DMS To Decimal Degrees Converter
40° 26′ 46″ is 40.4461 decimal degrees, because the minutes are divided by 60 and the seconds by 3,600.
Quick answer: Divide the minutes by 60, divide the seconds by 3,600, and add both to the degrees. For example, 40° 26′ 46″ is 40.446 deg, 38° 53′ 23″ is 38.89 deg and 51° 30′ 26″ is 51.507 deg.
The DMS to decimal degrees formula
The decimal degrees equal degrees plus minutes divided by 60 plus seconds divided by 3,600.
The degrees stay whole, and the minutes and seconds become a fraction.
Take 40° 26′ 46″. 40 + 26 ÷ 60 + 46 ÷ 3,600 gives 40.446 deg.
Take 38° 53′ 23″. 38 + 53 ÷ 60 + 23 ÷ 3,600 gives 38.89 deg.
Sixty and sixty again
One degree has 60 arcminutes, and one arcminute has 60 arcseconds (Wikipedia: Minute and second of arc). So one arcsecond is 1/3,600 of a degree.
That is why minutes are divided by 60 and seconds by 3,600 before they are added to the degrees.
How to convert DMS to decimal degrees step by step
- Read the degrees, minutes and seconds.
- Divide the minutes by 60.
- Divide the seconds by 3,600.
- Add both to the degrees.
Example 1: 40° 26′ 46″
- Start with 40° 26′ 46″.
- 40 + 26 ÷ 60 + 46 ÷ 3,600 = 40.446.
- The decimal angle is 40.446 deg.
40° 26′ 46″ = 40.446 deg
Example 2: 38° 53′ 23″
- Start with 38° 53′ 23″.
- 38 + 53 ÷ 60 + 23 ÷ 3,600 = 38.89.
- The decimal angle is 38.89 deg.
38° 53′ 23″ = 38.89 deg
Example 3: 51° 30′ 26″
- Start with 51° 30′ 26″.
- 51 + 30 ÷ 60 + 26 ÷ 3,600 = 51.507.
- The decimal angle is 51.507 deg.
51° 30′ 26″ = 51.507 deg
The three examples below use common sizes.
Each one shows the sum in full.
DMS to decimal degrees conversion table
| Degrees, minutes, seconds | Decimal degrees | Total arcminutes |
|---|---|---|
| 10° 0′ 0″ | 10 deg | 600 arcmin |
| 10° 30′ 0″ | 10.5 deg | 630 arcmin |
| 12° 45′ 0″ | 12.75 deg | 765 arcmin |
| 25° 15′ 30″ | 25.258 deg | 1,515.5 arcmin |
| 34° 3′ 8″ | 34.052 deg | 2,043.13 arcmin |
| 38° 53′ 23″ | 38.89 deg | 2,333.38 arcmin |
| 40° 26′ 46″ | 40.446 deg | 2,426.77 arcmin |
| 48° 51′ 24″ | 48.857 deg | 2,931.4 arcmin |
| 51° 30′ 26″ | 51.507 deg | 3,090.43 arcmin |
| 77° 0′ 32″ | 77.009 deg | 4,620.53 arcmin |
| 89° 59′ 59″ | 90 deg | 5,399.98 arcmin |
The highlighted row is the default of the calculator. The last column gives arcmin.
A quick mental shortcut for DMS to decimal degrees
Think of minutes as a fraction of an hour. 30 minutes is 0.5 and 15 minutes is 0.25.
Seconds add very little. 36 seconds is just 0.01 of a degree.
South and west
For southern latitudes and western longitudes, the decimal result is negative. A point at 77° 00′ 32″ west becomes about −77.0089 (Wikipedia: Decimal degrees).
Work out the number as usual, then add the minus sign at the end.
Maps and GPS
Many maps show degrees, minutes and seconds, while GPS tools and web maps use decimal degrees. This sum links the two.
Keep at least four decimals for a position that is accurate to about ten metres.
Quick conversion answers
| Conversion | Result |
|---|---|
| 10° 30′ 0″ | 10.5 deg |
| 40° 26′ 46″ | 40.446 deg |
| 51° 30′ 26″ | 51.507 deg |
| 89° 59′ 59″ | 90 deg |
Where this conversion is used
Map users and surveyors turn a DMS position into decimal degrees.
Students practise base 60 sums.
Common mistakes to avoid
- Dividing seconds by 60. Divide seconds by 3,600.
- Adding minutes as decimals. 26 minutes is not 0.26.
- Losing the sign. South and west are negative.
- Using 100. A degree has 60 minutes, not 100.
Related converters
More DMS values
5° 15′ 0″ is 5.25 deg. 15° 20′ 10″ is 15.34 deg. 22° 30′ 0″ is 22.5 deg.
33° 45′ 15″ is 33.75 deg. 45° 10′ 30″ is 45.18 deg. 52° 12′ 36″ is 52.21 deg.
60° 5′ 5″ is 60.08 deg. 75° 40′ 20″ is 75.67 deg. 85° 59′ 1″ is 85.98 deg.
Doubling the first number
10° 15′ 0″ is 10.25 deg. 30° 20′ 10″ is 30.34 deg. 44° 30′ 0″ is 44.5 deg.
66° 45′ 15″ is 66.75 deg. 90° 10′ 30″ is 90.18 deg. 104° 12′ 36″ is 104.2 deg.
120° 5′ 5″ is 120.1 deg. 150° 40′ 20″ is 150.7 deg. 170° 59′ 1″ is 171 deg.
Doubling and halving
If you double all three parts, the decimal doubles. So 80° 52′ 92″ is about 80.8922, where 40° 26′ 46″ was 40.4461.
Every 30 arcminutes adds exactly 0.5 degrees.
Use these rules to catch slips.
Checking the answer
Take the whole part of your answer as the degrees. Multiply the fraction by 60 to get the minutes.
For 40.4461, the fraction 0.4461 × 60 gives 26.77 minutes, and 0.77 × 60 gives about 46 seconds.
Rounding the answer
Four decimals of a degree is about ten metres on the ground. Five decimals is about one metre.
Round only at the end. Rounding early can add a small error to the final number.
Checking with minutes only
If the seconds are zero, the sum is easy. 30 minutes is 0.5 degrees, 15 minutes is 0.25 and 45 minutes is 0.75.
Latitude and longitude limits
Latitude runs from 0 to 90 degrees, and longitude runs from 0 to 180 degrees. Minutes and seconds must stay below 60.
If a part is out of range, check the numbers before you convert.
Frequently asked questions
How do I convert DMS to decimal degrees?
Add the degrees, the minutes divided by 60 and the seconds divided by 3,600.
Why 3,600?
Because there are 60 arcseconds in an arcminute and 60 arcminutes in a degree.
How do I treat south and west?
Make the decimal result negative.
Is 26 minutes the same as 0.26 degrees?
No. It is 26 ÷ 60, about 0.4333 degrees.
How many decimals should I keep?
Four decimals is about ten metres on the ground.
How do I go back to DMS?
Use the DMS calculator page.
Sources
- Wikipedia: Minute and second of arc (en.wikipedia.org)
- Wikipedia: Decimal degrees (en.wikipedia.org)
