Convert Between Degrees, Radians & Gradians Convert between degrees, radians, gradians, arcminutes, arcseconds, and turns.

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Angle Converter

Convert between degrees, radians, gradians, arcminutes, arcseconds, and turns.

Enter the angle

Type the angle value to convert.

Select units

Choose source and target angle units.

Read the converted angle

Converted angle appears instantly.

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What Is Angle Converter?

An angle converter translates between different angular measurement systems. Degrees (°) divide a full rotation into 360 parts and are the most familiar system. Radians are the SI unit, where a full rotation equals 2π radians — they simplify calculus and trigonometry formulas. Gradians (gon) divide a rotation into 400 parts, making right angles exactly 100 gradians — useful in surveying. Arcminutes (1/60 degree) and arcseconds (1/3600 degree) are used in astronomy and navigation. Turns express angles as fractions of a full rotation.

Why Use Angle Converter?

Covers all major angle units for math, science, and engineering.
Essential for converting between degrees and radians in programming.
Includes arcminutes and arcseconds for astronomy.
Real-time bidirectional conversion.
Quick reference table.

Common Use Cases

Mathematics

Convert between degrees and radians for trigonometry and calculus.

Programming

Translate angles for graphics, game development, and scientific computing.

Astronomy

Work with arcminutes and arcseconds for celestial coordinates.

Surveying

Switch between degrees and gradians for land surveying instruments.

Technical Guide

Angular measurement systems:

• Degree (°): 360° = full rotation. Origin: Babylonian base-60 system.
• Radian (rad): 2π rad = full rotation. The natural unit where arc length = radius × angle.
• Gradian (grad/gon): 400 grad = full rotation. Right angle = 100 grad exactly.
• Arcminute (′): 1° = 60 arcminutes.
• Arcsecond (″): 1′ = 60 arcseconds, so 1° = 3,600 arcseconds.
• Turn: 1 turn = 360° = 2π rad.

Key conversion: 180° = π radians, so:
• degrees to radians: multiply by π/180
• radians to degrees: multiply by 180/π

Most programming languages use radians for trigonometric functions (sin, cos, tan). When calling Math.sin(x) in JavaScript, x must be in radians.

Tips & Best Practices

1
π radians = 180°. Memorize this and all degree-radian conversions follow.
2
In programming, always convert degrees to radians before using trig functions.
3
Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2.
4
Gradians are rare but still used in some surveying instruments (total stations).

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Frequently Asked Questions

Q How do I convert degrees to radians?

Multiply degrees by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 radians.

Q What is a radian?

A radian is the angle subtended by an arc equal in length to the radius of the circle. One full circle = 2π ≈ 6.2832 radians.

Q Why do programming languages use radians?

Radians simplify mathematical formulas — derivatives, Taylor series, and other calculus operations are cleaner in radians.

Q What is a gradian used for?

Gradians (also called gon) are used in surveying because a right angle is exactly 100 gradians, making angle calculations simpler.

Q How many arcseconds in a degree?

One degree = 60 arcminutes = 3,600 arcseconds.

About This Tool

Angle Converter is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.