Angle Converter | Degrees, Radians, Gradians, Arcminutes, Arcseconds

📖 How to Use This Angle Converter

Enter the value - Type the angle number you want to convert.

Select the source unit - Choose from Degrees, Radians, Gradians, Arcminutes, or Arcseconds.

Select the target unit - Choose the unit you want to convert to.

See instant result - The converted value appears automatically.

📐 Understanding Angular Units

Angles are measured in various units depending on the application. The most common units are degrees and radians, but other units like gradians, arcminutes, and arcseconds are important in specific fields.

Degrees (°): 1 full circle = 360°. Most common unit for everyday use, navigation, and geography.
Radians (rad): 1 full circle = 2π rad. The standard unit in mathematics, physics, and engineering.
Gradians (grad): 1 full circle = 400 grad. Used in surveying and some engineering applications.
Arcminutes ('): 1° = 60 arcminutes. Used in astronomy, navigation, and precision measurements.
Arcseconds ("): 1° = 3600 arcseconds. Used in astronomy (stellar positions) and geodesy.

🧮 Conversion Formulas

To Degrees:
• Radians → Degrees: deg = rad × (180/π)
• Gradians → Degrees: deg = grad × 0.9
• Arcminutes → Degrees: deg = arcmin ÷ 60
• Arcseconds → Degrees: deg = arcsec ÷ 3600

From Degrees:
• Degrees → Radians: rad = deg × (π/180)
• Degrees → Gradians: grad = deg ÷ 0.9
• Degrees → Arcminutes: arcmin = deg × 60
• Degrees → Arcseconds: arcsec = deg × 3600

💡 Common Applications

Astronomy: Arcminutes and arcseconds measure angular distances between stars (e.g., full moon ≈ 30 arcminutes)
Navigation: Degrees, minutes, seconds used in GPS coordinates (e.g., 40° 42' 51" N)
Trigonometry: Radians are the natural unit for calculus and trigonometric functions
Surveying: Gradians simplify right-angle calculations (100 grad = 90°)
Photography: Lens field of view measured in degrees

❓ Frequently Asked Questions (FAQ)

Why do we use radians instead of degrees?

Radians are the natural unit for angle measurement in calculus and physics because they simplify derivatives and integrals of trigonometric functions. For example, d(sin x)/dx = cos x only when x is in radians.

What is the difference between arcminutes and minutes of time?

Arcminutes (') measure angle (1° = 60 arcminutes). Minutes of time measure time (1 hour = 60 minutes). They are different units entirely, though both use similar notation.

What is 1 radian in degrees?

1 radian = 180/π degrees ≈ 57.2957795°. This is because a full circle is 2π rad = 360°.

What are gradians used for?

Gradians (also called gons) are primarily used in surveying and some engineering applications. They make right angles = 100 grad, which simplifies calculations involving perpendicular lines.

How many arcseconds are in a degree?

There are 3,600 arcseconds in one degree (60 arcminutes × 60 arcseconds per arcminute = 3,600 arcseconds).

When should I use DMS (Degrees, Minutes, Seconds) format?

DMS format is commonly used in GPS coordinates, navigation, astronomy, and mapping. Example: 40° 26' 46" N, 79° 58' 56" W for Pittsburgh. Our converter can help convert between decimal degrees and DMS components.