Calculate the angle between hour hand and minute hand

Simplest method to calculate the angle between hour hand and minute hand within 10 seconds

This problem also is know as Clock angle problem. Here we need to find out the angle between hour hand and minute hands of an analog clock at a given time.

Only thing to remember for the above mentioned method is 

Each of the five minute separation in an analog clock is equal to 30° 

Example 1

What is the reflex angle between the hands of the clock  at 10.25 ?

Answer :

Step 1 : Draw a clock showing above given time (10.25).

Step 2 : Count the five minute separation between the hour hand and minute hand.

For the given time 10.25 count is equal to 7 .

We have already know that each of the five minute separation is equal to 30°

So angle = 7 (count) * 30° =  210°

Here we know that the hour hand is not exactly pointed to 10 digit in clock, its slightly shifted to 11.So we can make up this angle by subtracting the half of the minute part in the given time from the above angle.

Given time : 10.25

Half of minute part =25/2 =12.5

Exact angle at 10.25  = 210° - 12.5 = 197.50°

Example 2

What is the reflex angle between the hands of the clock  at 03.35 ?

Answer : 

                              

                                

Time = 03.35

Count = 4

Angle = 4 * 30° = 120°

Exact angle = 120° - 35/2 = 120 - 17.5 = 102.50°

So the Answer is 102.50°

Example 3

What is the reflex angle between the hands of the clock  at 03.10 ?

Answer : 

Time = 03.10

Count = 1

Angle = 1* 30° = 30°
Here hour hand is moving away from the digit "3" and shifted to "4" in the clock,so we are adding the half of minute part.

Exact angle = 30° + 10/2 =  30 + 5 = 35°

So the Answer is 35°