clock face is a circle (360 degrees), divided into 12 hours. Each hour represents 30 degrees (360 / 12). The minute hand moves 360 degrees in 60 minutes (6 degrees per minute).
Step-by-Step Method
Know the basics
The hour hand moves 30 degrees per hour (0.5 degrees per minute). The minute hand moves 6 degrees per minute (360 degrees per hour).
Find starting positions
Work out where each hand starts. At 3 o’clock the hour hand is at 90 degrees from 12, at 6 o’clock it is at 180 degrees.
Apply the rotation
If the question asks about a rotation, add (clockwise) or subtract (anticlockwise) the angle from the starting position.
Calculate the answer
Convert your result back to a clock position or angle between the hands.
Worked Examples
What is the angle between the hands at 3 o’clock?
Working
- At 3 o’clock: minute hand points to 12 (0 degrees), hour hand points to 3 (90 degrees).
- Angle between them: 90 – 0 = 90 degrees.
What is the angle between the hands at 6 o’clock?
Working
- Minute hand at 12 (0 degrees). Hour hand at 6 (180 degrees).
- Angle between them: 180 – 0 = 180 degrees.
The minute hand is pointing at 12. It rotates clockwise by 90 degrees. Where does it point now?
Working
- Starting at 12 (top of the clock).
- 90 degrees clockwise = quarter turn to the right.
- It now points at 3.
Common Mistakes
Forgetting that the hour hand moves continuously, not in jumps. At 3:30 the hour hand is halfway between 3 and 4.
The hour hand moves 0.5 degrees per minute. At 3:30 it has moved an extra 15 degrees past the 3.
Confusing clockwise and anticlockwise when calculating rotations.
Clockwise goes 12, 3, 6, 9. Anticlockwise goes 12, 9, 6, 3. Draw arrows if unsure.
Top Tips
- Key angles: 12=0, 3=90, 6=180, 9=270 degrees.
- Each number on the clock is 30 degrees from the next (360/12=30).
- Each minute mark is 6 degrees (360/60=6).
- Always draw a quick clock face if you are unsure.
- For the angle between hands, always give the smaller angle (no more than 180 degrees) unless the question says otherwise.
Ready to practise?
Put these techniques into action with our free practice papers.
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