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Convert between Degrees, Minutes and Seconds and Decimal Degrees of Latitude and Longitude



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Traditionally geographic coordinates in maps over the ages have been measured by degrees, minutes and seconds of latitude and longitude. However many modern systems, for example most GPS devices, use decimal degrees these days.  If you're off by even just a few decimal places or minutes of arc, you could end up miles away from your intended location, or even worse, up above your neck in the sea!  Springfrog's handy and easy to use online converter will save you from the inconvenience and embarassment of getting lost, by accurately converting either from degrees, minutes and seconds to decimal degrees, or back in the other direction.  

To convert from degrees, minutes and seconds to decimal degrees, enter the latitude and logitude coordinates in the top blue boxes and click on the "Convert Degrees, Minutes and Seconds to Decimal Degrees!" button.
 The conversion results, in decimal degrees, will then show in the yellow input boxes below.  You'll also be presented with a map centered on the exact lat. and long. coordinates that you entered. This enables you to confirm the location visually to ensure you've input the correct geographic coordinates. You can zoom in further to these coordinates by using the + button on the map, or zoom out using the - button.  Alternatively pointing and double-clicking your mouse on any part of the map will zoom in to the location you've clicked on. You can also pan across the map by holding your left mouse button down and dragging in any direction.  At the bottom left of the map you'll find a box which gives you a wider view of the location that you're centered on, and below that there's a nifty scale measurement for the current map.  

To convert from decimal degrees to degrees, minutes and seconds, enter the decimal latitude and longitude co-ordinates in the bottom yellow boxes and click on the "Convert Decimal Degrees to Degrees, Minutes and Seconds!" button.
 Remember that when entering latitude co-ordinates in decimal, a negative number indicates South of the equator, whereas a positive figure denotes North.  When it comes to longitude, a negative number means West of the prime meridian at Greenwhich, London, whereas posiitive indicates East.  The results in Degrees, Minutes and Seconds will be displayed in the top blue boxes.  Just like when converting from DMS to decimal, you'll get a useful map centered on the coordinates that you've entered, which will help you to visually check that you've got the correct location.



Why are there 60 Minutes in a Degree and 60 Seconds in each Minute?

The use of 60 minutes per degree, and 60 seconds in each of those minutes dates has its origins in ancient Sumeria over 4,000 years ago.  The ancient Sumerians devised what is known as the sexagisimal system, a method of counting using base 60 rather than base 10 which we use today.  This was later adopted by the Babylonians and continued to be used by astronomers and scientists through the ages until it continues to be used in maps today.


Circle divided into 6 sectors of 60 degrees
Different theories abound for the reason why specifically 60 was used as a base for those cultures.  The world rotates around the sun in one year which we know today is approximately 365 and a quarter days.  Back in Sumerian times it may not have been clear to the ancients whether the Earth rotated around the Sun or vice-versa, but they are likely to have realised that some circular motion was going on,  even if it was just by looking at the way the stars rotate in the night sky. By judging how seasons repeat they may have approximated the period of one year, or one Earth-solar rotation to 360 days, which may explain division of a circle into 360 degrees.  Circles themselves can very naturally be divided into 6 parts.  If you take a round coin for example and place at the centre of other coins of the same size around it, which all touch the center coin, exactly 6 coins will fit around the central coin.  Extend lines of diameter through these six outer circles through the mid-point of the central circle and you'll divide the central circle into 6 sectors.  Each of these sectors is therefore 360/6, which equals 60 degrees forming the base of the Sumerian and Babylonian numerical system.

Another explanation for 60 being used as the base is that it is a number which can be divided by a large amount of smaller numbers (other than 1) to get a whole number - in other words it has many prime factors.  Indeed, 60 can be divided by all of the whole numbers between 2 and 6, as well as 10,12, 15, 20 and 30 to give another whole numbers.  In other words it has a total of ten prime factors.  It is, in fact, the lowest number to have 10 prime factors, and the next number to have more than 10 is 120 which has 14 prime factors.  The ten prime factors of base 60 can be compared to our modern base 10 which only has 2 prime factors (2 and 5), or the decimal number 100 which has only 7 prime factors.  Ancient Sumerians didn't carry pocket calculators around with them as far as we know, so such a large amount of prime factors makes the number 60 very convenient when dividing up crops or livestock.  

The number 60 is also very handy in another, more literal sense. You may have thought you could only count up to 10 using your fingers and thumbs but by using two hands, ancient farmers could easily count up to 60.  You can try it yourself.  Look at your fingers and you'll see that each finger (but not your thumb) consists of 3 bones.  Using the thumb of your left hand, point to each bone of the fingers of that hand to count up to 12.  Then use a finger or thumb of your right hand to denote each lot of 12, giving you a total 60 that you can count up to.  
    
So when you'e using our handy converter just think - you're converting a latitude and longitude system whose origins are way back in those ancient times thousands of years ago, and transforming the numbers into coordinates which be may used in GPS and other mapping systems which those ancients would marvel at - kind of like time-travelling with numbers!  



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