Clock Angle - ganeshahv/Contrail_SRE GitHub Wiki

Clock Angle problem

Hour-hand moves 360deg in 12h or 720m Hour-hand moves 360deg/12h = 30deg/h and 360deg/720m = 0.5deg/m

Minute-hand moves 360deg in 1h or 60m Minute-hand moves 360deg/60m = 6deg/m

To calculate the angle formed by the minute and hour hands at any time, use the following formula:

**Time: Hh:Mm**

Hour-Hand Angle = ((H * 30) + (M * 0.5))deg
Minute-Hand Angle = (M * 6)deg

Clock Angle = Diff(Hour-Hand Angle, Minute-Hand Angle)

**Example**

Time : 10:24

Hour-Hand Angle = (10 * 30) + (24*0.5) = 312deg
Minute-Hand Angle = 24 * 6 = 144deg

Clock Angle = 168deg

Problem

Q: When do the hour-hand and the minute-hand overlap?

Ans: Overlap happens when the angle between the two hands is 0.

Hour-Hand Angle = ((30 * H) + (0.5 * M))deg
Minute-Hand Angle = 6 * Mdeg
30H+0.5M = 6M
5.5M = 30H
M = (30/5.5)H

Solution: M = 5.45H