Angle Converter
Convert angles between Degrees (°), Radians (rad), Gradians (grad), and full Turns.
Angle Converter: Degrees, Radians, Gradians, Arcminutes & Arcseconds
Angle measurement quantifies circular rotation, trigonometric functions, astronomical coordinates, and civil surveying grades. While mechanical engineering and navigation rely on the sexagesimal 360-degree circle, pure mathematics and calculus require natural radians (rad) for clean trigonometric derivatives without scaling factors.
ToolQix Angle Converter translates rotational angles across mathematical, navigational, and astronomical units. Convert instantaneously between Degrees (°), Radians (rad), Gradians (gon/grad), Arcminutes (MOA / '), Arcseconds ("), Milliradians (mrad), and Revolutions (turns).
Radian Calculus Foundation & Sexagesimal Circle Subdivision
A full circle equals 360 degrees (sexagesimal convention dating to ancient Babylon), equivalent to 2π radians (the ratio of circumference to radius). One radian represents the angle subtended by an arc equal in length to the circle's radius (~57.2958°). Gradians subdivide a right angle into 100 decimal units (400 gon per full turn).
How to Use Angle Converter Step-by-Step
Select Source & Target Angle Units
Choose your input unit (e.g., Degrees) and desired output unit (e.g., Radians or Arcminutes).
Input Angle Value
Type any numeric angle value into the input field.
Review Multi-Unit Grid
View the converted angle across degrees, radians, gradians, arcminutes, and full revolutions.
Copy Converted Angle
Copy your result with customizable decimal precision for programming or ballistic tables.
Angle Converter Industry Use Cases
Computer Graphics & Game Development
Convert between human-friendly degrees (inspector controls) and math library radians (Math.sin/cos in JavaScript/C++).
Ballistics & Optical Scope Adjustment
Convert scope reticle adjustments between Minutes of Angle (MOA) and Milliradians (MIL / mrad).
Astronomy & Telescope Tracking
Convert small celestial angular separations into arcminutes and arcseconds.
Civil Surveying & Geodesy
Convert land boundary azimuth bearings between degrees-minutes-seconds and decimal degrees.
Angle Converter Best Practices & Tips
- In programming languages (JavaScript, Python, C++), standard trigonometric functions (sin, cos, tan) expect radians, NOT degrees.
- 1 Minute of Angle (MOA) subtends approximately 1.047 inches at 100 yards, commonly rounded to 1 inch per 100 yards in practical shooting.
- 1 Milliradian (MIL) subtends exactly 10 centimeters at 100 meters (or 1 meter at 1,000 meters).
- A right angle equals 90 degrees, π/2 radians (≈ 1.5708 rad), or 100 gradians.
Key Angular Geometric Reference Benchmarks
| Geometric Angle | Degrees (°) | Radians (Exact) | Radians (Decimal) | Gradians (gon) |
|---|---|---|---|---|
| Zero Angle | 0° | 0 rad | 0.0 rad | 0 gon |
| Acute Cardinal Angle | 30° | π / 6 | 0.5236 rad | 33.33 gon |
| Half Right Angle | 45° | π / 4 | 0.7854 rad | 50.00 gon |
| Equilateral Triangle Corner | 60° | π / 3 | 1.0472 rad | 66.67 gon |
| Right Angle (Perpendicular) | 90° | π / 2 | 1.5708 rad | 100.00 gon |
| Straight Line Angle | 180° | π | 3.1416 rad | 200.00 gon |
| Full Circle Rotation | 360° | 2π | 6.2832 rad | 400.00 gon |
FAQs About Angle Converter
Why do mathematicians and programmers use radians instead of degrees?
In calculus, using radians allows the derivative of sin(x) to equal cos(x) directly without messy conversion constants like π/180. Radians represent natural geometric arc ratios rather than the arbitrary 360-degree historical Babylon division.
What is an Arcminute (MOA)?
An arcminute (Minute of Angle, or MOA) is 1/60th of a single degree. In shooting sports and optics, 1 MOA spreads by approximately 1.047 inches at 100 yards, providing a fine benchmark for rifle accuracy.
What is a Gradian (gon)?
A gradian (also called a gon) is a metric-style angle unit that divides a circle into 400 grads instead of 360 degrees, making each 90-degree right angle exactly 100 grads. It is still used in civil surveying in certain European countries.
How many radians are in a full 360-degree circle?
There are exactly 2π radians in a full circle, approximately 6.2831853 radians.
Is any angle conversion data stored on external servers?
No. All conversions execute 100% locally inside your web browser.
Tested Methodology & Client-Side Processing
Reviewed: October 21, 2026Calculations, algorithms, and transformations in this utility run directly in your browser without sending your private inputs to remote processing servers. Formulas reference established technical specifications and official documentation under our Editorial & Testing Policy.