Angle Converter - Degrees, Radians, Gradians & Mils Calculator
📐 Geometry & Physics

Angle Converter

The ultimate geometry calculator. Convert accurately between Degrees, Radians, Gradians, and Turns. Perfect for trigonometry, machining, and ballistics.

Angle Engine

Enter angle value to convert.

🔄 Angle Value
🎯 Decimal Precision
CONVERTED ANGLE
3.1416
Radians (rad)
Conversion Logic:
180° × (π/180) ≈ 3.1416 rad
Turns 0.50 cycle
📐
Gradians 200 gon
🎯
Minutes (MOA) 10,800 ′

Radians vs. Degrees: The Mathematical Duel

Most people learn Degrees first, but Radians are the standard language of mathematics. Understanding the relationship is key to trigonometry.

🔵
Degrees (°)

Based on ancient astronomy (360 days in a year). 360° = Full Circle. Easy to divide by 2, 3, 4, 5, 6.

🔴
Radians (rad)

Based on the radius of the circle. 2π rad = Full Circle. Essential for calculus because it simplifies derivatives.

⚖️
The Golden Ratio

180° = π radians (approx 3.14159). This is the key conversion factor for everything.

Angle Conversion Formulas

Conversion Formula Approx Factor
Degrees to Radians deg × (π / 180) × 0.01745
Radians to Degrees rad × (180 / π) × 57.296
Degrees to Gradians deg × (400 / 360) × 1.111
Degrees to Minutes deg × 60 × 60

Specialized Units Explained

🏗️

Gradians (gon)

Used in surveying and civil engineering. 100 Gradians = 90° (Right Angle). It makes calculating gradients easier.

🔭

Arcseconds

Used in astronomy to measure the tiny apparent size of stars and planets. 1 Degree = 3600 Arcseconds.

🎯

Milliradians (mrad)

Used in rifle scopes and artillery. 1 mrad ≈ 1 meter height at 1000 meters distance. NATO standard is 6400 mils per circle.

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Frequently Asked Questions

What is 1 Radian in Degrees?
1 Radian is approximately 57.2958 degrees. It is the angle created when the arc length is exactly equal to the radius of the circle.
Why is a circle 360 degrees?
It likely comes from the ancient Babylonian base-60 number system and their calendar of 360 days. 360 is highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, etc.), making early math easier.
What is a Milliradian?
A Milliradian (mrad or mil) is 1/1000th of a radian. It is extremely useful in trigonometry because for small angles, the tangent of the angle equals the angle itself in radians.
How many minutes in a degree?
There are 60 Minutes of Arc in 1 Degree. This is similar to time (60 minutes in an hour). There are 60 Seconds of Arc in 1 Minute.
What is a Grad?
A Grad (or Gradian) divides a right angle into 100 parts instead of 90. A full circle is 400 grads. It was an attempt to decimalize angles during the French Revolution.
How do I convert degrees to minutes?
Multiply the decimal part of the degree by 60. For example, 10.5° = 10 degrees and (0.5 × 60) = 30 minutes.
What is 2π radians?
2π radians is exactly one full circle, or 360 degrees. π radians is a half circle, or 180 degrees.
What is a "Turn"?
A Turn (or Cycle/Revolution) represents one full rotation. 1 Turn = 360° = 2π rad. It is often used in mechanical engineering and motors.
Is Pi infinite?
Pi (π) is an irrational number with infinite decimal places. For most engineering calculations, using 3.14159 is sufficient precision.
What is "MOA" in shooting?
MOA stands for Minute of Angle. 1 MOA is approx 1 inch at 100 yards. It allows shooters to adjust their sights precisely.