Maps, GPS units and surveying instruments use both formats. 40° 26′ 46″ is the same as 40.4461°. For coordinates, south latitudes and west longitudes are negative in decimal form.
How to use the Degrees Minutes Seconds Calculator
- Degrees
- Minutes
- Seconds
- Direction
- Or: decimal degrees to convert
- Every result field is editable: type into Decimal degrees and Seconds plus every other field update to match.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Minutes are divided by 60 and seconds by 3,600 and added to the degrees; the direction sets the sign. The second section turns any decimal angle into degrees, minutes and seconds.
Inputs explained
| Field | What to enter |
|---|---|
| Degrees | A number |
| Minutes | A number |
| Seconds | A number |
| Direction | Choose one: N or E (positive), S or W (negative) |
| Or: decimal degrees to convert | A number |
What each result means
- Decimal degrees = [Direction] × ([Degrees] + [Minutes]÷60 + [Seconds]÷3600)
- In radians = [Direction] × ([Degrees] + [Minutes]÷60 + [Seconds]÷3600) × pi ÷ 180
Example values
How the main result changes when Seconds changes and everything else stays at the example values above:
| Seconds | Decimal degrees (°) |
|---|---|
| 23 | 40.4397 |
| 34.5 | 40.4429 |
| 46 | 40.4461 |
| 57.5 | 40.4493 |
Formula
decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600Worked example
Inputs — Degrees: 40; Minutes: 26; Seconds: 46; Direction: N or E (positive); Or: decimal degrees to convert: -79.9822.
Results — Decimal degrees = 40.446111 °; In radians = 0.705918 rad; Decimal degrees as DMS = −79° 58′ 55.92″.
Frequently asked questions
What is 40° 26′ 46″ in decimal?
About 40.446111°.
How many seconds in a minute of arc?
60.
What formula does the Degrees Minutes Seconds Calculator use?
decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600.