Angle Conversion Calculator

What Is an Angle?

An angle measures rotation. It shows how much one line turns around a fixed point.

You see angles everywhere:

• The hands of a clock
• Corners of a room
• Directions on a map
• Rotations in machines
• Waves and motion in physics

Different fields use different units to describe the same rotation. That is why angle conversion matters.

Why Angle Conversion Is Important

Angle conversion helps when:

• You move between math formulas that require radians
• You read data given in degrees but need turns or gradians
• You work with precise measurements using minutes and seconds
• You compare angles from different sources

Manual conversion is slow and easy to mess up. A calculator removes guesswork and gives instant results.

Angle Units Supported by the Calculator

This calculator converts between all major angle units. Below is a clear explanation of each one.

Degrees (°)

Degrees are the most familiar angle unit.

• A full circle = 360°
• A right angle = 90°
• Common in geometry, navigation, and daily use

Radians (rad)

Radians are based on circle geometry.

• A full circle = 2π radians
• Used in trigonometry, calculus, and programming
• Required by most math libraries in code

Gradians (grad)

Gradians divide a circle into 400 parts.

• A full circle = 400 grad
• Often used in surveying and civil engineering
• A right angle = 100 grad

Turns (Revolutions)

Turns measure full rotations.

• 1 turn = one complete circle
• Common in mechanics and rotation problems
• Easy to understand for circular motion

Minutes of Arc (′)

Minutes split degrees into smaller parts.

• 1 degree = 60 minutes
• Used in navigation, astronomy, and mapping
• Helps with fine angle precision

Seconds of Arc (″)

Seconds divide minutes even further.

• 1 minute = 60 seconds
• 1 degree = 3600 seconds
• Used when very high accuracy is needed

How the Angle Conversion Calculator Works

The calculator follows a simple and reliable process.

Step 1: Enter the Angle Value

You type the number you want to convert. Decimals are allowed.

Step 2: Select the Original Unit

Choose whether your value is in degrees, radians, gradians, turns, minutes, or seconds.

Step 3: Click Convert

The calculator converts your value into degrees first.
From degrees, it calculates all other units.

Step 4: View All Results

You instantly see:

• Degrees
• Radians
• Gradians
• Turns
• Minutes
• Seconds
• Normalized angle
• Quadrant information

Normalized Angle Explained

The calculator also shows a normalized angle between 0° and 360°.

This is helpful because:

• Angles larger than 360° repeat in a circle
• Negative angles still point in a valid direction
• Normalized values are easier to compare

Example:

• Input: 450°
• Normalized angle: 90°

Quadrant and Axis Information

Along with the normalized angle, the calculator tells you where the angle lies:

• Positive X-axis
• Positive Y-axis
• Negative X-axis
• Negative Y-axis
• Quadrant I, II, III, or IV

This feature is useful for:

• Trigonometry problems
• Coordinate geometry
• Vector direction analysis

Common Conversion Rules Used

The calculator relies on standard angle relationships:

• 1 turn = 360° = 2π rad = 400 grad
• 1° = 60′ = 3600″
• 1 rad ≈ 57.2958°

These rules ensure accurate and consistent results.

Who Should Use This Calculator?

This angle conversion tool is helpful for:

• Students learning geometry or trigonometry
• Engineers and surveyors
• Programmers working with math functions
• Teachers and educators
• Anyone dealing with angles in real life

You do not need advanced math knowledge. Just enter a value and get results.

Benefits of Using an Angle Conversion Calculator

• Saves time
• Reduces calculation errors
• Supports multiple units at once
• Handles negative and large angles
• Gives clear quadrant information
• Works instantly in your browser