Indeetools

Angle Calculator

Free online angle calculator for converting between degrees, radians, and grads. Essential tool for students, engineers, mathematicians, and anyone working with trigonometry.

Angle Calculator
Calculate angle properties, conversions, and classifications. Enter any angle in degrees to see its characteristics.

Enter any angle value in degrees. Can be positive, negative, or zero.

Enter an angle value to see results

How to Use the Angle Calculator

Step-by-Step Instructions:

  1. Enter your angle value in any of the input fields
  2. Select the input unit (degrees, radians, or grads)
  3. The calculator automatically converts to other units
  4. View the converted results in real-time
  5. Copy results for your calculations or documentation

Supported Conversions

  • ✓ Degrees to Radians conversion
  • ✓ Radians to Degrees conversion
  • ✓ Degrees to Grads conversion
  • ✓ Grads to Degrees conversion
  • ✓ Radians to Grads conversion
  • ✓ Grads to Radians conversion
  • ✓ Decimal and fraction input support
  • ✓ Negative angle calculations

Understanding Angle Units

Degrees (°)

The most common angle unit, where a full circle equals 360°. Used in everyday measurements, navigation, and basic geometry. Each degree represents 1/360th of a complete rotation.

Radians (rad)

The standard unit in mathematics and physics, where a full circle equals 2π radians. Essential for calculus, trigonometric functions, and advanced mathematics. One radian equals approximately 57.2958 degrees.

Gradians (gon)

Also known as grads or gons, where a full circle equals 400 grads. Used in surveying, civil engineering, and some European countries. Each grad represents 1/400th of a complete rotation.

Common Applications

Mathematics & Science

  • • Trigonometry calculations
  • • Calculus and analysis
  • • Physics problems
  • • Engineering mathematics
  • • Complex number operations
  • • Wave and signal processing

Practical Uses

  • • Navigation and GPS
  • • Construction and architecture
  • • Computer graphics
  • • Robotics and automation
  • • Surveying and mapping
  • • Game development

Angle Conversion Formulas

Mathematical Relationships:

From Degrees to Radians:

radians = degrees × (π/180)

From Radians to Degrees:

degrees = radians × (180/π)

From Degrees to Grads:

grads = degrees × (400/360)

From Grads to Degrees:

degrees = grads × (360/400)

Key Values: π ≈ 3.14159, 180° = π radians, 90° = π/2 radians, 200 grads = 180° = π radians

Frequently Asked Questions

What is the difference between degrees and radians?

Degrees divide a circle into 360 equal parts, while radians use the radius of the circle as the unit of measurement. A full circle equals 360° or 2π radians. Radians are the standard unit in higher mathematics and physics.

When should I use radians instead of degrees?

Use radians for calculus, trigonometric functions, physics calculations, and mathematical analysis. Degrees are better for everyday measurements, navigation, construction, and when working with angles that are commonly expressed in degrees (like 30°, 45°, 90°).

What are gradians used for?

Gradians are primarily used in surveying, civil engineering, and some European countries. They divide a right angle into 100 equal parts, making calculations easier in decimal form. A full circle equals 400 grads.

How accurate is this angle calculator?

Our angle calculator provides highly accurate conversions using JavaScript's built-in mathematical functions. It's suitable for most educational, engineering, and scientific applications with precision up to 15 decimal places.

Can I convert negative angles?

Yes, the calculator supports negative angles. Negative angles represent clockwise rotation and can be converted between all three units. The sign is preserved in all conversions.

What are some common angle conversions?

Common conversions include: 90° = π/2 radians = 100 grads, 180° = π radians = 200 grads, 270° = 3π/2 radians = 300 grads, 360° = 2π radians = 400 grads.

Common Special Angles

AngleDegreesRadiansGradsCommon Name
000Zero angle
π/630°π/633⅓30° angle
π/445°π/45045° angle
π/360°π/366⅔60° angle
π/290°π/2100Right angle
π180°π200Straight angle

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