Angle Converter

What this tool does

Angle Converter handles the angle units used in maths, engineering, surveying, astronomy and navigation. It also converts coordinates between degrees-minutes-seconds and decimal degrees for maps and GPS.

Angles are measured in degrees in everyday life, radians in calculus and programming, gradians on some surveying instruments and arcseconds in astronomy. Maps add another twist by writing coordinates as degrees, minutes and seconds, while GPS devices and web maps expect decimal degrees.

This converter uses the radian as its base. A degree is π/180 rad, a gradian π/200 rad, an arcminute one sixtieth of a degree and an arcsecond one sixtieth of that. A turn is a full revolution (2π rad) and the NATO mil divides a circle into 6,400 parts. The DMS panel parses entries like 40° 26′ 46″ N or plain space-separated numbers and gives decimal degrees, and also turns decimal degrees back into DMS. Everything is computed locally.

How to use Angle Converter

1. Enter an angle in the Value field.
2. Select the From unit, for example Degree.
3. Select the To unit, for example Radian, and read the Result.
4. Use the swap button or Decimal places slider as needed.
5. In the DMS panel, type a coordinate such as 40° 26′ 46″ N to get decimal degrees.
6. Type a decimal value such as -73.9857 to get degrees, minutes and seconds, then copy it.

Tips for better results

• A full circle is 360°, 2π rad, 400 gon or 6,400 NATO mils.
• One radian is about 57.2958°, and 1° is about 0.01745 rad.
• Add S or W after a DMS coordinate to make it negative in decimal form.
• JavaScript and most programming maths functions expect radians, not degrees.

Common use cases

• Converting angles for trigonometry homework and programming.
• Converting map coordinates from DMS to decimal degrees for GPS or web maps.
• Working with surveying data in gradians.
• Converting telescope or astronomy measurements in arcminutes and arcseconds.

Common mistakes to avoid

• Passing degrees to a sine or cosine function that expects radians.
• Writing 40.30° when 40° 30′ is meant; 30 minutes is 0.5°, not 0.30°.
• Forgetting that south and west coordinates are negative in decimal degrees.