Hours and Seconds Converter

This calculator offers you the option to convert hours into seconds, or the other way around. Start by choosing the value you want to be converting from (hours or seconds). Afterward, choose the value you will be converting to (once again hours or seconds).

Once your settings are done, choose how many decimal spaces would you like your result to be rounded to. In case you do not choose a value, the result will be shown with a precision of up to 15 decimal spaces.

Click on CONVERT and you will receive your result, including the conversion rate. The conversion rate is a ratio of 1 of your base unit to the equivalent value of the other unit you are converting to.

Converting Hours and Seconds manually

In order to be able to perform these calculations manually, two things must be established:

• 1. The ratios between the two units.
• 2. The method of conversion using said ratios.

Conversion ratios

First, we will establish some basic conversion ratios.

We know that 1 hour has 60 minutes, and we know that each minute consists of 60 seconds. Hence 1 hour consists of 60×60 = 3,600 seconds.

This means that the ratio of hours to seconds is 1:3,600.

This ratio can then be used to find the conversion from seconds to hours. If 1 hour is equal to 3,600 seconds, then 1 second is equal to 1÷3,600 = 0.00028 hours, if rounded to two significant digits.

Hence the ratio of seconds to hours is 1:0.00028.

Calculating the conversions

Using the ratios we just discovered for calculations works in the following ways:

Example 1: Converting seconds to hours

Martin has been playing a video game for exactly 1,354 seconds. How many hours (rounded to three decimal spaces) is this equal to?

The solution lies in method 1 above. We take 1,354 seconds and divide them by 3,600. The result of this division is 1,354÷3,600 = 0.376 rounded to three decimal spaces. Hence he played the game for approximately 0.376 of an hour. 

Example 2: Converting hours to seconds

A bus ride took 0.75 of an hour. How many seconds long was it? Round your answer to the nearest second.

Referring to method 2, we take 0.75 of an hour and divide it by 0.00028. This division results in 0.75÷0.00028 = 2,679 seconds rounded to the nearest second. 

History of seconds and hours

The first mentions referencing current day seconds in the context of time measurements are from the year 1,000 AD. They were made by a Persian scholar Al-Biruni, who used seconds to describe phases of the moons with exact timing, all the way to partial seconds.

On the other hand, hours have been used for a long time already. Ancient Greek philosophers and early scientists like Ptolemy or Hipparchus were using the sexagesimal concept, which simply means splitting something into 60 parts.

Although at the time, the concept was inverted into a day of 60 hours, where each hour would technically have a duration of 24 minutes today. We intuitively see that this was swapped with time for convenience. Scientists are divided on whether this concept was true or whether it was as widespread as some sources claim.

Some other ancient references come from the Babylonians who split the days into 12 parts, hence having hours that lasted an equivalent of 2 modern-day hours. This system was later adopted by other cultures as well.

The reason why the sexagesimal base is so useful is, that 60 has a lot of very useful factors that allow us to split the time further.

As we know, 60 has the following factors: 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. We recognize most of these values from time references, such as 5 minutes between each hour point on the clock, 15 minutes being a quarter of an hour, the clock being split into 12 hours, and so on.

References

https://www.scientificlib.com/en/Physics/LX/Second.html
https://en.wikipedia.org/wiki/Al-Biruni
https://en.wikipedia.org/wiki/Hour#Antiquity