Clock Angle Formula
Clocks are used to tell the time of the day. The clock is provided with three hands to measure time which are an hour hand, minute hand, and second hand. A clock has a total of 12 divisions of total measure of angle 360^{o}. The clock angle formula is used to calculate the time between any two hands of the clock. The clock angle formula is explained below with solved examples.
What Is the Clock Angle Formula?
Before learning the clock angle formula, let us understand a few things about a clock. There are 12 divisions in a clock. The angle between any two divisions is 30^{o}. Each division is further divided into 5 equal parts and each part equals 1 minute and has an angular distance of 6^{o}. A list of parts and their corresponding angles are given below.
Minutes  Angular Value 
1 minute  6^{o} 
2 minute  12^{o} 
3 minute  18^{o} 
4 minute  24^{o} 
5 minute  30^{o} 
6 minute  36^{o} 
7 minute  42^{o} 
8 minute  48^{o} 
9 minute  54^{o} 
10 minute  60^{o} 
Let us see the applications of the clock angle formula in the following section.
Solved Examples Using Clock Angle Formula

Example 1: Find the clockwise angle between the hour hand and minute hand at 3:30 P.M.(assume the hour hand is fixed at 3 for this hour).
Solution
To find: Angle between the hour hand and minute hand
Divisions between the hour hand and minute hand at 3:30 P.M. is 3.
Using the clock angle formula,
The angle between any two divisions is 30^{o}.
Therefore, the angle will be 3 × 30^{o} = 90^{o}
Answer: The angle between the hour hand and minute hand at 3:30 P.M. is 90^{o}.

Example 2: Find the clockwise angle between the minute hand and the hour hand at 12:55 A.M (assume the hour hand is fixed at 12 for this hour).
Solution
To find: Angle between the hour hand and minute hand
Divisions between the hour hand and minute hand at 12:55 P.M. is 11.
Using the clock angle formula,
The angle between any two divisions is 30^{o}.
Therefore, the angle will be 11 × 30^{o} = 330^{o}
Answer: The angle between the hour hand and minute hand at 12:55 P.M. is 330^{o}.