Angle Converter
Convert between degrees, radians, and DMS (degrees-minutes-seconds). Pick a format on the left and one on the right, enter a value, and copy the result.
Convert between degrees (°), radians (rad), and DMS (degrees-minutes-seconds). Select the From format in the left table and the To format in the right table. For DMS input, use the degrees, minutes, and seconds fields. You can set decimal places and copy the result or copy with labels.
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Examples
- 180° → 3.1416 rad
- π/2 rad → 90°
- 45° 30′ 0″ → 45.5°
FAQ
How do I convert degrees to radians?
Radians = degrees × (π/180). Select degrees on the left and radians on the right, then enter the angle in degrees.
What is DMS?
DMS is degrees, minutes, and seconds. For example, 45° 30′ 0″ means 45 degrees, 30 arcminutes, 0 arcseconds. 1 degree = 60 minutes, 1 minute = 60 seconds.
How do I enter DMS?
Select DMS as the From unit. Enter the degrees, minutes, and seconds in the three fields that appear.
What is a radian?
A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle is 2π radians (≈ 6.2832 rad). Radians are the natural unit in mathematics and physics.
How many degrees in a full circle?
360 degrees = 2π radians = 400 gradians. A right angle is 90° = π/2 rad. A straight line is 180° = π rad.
What are gradians (gon)?
Gradians divide a circle into 400 equal parts, making a right angle exactly 100 gradians. They are used in surveying and some European engineering contexts. 1 gradian = 0.9 degrees.
Why do programming languages use radians?
Math functions like sin(), cos(), and tan() in most languages (JavaScript, Python, C) accept radians because the calculus formulas are simpler in radians. Convert degrees to radians before calling these functions: radians = degrees × Math.PI / 180.
How are GPS coordinates expressed in DMS?
GPS coordinates are often given as DMS, e.g. 51° 30′ 26″ N, 0° 7′ 39″ W (near London). Decimal degrees (DD) like 51.5072° N, -0.1275° W are equivalent and easier to use in software.
What are compass bearings in degrees?
North is 0°/360°, East is 90°, South is 180°, West is 270°. Bearings are measured clockwise from north. A bearing of 135° points to the southeast.
How do I convert DMS to decimal degrees?
Decimal degrees = degrees + (minutes / 60) + (seconds / 3600). Example: 45° 30′ 15″ = 45 + 30/60 + 15/3600 = 45.5042°.
What is the difference between arcminutes and arcseconds?
1 degree = 60 arcminutes (′). 1 arcminute = 60 arcseconds (″). Arcseconds are used in astronomy and high-precision navigation. 1 arcsecond on Earth's surface ≈ 31 meters.