What Is the Clock Angle Formula?

Before learning the clock angle formula, let us understand a few things about a clock. The clock angle formula is used to calculate the time between any two hands of the clock. In this article, we will explore the clock angle formula and provide solved examples.

A clock has a total of 12 divisions of a total measure of angle 360 degrees. The clock is provided with three hands to measure time, which are an hour hand, minute hand, and second hand.

Finding the Angle between Clock Hands

Let's use these instructions to solve a clock math problem: Example 3. Second angle between clock hands = 360° − First angle between clock hands. In other words, find the absolute value of the difference of two angles:

First angle between clock hands = |Angle hrs − Angle mins|

The clock angle formula for the hour hand is:

Angle hrs = 30° × number of hours + 0.5° × number of minutes

This is because the hour hand moves 30° with every full hour and then 0.5° every minute. So, to find the correct angle, we also have to consider the number of minutes.

Now, mark the angle between the hour hand and 12 o'clock. To calculate the angle between the minute hand and 12 o'clock, multiply the number of minutes by 6 degrees. We already know that the minute hand moves by 6° each minute.

How to Find the Angle of Clock Hands in a Harder Example

Remember – there are two clock angles! The other one is:

60° − 137° = 223°

Method 2 - use a clock angle formula: The angle between the hour hand and the minute hand equals:

Angle between clock hands = 90° + 23° + 24° = 137°

We already know that it also moves 6° every minute. The minute hand moves between the number two to where it is now in four minutes. So, how far is the hour hand from the number 11? The angle between the hour hand and the number 10 on a clock is 14 minutes times 0.5°.

Converting Clock Time to Minutes

The easiest way to find a is to see how far the hour hand is from the number 10. We see from the image that it's smaller than 30°. Then, we marked two remaining spaces with a (next to the hour hand) and c (next to the minute hand).

First, let's find a. It contains 3 whole hours (from number 11 to number 2), so it equals:

We started by marking the angle b because it's the easiest to find its size.

In conclusion, the clock angle formula is an important tool for calculating the time between any two hands of a clock. By understanding how to use this formula, we can easily convert clock time to minutes and solve complex clock math problems.

Convert clock time to minutes