How to Read an Analog Clock and Find Angle Between Hands
I am sure you might have seen different types of clocks. Some might have numbers written on them, some might have hour, minute and second hands on them. There are basically two types of clocks - analogue and digital. Let’s first know what a clock is before going into the analogue clock.
A clock is a device that measures and represents time. Some clocks show only time, whereas others show temperature, date, weather, etc. Also, some clocks have a stopwatch and some have alarms.
The two clocks that are widely used are analogue clock and digital clock. Both the clocks have different ways to represent time. An analogue clock is a clock that shows time with two or three moving hands that move in a circular motion. On the other hand, a digital clock is a clock that simply uses numbers to represent time.
Here, we will discuss analogue clocks in detail.
What are Analogue Clocks?
A clock is known as an analogue clock when it has moving hands and is usually (hours) marked from 1 to 12 to show you the time of the day.
In some analogue clocks, hours are marked with Roman numerals (such as I, II, III, IV, etc.), while in others, there are no numbers marked in the clock.
What are the Hands of Analogue Clock?
As discussed above, analogue clocks commonly have two or three hands. If an analogue clock has two hands, then there is a:
Larger hand, known as a minute hand.
Image: Minute hand
Smaller hand, known as an hour hand.
Image: Hour hand
A clock with three hands has a second hand. The second hand is as long as the hour hand but much thinner.
Image: Second Hand
How Does Hour Hand, Minute Hand, and Second Hand Rotate in Analogue Clocks?
Hour Hand Rotation
The hour hand completes one rotation in 12 hours or two rotations in 24 hours.
Minute Hand Rotation
The minute hand completes one rotation in 60 minutes.
Second Hand Rotation
The second hand completes one rotation in one minute.
How to Read Time in Analogue Clocks?
To read a time using an analogue clock, just look at the hands where they are pointing. The smaller hand, also known as the hour hand, will tell you the hour. The larger hand, also known as the minute hand, will tell you the minutes of the current hour. The thinnest hand, also known as the second hand, will tell you the seconds of the current minute.
Let’s learn to read the time.
Step 1: Look at the hour hand first. This will directly point to the number of hours, or somewhere between that number and the next number.
Example
Here, the hour hand is directly pointed at 10. Hence, the hour is 10.
Here, the hour hand is between 1 and 2. Hence, the hour is 1.
Image: An analogue clock showing time as 1:30
Step 2: Now, look at the minute hand. It starts at the top of the clock. For every minute that passes, it moves one tick around the clock.
Now, start from the top and count the tick marks to see how many minutes have passed.
You can count by 1’s
The minute hand in the above clock shows 20 minutes. Also, it is showing 8 hours as the hour hand is between 8 and 9. Therefore, the time is 20 past 8 or 8: 20.
Let’s take one more example to understand in a better way.
Image: An analogue clock showing time as 5
Here, the hour hand is at 5. Hence, the hour is 5.
The minute hand is pointing at 12. This implies 0 minutes after the hour. Therefore, the time is 5:00, or you can also say 5’0 clock.
Step 3: Now, look at the second hand. It works similarly as minute hands. It also starts at the top of the clock. For every second that passes, it moves one tick around the clock. Let us understand with an example:
Image: An analogue clock showing time as 8
Here, the hour hand is pointed at 8. Hence, the hour is 8.
The minute hand is pointed at 12. This implies 0 minutes after the hour.
The second hand is at 4. This implies that 20 seconds have passed. The time here is 8 hours 0 minutes and 20 seconds.
Conclusion
In short, an analogue clock is a clock with three moving hands, namely the hour hand, minute hand, and second hand to show you the time. Generally, in an analogue clock, the hour hand is marked from 1 to 12. Also, an analogue clock is named as analogue because it moves smoothly from one point to another without any sudden break or jumps.
FAQs on Analog Clock in Maths Concepts and Time Reading
1. What is an analog clock in mathematics?
An analog clock is a circular clock that shows time using moving hands to represent hours, minutes, and seconds. In mathematics, it is commonly used to teach angles, fractions, time calculation, and circular motion.
- The clock face is divided into 12 equal parts.
- Each number represents 5 minutes.
- A full rotation equals 360°.
2. How many degrees are there between two numbers on an analog clock?
The angle between two consecutive numbers on an analog clock is 30°. Since a full circle is 360° and there are 12 equal divisions, we calculate:
- 360° ÷ 12 = 30°
3. What is the formula to find the angle between the hour and minute hands?
The formula to calculate the angle between the hour and minute hands is |30H − 5.5M|, where H is the hour and M is the minutes. This formula works because:
- The hour hand moves 30° per hour.
- The minute hand moves 6° per minute.
- The hour hand also moves 0.5° per minute.
4. How do you calculate the angle at 3:15 on an analog clock?
The angle between the hands at 3:15 is 7.5°. Using the formula |30H − 5.5M|:
- H = 3, M = 15
- 30 × 3 = 90
- 5.5 × 15 = 82.5
- |90 − 82.5| = 7.5°
5. How many times do the hands of an analog clock overlap in 12 hours?
The hour and minute hands overlap 11 times in 12 hours. Although there are 12 hours, the hands coincide approximately every 65 minutes and 27 seconds, resulting in only 11 overlaps within one 12-hour cycle. This is a common clock reasoning question in quantitative aptitude and time and work problems.
6. What is the angle of the minute hand at 20 minutes past any hour?
At 20 minutes past the hour, the minute hand forms an angle of 120° from 12 o’clock. Since the minute hand moves 6° per minute:
- 6 × 20 = 120°
7. Why does the hour hand move between numbers on an analog clock?
The hour hand moves continuously because it travels 0.5° per minute, not just 30° every hour. In 1 hour, it moves 30°, but in 1 minute, it moves:
- 30° ÷ 60 = 0.5°
8. What is a right angle on an analog clock?
A right angle on an analog clock is an angle of 90° formed between the hour and minute hands. For example:
- At approximately 3:00, the hands form 90°.
- At approximately 9:00, they also form 90°.
9. How do you find the smaller and larger angle between clock hands?
The smaller angle is found using |30H − 5.5M|, and the larger angle equals 360° − (smaller angle). Steps:
- Calculate the angle using the formula.
- If the result is more than 180°, subtract it from 360°.
10. How is an analog clock related to fractions and multiples?
An analog clock represents fractions of a full circle, where each hour mark equals 1/12 of 360° or 30°. It also shows time as fractions:
- 15 minutes = 1/4 hour
- 30 minutes = 1/2 hour
- 45 minutes = 3/4 hour
