Angle Converter

About Angle Converter

This angle converter allows you to quickly convert between common angle units such as degrees, radians, and gradians. It is designed for everyday use where fast and accurate angle conversion is required.

Angle measurement is fundamental to mathematics, engineering, navigation, and countless scientific disciplines. From calculating trigonometric functions in calculus to designing mechanical components in engineering, from navigating ships across oceans to programming computer graphics, accurate angle conversion is essential in our technical world where different fields use different angular measurement systems.

🌟 Why Choose ConvertPedia's Angle Converter?

Instant Results: Get angle conversions in real-time as you type
100% Accurate: Using exact mathematical formulas (π-based for radians)
Math & Science Ready: Perfect for trigonometry and calculus problems
Engineering Precision: Accurate conversions for mechanical and civil engineering
Navigation & Surveying: Convert between degrees and gradians for land surveying
No Registration: Use immediately without sign-up
Completely Free: No hidden charges or premium versions

Supported Angle Units

Our converter supports all major angle measurement units used globally. Here's a detailed overview:

Degree (°)

Radian (rad)

Gradian (gon)

Understanding Angle Unit Relationships

Unit	Symbol	Full Circle	Right Angle	Typical Use Cases
Degree	°	360°	90°	Everyday use, geometry, navigation, education
Radian	rad	2π rad ≈ 6.28318 rad	π/2 rad ≈ 1.5708 rad	Calculus, physics, engineering, advanced mathematics
Gradian	gon or grad	400 gon	100 gon	Land surveying, civil engineering, some European countries

Angle Conversion Formulas

Degrees to Radians

radians = degrees × (π/180)

Example: 180° = 180 × (π/180) = π rad ≈ 3.14159 rad

Radians to Degrees

degrees = radians × (180/π)

Example: π/2 rad = (π/2) × (180/π) = 90°

Degrees to Gradians

gradians = degrees × (10/9)

Example: 90° = 90 × (10/9) = 100 gon

Gradians to Degrees

degrees = gradians × (9/10)

Example: 200 gon = 200 × (9/10) = 180°

Radians to Gradians

gradians = radians × (200/π)

Example: π rad = π × (200/π) = 200 gon

Gradians to Radians

radians = gradians × (π/200)

Example: 100 gon = 100 × (π/200) = π/2 rad

                    💡 Key Angles to Remember
                    0° = 0 rad = 0 gon
30° = π/6 rad ≈ 0.5236 rad = 33.333 gon
45° = π/4 rad ≈ 0.7854 rad = 50 gon
60° = π/3 rad ≈ 1.0472 rad = 66.667 gon
90° = π/2 rad ≈ 1.5708 rad = 100 gon
180° = π rad ≈ 3.1416 rad = 200 gon
270° = 3π/2 rad ≈ 4.7124 rad = 300 gon
360° = 2π rad ≈ 6.2832 rad = 400 gon

                

How to Use ConvertPedia's Angle Converter

Step_1

Enter Your Value

In the "FROM" section, enter the numerical value you want to convert. For example, type "180" if you want to convert 180 degrees.

Step_2

Select Source Unit

Choose your input unit from the dropdown menu. Options include Degree (°), Radian (rad), and Gradian (gon).

Step_3

Select Target Unit

Choose the unit you want to convert to. For example, select "Radian" to convert degrees to radians.

STep_4

Get Instant Results

The converted value appears immediately in the "TO" section. No button clicks needed - it's real-time!

Professional Applications

📐

Mathematics & Trigonometry

Common conversions: Trigonometric functions, calculus problems, geometric calculations

Example: A student solving sin(π/6) needs to know this equals sin(30°) = 0.5. Using ConvertPedia, they verify π/6 rad = 30°.

⚙️

Engineering & Design

Common conversions: Mechanical angles, gear teeth, structural calculations, CAD designs

Example: A mechanical engineer designing a gear system with 20° pressure angle needs to convert to radians (0.349 rad) for mathematical modeling.

🧭

Navigation & Surveying

Common conversions: Bearing angles, land surveying, GPS coordinates, compass directions

Example: A land surveyor working with European equipment calibrated in gradians receives data in degrees: 45° needs to be converted to 50 gon for equipment setup.

🖥️

Programming & Graphics

Common conversions: Game development, computer graphics, 3D modeling, animation rotations

Example: A game developer programming rotation in radians (2π for full circle) needs to convert user input from degrees (360°) to radians for calculations.

🔭

Astronomy & Physics

Common conversions: Celestial coordinates, telescope pointing, angular velocity, wave phases

Example: An astronomer calculating planetary positions uses radians but needs to report findings in degrees for publications.

🏗️

Architecture & Construction

Common conversions: Roof pitches, stair angles, slope calculations, structural angles

Example: An architect specifying a 30° roof pitch needs to ensure construction teams using different measurement systems understand the angle.

Common Angle Conversion Examples

Conversion	Input Value	Result	Use Case
Degrees to Radians	180°	π rad (3.14159 rad)	Half circle conversion
Radians to Degrees	π/2 rad	90°	Right angle conversion
Degrees to Gradians	90°	100 gon	Right angle in surveying
Gradians to Degrees	200 gon	180°	Straight line conversion
Radians to Gradians	π rad	200 gon	Half circle in gradians
Gradians to Radians	100 gon	π/2 rad (1.5708 rad)	Right angle in radians
Degrees to Radians	45°	π/4 rad (0.7854 rad)	Common geometric angle
Radians to Degrees	1 rad	57.2958°	Unit radian conversion

Understanding Radians: The Natural Angle

Radians are the SI unit for angular measurement and are considered the "natural" way to measure angles because they relate directly to the radius of a circle. One radian is the angle created when the arc length equals the radius.

📐 Why Use Radians?

Calculus: Derivatives and integrals of trigonometric functions are simpler in radians
Physics: Angular velocity and acceleration formulas use radians naturally
Engineering: Many mathematical models assume radian measure
Programming: Most math libraries (Python's math, JavaScript's Math) use radians

Key Radian Values

Degrees	Radians (exact)	Radians (decimal)
0°	0	0
30°	π/6	0.523599
45°	π/4	0.785398
60°	π/3	1.047198
90°	π/2	1.570796
180°	π	3.141593
270°	3π/2	4.712389
360°	2π	6.283185

Understanding Gradians: The Decimal Angle

Gradians (also called gons or grades) divide a right angle into 100 parts, making a full circle 400 gradians. This decimal-based system is particularly useful in surveying and civil engineering.

                    🌍 Where Are Gradians Used?
                    Land Surveying: Common in European surveying instruments
Civil Engineering: Used in some countries for road gradients
Artillery: Military applications in some nations
Advantage: Right angle = 100, straight line = 200, full circle = 400 (all decimal)

                

Key Gradian Values

Degrees	Radians	Gradians
0°	0	0 gon
30°	π/6	33.333 gon
45°	π/4	50 gon
60°	π/3	66.667 gon
90°	π/2	100 gon
180°	π	200 gon
270°	3π/2	300 gon
360°	2π	400 gon

Technical Specifications & Accuracy

Precision Standards

ConvertPedia uses double-precision floating-point arithmetic (IEEE 754 standard) ensuring 15-17 significant digits of accuracy. Our conversion factors are based on:

SI Definition: Radian is the SI derived unit for angle
ISO 80000-3:2019 (International standard for quantities and units of space and time)
NIST (National Institute of Standards and Technology) guidelines
BIPM (International Bureau of Weights and Measures) definitions

Mathematical Constants Used

π (pi): 3.14159265358979323846 (sufficient for all practical purposes)
π/180: 0.017453292519943295 for degrees to radians
180/π: 57.29577951308232 for radians to degrees

Important Notes

Angles > 360°: Our converter handles any angle value, including those beyond a full circle
Negative Angles: Negative values are supported for directional angles
Precision: For critical engineering work, use the full precision provided by our converter

Frequently Asked Questions

❓ How do I convert degrees to radians?

Answer: Multiply degrees by π/180 (approximately 0.0174533). For example, 180° × π/180 = π radians (3.14159 rad). Our converter does this instantly.

❓ What is a radian and why is it used?

Answer: A radian is the angle where the arc length equals the radius. It's used in calculus and physics because it makes mathematical formulas simpler and more natural.

❓ What are gradians used for?

Answer: Gradians (400 in a circle) are primarily used in land surveying and civil engineering in some European countries because they provide decimal subdivisions (100 gon = right angle).

❓ Is your converter accurate for mathematical calculations?

Answer: Yes, our converter uses exact formulas with 15-17 decimal precision, suitable for all mathematical applications including calculus and trigonometry.

❓ Can I convert between all angle units?

Answer: Yes! Our converter supports seamless conversion between degrees, radians, and gradians. Simply select your source and target units.

❓ How do I convert radians to degrees for a calculator?

Answer: Multiply radians by 180/π (approximately 57.2958). For example, 1 radian × 180/π = 57.2958°. Our converter does this instantly.

❓ Does your converter handle angles in DMS format?

Answer: Currently, our converter handles decimal degrees. For Degrees-Minutes-Seconds (DMS) format, convert to decimal degrees first, then use our tool.

supported Angle units