Angle Unit Converter: Degrees, Radians, Gradians Online
Whether you’re a student grappling with trigonometry, a land surveyor mapping terrain, an astronomer searching for stars, or a sport shooter adjusting optics, our calculator provides an instant answer.
We support lightning-fast conversions between all mathematical and practical units (degrees, radians, gradians, arcminutes and arcseconds, milliradians). Our tool connects the world of theoretical mathematics with practical applications in the field. Everything works online, free, and without any installation.
Smart Calculations: Why Convert Angles Here?
Angles aren’t just about compasses and protractors. In practice, various systems converge – sexagesimal (degrees), decimal (gradians), and mathematical (radians). Our tool helps you make sense of it all.
- Real-time Calculations: No waiting. Enter a value and see the result instantly. Ideal for quickly checking homework or workshop calculations.
- Precision for Science and Navigation: We handle conversions with high accuracy, which is crucial for astronomy or GPS coordinate conversions (arcminutes and arcseconds).
- Specialized Units: Unlike standard calculators, we also support milliradians (mrad) for ballistics or gradians (grad) for geodesy.
Comprehensive Overview: Understanding Angle Units
Each field uses a different unit to measure rotation or inclination. Here’s a table of relationships our converter works with.
| Unit | Abbreviation | Full Circle Value | Practical Use |
|---|---|---|---|
| Degree | ° (deg) | 360° | Basic geometry, navigation, everyday life, construction. |
| Radian | rad | 2π (approx 6.28) | Mathematics, physics, game programming, working with sin/cos functions. |
| Gradian | grad (gon) | 400 grad | Geodesy and surveying (right angle = 100 grad). |
| Arcminute | ’ (MOA) | 21 600’ | GPS coordinates, astronomy, shooting (Minute of Angle). |
| Arcsecond | ” | 1 296 000” | Extremely precise measurements of star positions and mapping. |
| Milliradian | mrad | approx 6 283 (or 6400*) | Military targeting, rifle scopes, distance estimation. |
| Turn | turn | 1 | Engineering, engines, mechanics. |
*Note: In NATO, for simplification, a circle is considered to have 6400 mils; in mathematics, the exact multiple of pi applies.
Guide: How to Use the Converter in Practice
Operation is simple, whether you’re solving a mathematical equation or adjusting a telescope.
1. Enter the value
Type a number into the left field.
- Tip: The calculator also handles decimal numbers (e.g.,
45.5degrees).
2. Select the correct units
- For Mathematics: Most often you will convert Degrees ↔ Radians.
- For GPS/Astronomy: You will use Degrees ↔ Arcminutes.
- For Geodesy: Choose Gradians.
3. Monitor the “Quick Overview”
This table below the widget gives you immediate context.
- For example, if you enter 100 degrees, you will see that it corresponds exactly to 6000 arcminutes (because 1° = 60’), but it is also 1.745 radians. Seeing all these values at once is a great aid for understanding the relationships between systems.
Common Mistakes: Why 1.5 Degrees Is Not 1 Degree and 50 Minutes
The biggest pitfall with angles is mixing decimal and sexagesimal systems.
The Problem: One degree (1°) is divided into 60 minutes (60’), not 100.
- If you have an angle of 1.5°, it means “one and a half degrees”.
- Half of 60 minutes is 30. Thus, 1.5° = 1° 30’.
- Many people mistakenly write 1° 50’. Our converter allows you to enter “1.5 degrees” and in the “arcminute” row, you will see the correct mathematical conversion (90 minutes total), or you can verify partial conversions.
Radians vs. Degrees
Most programming languages (Excel, JavaScript, Python) calculate sin() and cos() functions in radians. If you enter the number 90 (thinking degrees), you will get a meaningless result. You must convert the number.
- Our tool will quickly tell you that 90° = 1.5707… rad (which is $\pi/2$).