how to calculate angle between hour hand and minute hand in a clock in radians?

Question

calculation of angle through radians

Answer 1

radians = degrees * π / 180

eg at 2:00, the angle = 2/12 * 360 = 60 degrees
= 60*π / 180 = π / 3 rads

Answer 2

First find the angle in degrees and then convert into radians by using the relationship pi radians = 180 degrees. I hope you know how to convert the figures into angles. An example:

3:00 hours is an angle of 90 degrees and will be pi/2 radians.

0:00 will be zero degrees and so zero radians.

2:00 will be 60 degrees and will be approximately 1 radian ( slightly more). pi / 3 radians to be exact.

Answer 3

if the time is hh:mm

then I would calculate the angle as

the hour hand being at hh, but it will be past that depending on mm...

hour hand is at hh+mm/60
minute hand is at mm

Let 12:00 represent 0 degrees and go positive angle as clockwise... (0 rads, I will do this in degrees then convert to radians after)

then the hour hand is at the angle H
H = (hh + mm/60 - 12*n)*30 (subtract of 12 if H>=12 => n=0 if 0<=H<12, n=1 if 12<=H<24, etc)

because each hour represents 30 degrees.

then the minute hand is at the angle M
M = mm*6 ( you could include a -60*n term here too, but I will assume that 0<=M<60, whereas the hour could be 12 or higher if you use military time)

then the angle between them is A = H-M

A = H-M, multiply by pi/180 to convert to radians

A_rad = (H - M)*pi/180 in radians.

Answer 4

Use the bignose expression: angle = 6M-(30H+M/2)

this will give degrees. To convert to radians multiply by Pi/180

Angle Radians = (6M-(30H+M/2))Pi/180

a negative angle will indicate that the hour hand is ahead of the minute hand.

EDIT: Agnau almost got it right. He forgot that in 27 minutes the hour hand would move past the 11. this will add (27/60)(30)=13.5 degrees making the total 181.5 degrees

Answer 5

The time on the clock does not matter.
Each minute is 6 degrees (360/60).
Each hour is 30 degrees (360/12).
Convert the time into degrees.
Then remember that 2pi = 360 degrees.
You can also do this... each minute is (1/60)2(pi) or pi/30, each hour is (1/12)2(pi) or pi/6.
So 6:30 is min = 30*pi/30; hr = 6*pi/6 and min = pi, hr = pi and min-hr = 0rad.

Hope this process helps.

Here's the alternate... 11:27 is
min = 6*27 = 162
hr = 11 * 30 = 330
hr-min = 168 deg = (2/168)pi rads = pi/84 rads.

Answer 6

Entire cycle is 2*pi. Every 5 minutes will be pi/6, and every minute will be pi/30. So now check distance in minutes betwee two hand and get angle in radians.

Answer 7

radians = degrees * π / 180

eg at 2:00, the angle = 2/12 * 360 = 60 degrees
= 60*π / 180 = π / 3 rads

Answer 8

(1) 6 hours = 3.14 radians;

(2) Each big-division measures 0.52 radians.

(for example, the angle between the '12' and '1' is 0.52 radians, the angle between the '1' and '2' is 0.52 radians, and so forth.)

(3) Each small-division measures 0.105 radians.
(it is assumed that there are 5 small-divisions between two consecutive big-divisions)

Answer 9

1 degree equals pi divided by 180 radians

Answer 10

Assumptions:
Hour = hr
Mins = min
angle = Ag
now.

Ag = [ (360/12)*hr + (360/12)*(min/60) ] - (360/60)*min
Note: Here discard the negative sign