Angle Converter

Convert between degrees, radians, gradians, and turns for any angle measurement quickly.

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1. Select the angle unit you are converting from (degrees, radians, gradians, or turns). 2. Enter the angle value in the input field - decimal values and negative angles are supported. 3. Instantly see the equivalent angle in all four measurement systems. 4. Use the radian result for programming trigonometric functions or the degree result for everyday measurements. 5. Copy any converted angle value to your clipboard by clicking the copy button next to it.

About This Tool

The Angle Converter provides instant conversions between all four commonly used angle measurement units: degrees, radians, gradians, and turns. Whether you are working on trigonometry homework, programming rotations in a game engine, calculating surveying angles, or solving physics problems, this tool converts between angle units effortlessly.

Our converter handles degrees (the most familiar unit, with 360 in a full circle), radians (the SI unit used in mathematics and physics, with 2*pi in a full circle), gradians (used in surveying, with 400 in a full circle), and turns (complete rotations, where 1 turn = 360 degrees). Enter any angle value in one unit and see all equivalent measurements instantly.

Angle conversion is critical in mathematics, physics, computer graphics, navigation, surveying, and engineering. Programming languages and scientific calculators often require radians for trigonometric functions, while everyday measurements use degrees. Surveyors may work in gradians for slope calculations. This converter bridges all of these systems, ensuring you always have the right angle value for your specific application.

Formula / How It Works

360 degrees = 2*pi radians = 400 gradians = 1 turn | 1 degree = 0.0174533 rad = 1.11111 grad = 0.00277778 turns

Frequently Asked Questions

To convert degrees to radians, multiply by pi/180 (approximately 0.0174533). For example, 90 degrees equals pi/2 radians (approximately 1.5708). Common conversions: 180 degrees = pi radians, 360 degrees = 2*pi radians.
A gradian (also called gon or grad) divides a right angle into 100 parts, making a full circle 400 gradians. Gradians are used primarily in surveying, civil engineering, and some European countries because they make slope calculations more intuitive - a 1% slope equals 1 gradian.
A turn is a full rotation of 360 degrees (or 2*pi radians, or 400 gradians). One turn = 1 complete revolution. Half a turn is 180 degrees. A quarter turn is 90 degrees. Turns are useful in engineering and computer graphics for expressing rotational quantities.
Radians are the natural unit of angle measurement in mathematics because they simplify many formulas. In radians, the arc length formula is simply s = r*theta (no conversion needed), and calculus formulas for trigonometric functions are cleaner. One radian is the angle where the arc length equals the radius.

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