# Angle Converter

> Convert angles between degrees, radians, gradians, and turns instantly. Online angle calculator for geometry, trigonometry, and practical applications.

URL: https://acrafto.com/en/angle-unit-converter/

Tools are interactive browser apps; there is no public API, no endpoints to call and no server-side processing. To use a tool, open its HTML page in a browser.

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.

1. **Real-time Calculations:** No waiting. Enter a value and see the result instantly. Ideal for quickly checking homework or workshop calculations.
2. **Precision for Science and Navigation:** We handle conversions with high accuracy, which is crucial for astronomy or GPS coordinate conversions (arcminutes and arcseconds).
3. **Specialized Units:** Unlike standard calculators, we also support **milliradians (mrad)** for ballistics or **gradians (grad)** for geodesy.

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## 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., `45.5` degrees).

### 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 $\\pi/2$).

---

## Frequently Asked Questions (FAQ)

### What is the formula for converting degrees to radians?

The formula is simple, based on the number Pi ($\\pi$). A full circle has 360° or $2\\pi$ radians. The conversion is: **Radians = Degrees × ($\\pi$ / 180)**. Example: 180° × 3.14159 / 180 = 3.14159 rad. Our calculator computes with high precision Pi for you.

### What are MOA and mrad?

These units are primarily known to shooters. **MOA** (Minute of Angle) is an arcminute. 1 MOA corresponds to approximately 2.9 cm at a distance of 100 meters. **Mrad** (Milliradian) is one-thousandth of a radian. 1 mrad corresponds precisely to 10 cm at 100 meters. Our converter allows you to accurately convert rifle scope clicks between these systems.

### What are gradians (grad) used for?

A gradian is an attempt to introduce a decimal system for angles. A right angle has 90 degrees, but **100 gradians**. This simplifies calculations in surveying (geodesy), where this unit is still encountered. If you come across an older compass or map with a "strange" division of a circle into 400 parts, those are gradians.

### How do I convert GPS coordinates?

GPS coordinates are given either in decimal form (e.g., 50.088°) or in degrees, minutes, and seconds (50° 5' 16"). Our converter will help you convert the decimal part. Example: Do you have 0.5 degrees? Enter it into the calculator and you will see that it is 30 minutes.

## Other languages

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- Español (es): [Conversor de ángulos](https://acrafto.com/es/conversion-angulos/) ([Markdown](https://acrafto.com/es/conversion-angulos/index.md))
- Italiano (it): [Convertitore di angoli](https://acrafto.com/it/convertitore-unita-angolari/) ([Markdown](https://acrafto.com/it/convertitore-unita-angolari/index.md))
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- Русский (ru): [Конвертер углов](https://acrafto.com/ru/konverter-uglov/) ([Markdown](https://acrafto.com/ru/konverter-uglov/index.md))
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