# Degrees Minutes Seconds Calculator (DMS to Decimal)

URL: https://speedycalculator.com/calculators/conversion/degrees-minutes-seconds/
Last updated: 2026-10-25

> The DMS calculator converts an angle or coordinate in degrees, minutes and seconds into decimal degrees, and converts decimal degrees back into DMS notation.

## Inputs

- Degrees
- Minutes
- Seconds
- Direction
- Or: decimal degrees to convert

## Results

- Decimal degrees
- In radians
- Decimal degrees as DMS

## Formula

```
decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600
```

## Explanation

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

FieldWhat to enterDegreesA numberMinutesA numberSecondsA numberDirectionChoose one: N or E (positive), S or W (negative)Or: decimal degrees to convertA 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:

SecondsDecimal degrees (°)2340.439734.540.44294640.446157.540.4493

## Worked 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″.

## FAQ

**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.


## Sources

- [NIST Special Publication 811 – Guide for the Use of the International System of Units](https://www.nist.gov/pml/special-publication-811)
- [NIST Handbook 44 Appendix C – General tables of units of measurement](https://www.nist.gov/pml/owm/nist-handbook-44-current-edition)