How can we determine the angle measurement of the time (e.g. 4:16, 12:22, 8:44, etc.)?

Question

the angle between the hands of time....
in radians and degrees

Answer 1

Let hh:mm be the time.

The angle between the hour-hand and the 12-line is (hh+mm/60)*30 (in degrees), and the angle between the minute-hand and the 12-line is (mm/60)*360. Then, the angle between the hour-hand and the minute-hand is:

(hh+mm/60)*30 - (mm/60)*360 = 30*hh - 5.5*mm (in degrees)

Examples:

4:16 => angle = 30*4 - 5.5*16 = 32 degrees
8:44 => angle = 30*8 - 5.5*44 = -2 degrees

where the negative sign indicates that the minute-hand is passed the hour-hand.

Note: To go from degrees to radians, just multiply by "pi" (3.14...) and divide by 180.

I hope this helps.

Answer 2

I suppose you could construct a formula. Lets say the time is m minutes past h hours. We want to know where both hands are as an angle, say in degrees to start with. so the hour hand is 360*h/12 degrees clockwise of noon. (you could also add in another small part depending on how far into the hour you are, but that's easily enough done, and the formula becomes 360*(h+m/60)/12.) and the minute hand is 360*m/60 degrees past noon. then, we can just take the difference. However, if this answer is more than 180 degrees you have to be careful. If its between 180 and 360 degrees, then you are measuring the long way round. the smaller angle between the hands will be 360 minus the original answer. If the answer is more than 360 degrees, we have gone past one of the hands, so we can just take away 360 from the original answer.

To change from degrees to radians, you can just multiply by Pi/180.

Hope this makes sense!

Answer 3

What angle do you want? The angle of the hour hand away from straight up? The angle of the minute hand from straight up? The angle between the hands? Do you need it in radians or degrees?

Answer 4

Using a clock, draw lines from one number to the other.