Clock angle calculator
Enter a time like 3:15 and see the angle between the two hands, the smaller angle first. It also shows how far each hand has turned from 12 o'clock, so you can follow the working in a maths problem.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Type a time in the box, for example
9:45.
- Read the smaller angle. The larger angle is its complement to 360 degrees.
- The two hand positions show how far each hand is from the 12, clockwise.
How it works
The minute hand makes a full turn of 360 degrees in 60 minutes, so 6 degrees per minute. The hour hand makes a full turn in 12 hours, so 30 degrees per hour and 0.5 degrees per minute. The difference of the two positions is the angle between them. When it exceeds 180 degrees, the smaller angle is 360 minus it.
Worked examples
- 3:00: hour hand 90°, minute hand 0°, angle 90°.
- 3:15: hour hand 97.5°, minute hand 90°, angle 7.5°.
- 9:45: hour hand 292.5°, minute hand 270°, angle 22.5°.
- 12:30: hour hand 15°, minute hand 180°, angle 165°.
Good to know
Analogue clock puzzles usually ask for the smaller angle, which is never more than 180 degrees. The larger angle is what you turn through going the other way round.
Frequently asked questions
What is the formula for the angle between clock hands?
With H hours and M minutes, the hour hand is at 30 × H + 0.5 × M degrees and the minute hand at 6 × M degrees. The angle is the absolute difference, and the smaller angle is the lesser of that and 360 minus it.
Why does the hour hand move between the numbers?
The hour hand turns 30 degrees in an hour, which is half a degree per minute. At 3:30 it is halfway between the 3 and the 4, not on the 3.
How many times a day are the hands at a right angle?
The hands form a right angle 22 times in 12 hours, which is 44 times in a full day. They point in exactly opposite directions 11 times in 12 hours, or 22 times a day.
Does 15:00 give the same angle as 3:00?
Yes. The tool reads hours past 12 on a 12-hour dial, so 15:00 is 3:00 and the angle is 90 degrees.