Angle Conversion Calculator (Degrees, Radians, Gradians & Mils

Angle measurement systems vary by discipline: mathematics and physics utilize radians for calculus; navigation and surveying use degrees, minutes, and seconds (DMS) or gradians; military artillery utilizes NATO mils (6,400 per circle).

To use the Angle Conversion Calculator (Degrees, Radians, Gradians & Mils), enter your Angle Value, Convert From Unit. The calculator instantly computes Degrees (°), Radians (rad) and more. Results update in real time as you change any input — no submit button needed.

How to Use This Calculator

Enter your Angle Value (e.g. 180) and Convert From Unit — choose from Degrees (°), Radians (rad), Gradians (grad / gon). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

1 Radian = 180° / π ≈ 57.2958°

1 Degree = π / 180° rad ≈ 0.0174533 rad

1 Gradian = 0.9° | 1 Circle = 360° = 2π rad = 400 grad = 6400 NATO Mils

Worked Example

Convert 180° to all units:

180° = 3.141593 rad (1.0000 π rad) = 200.000 grad = 10,800' = 648,000" = 0.500 rev = 3200 mils.

Understanding Your Result

Unit conversions are exact by definition within a given measurement system (e.g., 1 km = exactly 1,000 m). Cross-system conversions (metric to imperial) use defined exchange factors: 1 inch = exactly 2.54 cm; 1 pound = 0.45359237 kg. Round your converted result to match the precision of your original measurement — expressing more decimal places than your input justifies implies false accuracy. For regulatory, legal, or safety-critical applications, verify which measurement system is required by the applicable standard.