Angle Converter - Convert Degrees, Radians, and Gradians Instantly

Need a fast and accurate way to convert different angle units? Our Angle Converter lets you switch between degrees, radians, gradians, arcminutes, and arcseconds instantly. Just enter the value and get precise answers in seconds — perfect for geometry, trigonometry, or everyday calculations.

Why Users Love This Angle ⇄ Degrees ⇄ Radians Converter

• Exact in design: Uses the correct trigonometric formulas for accurate angle conversions.
• Instant answers: Get results as soon as you type — no waiting, no lag.
• Clear display: Shows both exact and rounded values with customizable decimal points.
• Two-way switch: Instantly switch between degrees to radians and radians to degrees, or any other unit.
• Works anywhere: Fully mobile and desktop-friendly — ideal for students, engineers, and scientists.

How to Use Our Converter

1. Enter your angle value.
2. Select the desired units — degrees, radians, gradians, arcminutes, or arcseconds.
3. Choose conversion direction — Angle A to Angle B.
4. Get the instant result and copy or save it for your report or project.

Degrees

The degree (°) is the most common unit for measuring angles. A full circle equals 360°, making it easy to use in geometry, navigation, and engineering.

Key Facts About Degrees

• Exact value: 360° = 2π radians
• Relationship to other units: 1° = 60 arcminutes = 3600 arcseconds
• Common abbreviation: °
• Notation tips: Always include the degree symbol (°) when writing values.

Radians

The radian (rad) is the SI unit for angular measurement and is based on the radius of a circle. It’s the most commonly used unit in mathematics and physics.

Key Facts About Radians

• Exact value: 1 rad = 180/π degrees
• Relationship to other units: 2π radians = 360°
• Common abbreviation: rad
• Notation tips: When no unit is mentioned in trigonometric equations, radians are assumed.

Gradians

Gradians (gon) divide a circle into 400 units, often used in surveying and civil engineering for simpler right-angle representation.

Key Facts About Gradians

• Exact value: 1 grad = 0.9 degrees
• Relationship to other units: 100 grads = 90°
• Common abbreviation: gon or grad
• Notation tips: Used in geographic and mapping systems.

Angle Conversion Formulas

1. Degrees to Radians:
   Radians = Degrees × (π / 180)
2. Radians to Degrees:
   Degrees = Radians × (180 / π)
3. Degrees to Gradians:
   Gradians = Degrees × (10 / 9)
4. Gradians to Degrees:
   Degrees = Gradians × (9 / 10)
5. Degrees to Arcminutes:
   Arcminutes = Degrees × 60
6. Arcminutes to Degrees:
   Degrees = Arcminutes / 60
7. Arcseconds to Degrees:
   Degrees = Arcseconds / 3600

Conversion Examples

Example 1: Convert 90° to Radians

Step 1: Formula = Radians = Degrees × (π / 180)
Step 2: Substitute = 90 × (π / 180)
Step 3: Result = π/2 radians

Example 2: Convert π radians to Degrees

Step 1: Formula = Degrees = Radians × (180 / π)
Step 2: Substitute = π × (180 / π)
Step 3: Result = 180°

Example 3: Convert 100 Gradians to Degrees

Step 1: Formula = Degrees = Gradians × (9 / 10)
Step 2: Substitute = 100 × (9 / 10)
Step 3: Result = 90°

Example 4: Convert 1° to Arcseconds

Step 1: Formula = Arcseconds = Degrees × 3600
Step 2: Substitute = 1 × 3600
Step 3: Result = 3600 arcseconds

Quick Reference Table for Angle Conversions

Applications of Angle Conversions

• Mathematics: Used in solving trigonometric and calculus equations.
• Physics: Converts angular velocity, torque, and wave rotations.
• Engineering: Essential for designing machinery, bridges, and circuits.
• Astronomy: Helps measure celestial positions and planetary rotations.

Use our Angle Converter at Digital Calculator for quick, accurate, and reliable conversions between degrees, radians, gradians, arcminutes, and arcseconds — perfect for students, teachers, and professionals in science, math, and engineering.