Unit Converter

Convert From Degrees to Radians and Vice Versa

Degrees ↔ Radians

Type in either degrees or radians — it’ll convert to the other automatically!


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🎯 Interactive Converter

90° = 1.571 radians

📐 What is a Degree?

A degree (°) is a measure of angle used in **geometry**, **navigation**, and **engineering**. A full circle is divided into 360 degrees, making it ideal for intuitive angle representation and compasses.

🌀 What is a Radian?

A radian is the **SI unit of angular measure**, defined as the angle formed when the arc length equals the radius. There are 2π radians in a circle, or approximately 6.283 radians = 360°.

🧠 Quick Comparison

Unit Equivalent Used In
1 degree (°) π/180 radians ≈ 0.01745 rad Navigation, basic geometry
1 radian 180°/π ≈ 57.296° Trigonometry, physics, calculus

🧮 How to Convert Degrees to Radians

Radians and degrees are two ways of measuring angles. A full circle is 360° or 2π radians, which means:

π radians = 180°

From this, we derive the conversion ratio:

1° = π / 180 ≈ 0.01745 radians

To convert any angle from degrees to radians, use this formula:

radians = degrees × (π / 180)

🧪 Worked Example:

Let’s convert 30 degrees into radians:

radians = 30 × π / 180  
                ≈ 30 × 3.1416 / 180  
                ≈ 0.5236 radians

This is useful in trigonometry, rotations in programming, or physics where radians are the standard.

💡 Pro Tip

Use **degrees** for drawing, navigation, and basic geometry. Use **radians** in calculus, physics, and programming (especially in functions like Math.sin() or Math.atan() which expect radians).

🎉 Did You Know?

One radian is the angle made when you wrap the radius of a circle along its circumference. It’s like folding a pizza slice equal to the crust’s length — you’d need just over 6 slices to make a full round!

🌍 Real-World Angle Examples

  • 30° – Common in triangles (≈ 0.524 rad)
  • 90° – Right angle (≈ 1.571 rad)
  • 180° – Straight line (π rad)
  • 360° – Full circle (2π rad)

📊 Degrees to Radians Conversion Chart

Degrees (°) Radians (rad)
0°0
30°0.524
45°0.785
90°1.571
180°3.142
360°6.283

📜 Timeline: Origin of Angle Units

  • Ancient Babylon: Introduced 360° circle (base-60 system)
  • 1700s: Radian introduced in calculus and physics
  • Modern era: Radians used in higher mathematics and programming

🌐 When to Use Degrees vs Radians

  • 📐 Degrees: Protractors, maps, compasses, construction
  • 📈 Radians: Calculus, trigonometry, computer graphics
  • 🧮 Quick Tip: Multiply degrees × 0.01745 to get radians fast