What is Angle Converter?

Angle Converter is a professional tool that converts between different angle measurement units instantly. Whether you're working with degrees, radians, gradians, or arc seconds, this converter handles all the math for you with precision and speed.

Angles are measured in various units depending on the field. Mathematicians prefer radians, surveyors use gradians, astronomers work with arc seconds, and most everyday applications use degrees. Converting between these units manually involves memorizing formulas and calculating precision decimals—this tool eliminates that work entirely.

Who Uses Angle Conversion?

Students

Learning trigonometry and solving geometry problems that require angle conversions

Engineers

Working with rotational mechanics, control systems, and CAD software

Programmers

Converting between degrees (user-friendly) and radians (used by most math libraries)

Navigators

Converting GPS coordinates and compass bearings

Astronomers

Measuring celestial positions in arc minutes and arc seconds

Surveyors

Working with gradians (also called gons) common in land measurement

Supported Units

This converter supports 13 angle units across four categories:

Common Units

Everyday angle measurements

Degree (°)
Radian (rad)
Milliradian (mrad)
Turn

Surveying Units

Land measurement standards

Gradian (grad)
Gon

Astronomy Units

Celestial position measurements

Arc Minute (′)
Arc Second (″)
Milliarcsecond (mas)

Special Units

Specialized angle divisions

Sign
Quadrant
Sextant

Privacy

100% Client-Side Processing: All calculations happen in your browser. No data is sent to any server, and nothing is stored or tracked.

Table of Contents

1. What is Angle Converter?
2. How to Use
3. Features
4. Frequently Asked Questions

How to Use

Converting angle units takes just a few seconds. Here's your complete guide to getting the most out of this tool:

Basic Conversion

Enter a Value

Type your angle value in the first input field (e.g., "90")

Select Source Unit

Choose your starting unit using the first dropdown (e.g., "Degree")

Select Target Unit

Choose your desired unit using the second dropdown (e.g., "Radian")

View Result

See the converted value instantly in the second field—no calculate button needed

Real-Time Updates: The converter updates as you type—no need to click a calculate button. Results appear instantly with every keystroke.

Convert to Multiple Units at Once

Below the main converter, you'll see results for all supported units simultaneously. This is useful when you need to see the same angle expressed in different measurement systems—perfect for comparing values across disciplines or verifying calculations.

Customize Visible Units

Click "Customize Units" to show or hide specific units. If you only work with degrees and radians, you can hide the surveying and astronomy units to keep the results clean and focused on what matters to you.

Adjust Decimal Precision

Use the "Decimals" dropdown to control how many decimal places appear in results:

2-8 decimals: Fixed number of decimal places for consistent formatting
Auto mode: Shows appropriate precision based on the value (recommended for most users)

Copy Results

Click the copy button next to any value to copy it to your clipboard instantly. Use "Copy All Results" to copy every visible conversion at once—perfect for pasting into spreadsheets or reports.

Reverse Conversion

Click the swap button (↔) between the input fields to reverse the conversion direction instantly. You can also type directly in the second field to convert in the opposite direction without manually switching units.

Features

Instant Real-Time Conversion

Results update as you type with no delay. Uses precise mathematical formulas—for example, 1 radian equals exactly 180/π degrees (approximately 57.29577951°).

Multi-Unit Results Display

See your angle converted to all supported units at once. The source unit is highlighted so you can easily identify which row represents your input value.

Bidirectional Input

Type in either field and the other updates automatically. This makes it easy to work in whichever direction you need without switching units manually.

Customizable Unit List

Toggle individual units on or off based on your needs. Students might only need degrees and radians, while surveyors might focus on gradians. Your preferences are saved for future visits.

Precision Control

Choose from 2, 4, 6, or 8 decimal places, or use "Auto" mode which displays an appropriate number of digits based on the value. Very large or very small numbers automatically switch to scientific notation.

Unit Reference Table

Click "Unit Reference" to see a table explaining each unit, its symbol, equivalent value, and typical use cases. This is helpful when learning about unfamiliar angle units.

Searchable Unit Dropdowns

Each unit dropdown includes a search box. Start typing a unit name or symbol to filter the list quickly—no more scrolling through long lists.

Keyboard Friendly

Navigate the entire converter using your keyboard. Tab through fields, use arrow keys in dropdowns, and press Enter to select options.

Works on All Devices

The converter is fully responsive and works on desktop, tablet, and mobile. Touch targets are sized appropriately for finger navigation on smaller screens.

Dark Mode Support

The converter respects your system's dark mode preference and includes a manually toggleable dark theme for comfortable use in low-light environments.

Frequently Asked Questions

How do I convert degrees to radians?

Multiply the degree value by π/180 (approximately 0.01745329). For example, 90° × (π/180) = π/2 radians ≈ 1.5708 radians. This converter handles the calculation automatically with high precision—simply enter your degree value and read the radian result.

Quick Formula: radians = degrees × (π / 180)

How do I convert radians to degrees?

Multiply the radian value by 180/π (approximately 57.29577951). For example, π radians × (180/π) = 180°. Simply enter the radian value and read the degree result instantly.

Quick Formula: degrees = radians × (180 / π)

What is a radian?

A radian is the SI unit for measuring angles. It's defined as the angle at the center of a circle subtended by an arc equal in length to the radius. One full rotation (360°) equals 2π radians, approximately 6.283 radians.

Key conversions:

π radians = 180°
2π radians = 360° (full circle)
π/2 radians = 90° (right angle)
1 radian ≈ 57.2958°

What is a gradian (gon)?

A gradian (also called gon or grade) divides a right angle into 100 parts instead of 90. A full circle is 400 gradians. This makes certain calculations easier in surveying and civil engineering.

Common in: European surveying, civil engineering, and land measurement applications where decimal divisions simplify calculations.

What are arc minutes and arc seconds?

These are subdivisions of a degree. One degree equals 60 arc minutes (′), and one arc minute equals 60 arc seconds (″). They're commonly used in astronomy for precise angular measurements and in geographic coordinates (latitude/longitude).

Unit	Symbol	Relation
Degree	°	Base unit
Arc Minute	′	1° = 60′
Arc Second	″	1′ = 60″ (1° = 3,600″)

Why do programming languages use radians?

Most math libraries (JavaScript, Python, C++) use radians because they simplify calculus operations. The derivative of sin(x) is cos(x) only when x is in radians. Many formulas in physics and engineering also assume radians.

Developer Tip: Always convert user-friendly degree inputs to radians before passing them to trigonometric functions like Math.sin(), Math.cos(), or Math.tan().

What is a turn?

A turn represents one complete rotation, equal to 360 degrees or 2π radians. It's intuitive for describing full rotations—"half a turn" is 180°, "quarter turn" is 90°.

Examples:

1 turn = 360° = 2π radians
0.5 turn = 180° = π radians
0.25 turn = 90° = π/2 radians

Are the conversion results accurate?

Yes. The converter uses mathematically precise conversion factors. For irrational ratios (like degrees to radians which involves π), we use high-precision values to ensure accuracy for scientific and engineering applications.

Precision Guarantee: All calculations maintain accuracy suitable for professional engineering, scientific research, and academic applications.

Does this work offline?

Once the page loads completely, all calculations happen in your browser with no internet connection required. However, you need to be online for the initial page load.

After loading, you can disconnect from the internet and continue using the converter without any limitations.

Can I bookmark a specific conversion?

The main converter always starts with default units (degrees to radians). For specific conversions like "degrees to arc seconds," use the dedicated sub-tool pages which can be bookmarked for quick access to your most-used conversions.