In a round clock, we have 12 hours and for the full round, we can say 360 degrees.
Each hour has 30 degrees, we can calculate this as 360/12 =30
If we consider 60 minutes, we will get 360/60 = 6
We can clearly say, Hour hand is fully depending on Minutes hand.
Let us assume
x= Starting position of hour angle
y= Starting position of minute angle
The formula for finding the angle between starting position and hour hand at a specific time can be written as x = ( hour + minute / 60 ) * 30
To find the angle between starting position and minute hand at a specific time can be written as y=minute * 6
The absolute difference is exactly what we are looking for,
angle=|(x-y)|
If we want to find the minimum angle,
Minimum (angle, 360 - angle)
Note: The starting position of the clock is when hour =12.
Consider hour=0 (hour>=12 => hour=hour%12).
Let us implement the above concept using Python
def angleclock(hour,minute):
hourangle=(hour%12+(minute)/60)*30
minuteangle=minute*6
angle=abs(h-m)
return min(angle,360-angle)
if __name__=='__main__':
hour=int(input("hour"))
minute=int(input("minute"))
print(angleclock(hour,minute))
Example1 Input:hour=12,minute=30 output:165
Example2 Input:hour=3,minute=30 output:75