Free Angle Converter
Convert angles between degrees, radians, gradians, and turns. Live conversion as you type.
The Angle Converter switches values between degrees, radians, gradians, and turns as you type. It is useful for trigonometry, engineering drawings, and any work that mixes angular units.
About Angle Converter
An angle converter changes values between different units of angular measurement: degrees (°), radians (rad), gradians (gon), and turns (full circles). These units are used in mathematics, physics, engineering, and computer graphics to measure rotation and orientation. Degrees are the most common unit globally, with 360 degrees in a full circle, making them intuitive for everyday use in navigation, surveying, and basic geometry. Radians are the SI unit and are essential in higher mathematics, particularly calculus and trigonometry, where they simplify derivative and integral formulas. Gradians, also called gon or grade, divide a right angle into 100 equal parts, which was historically useful in surveying and some European engineering disciplines before decimalization became widespread. Turns, representing complete rotations or revolutions, are often used in physics when describing rotational motion, angular velocity, and wave phenomena.
Degrees are the most common unit, with 360 degrees in a full circle. Radians are the SI unit and are essential in calculus and trigonometry, where one radian equals approximately 57.3 degrees. Gradians divide a right angle into 100 equal parts, and turns represent complete rotations (1 turn = 360°). The relationships between these units are precise and fixed: 1 turn = 360° = 2π rad ≈ 400 grad. This means that to convert from degrees to radians, you multiply by π/180, and to convert from radians to degrees, you multiply by 180/π. Gradians are exactly 10/9 of a degree, and a turn is exactly 360 degrees or 2π radians. Our converter uses these exact mathematical relationships to ensure precise conversions every time, with six decimal places of precision in the output.
Our tool displays all four angular units simultaneously, updating instantly as you type. This real-time conversion helps you understand equivalent measurements across different systems without manual calculations. The converter handles decimal inputs for precise conversions in scientific and technical applications. Since all processing happens locally in your browser using JavaScript, no data is ever uploaded to a server, ensuring complete privacy and security for your calculations. The real-time nature of the tool means you can immediately see how changes in one unit affect all others, making it easier to grasp the relationships between different angular measurements. This immediate feedback is especially valuable for students learning trigonometry, engineers working on rotation problems, and scientists dealing with wave mechanics or orbital calculations.
How to use this Angle Converter
- Enter an angle value in the input field (e.g., 180, π, or 200).
- Select the source unit (degree, radian, gradian, or turn) from the dropdown.
- View the converted values in all four angular units below.
- Click on the result box to copy the degree value to your clipboard.
FAQ
What is an angle converter?
An angle converter changes values between different units of angular measurement: degrees (°), radians (rad), gradians (gon), and turns (full circles). Essential for math, physics, and engineering.
Does the angle converter send any data to a server?
No. All calculations happen locally in your browser. No data is uploaded or stored.
Is this angle tool free?
Yes, it's completely free with no limits on usage.
What are the relationships?
1 turn = 360° = 2π rad ≈ 400 grad. Radians are the SI unit: 1 rad = 180/π degrees ≈ 57.3°.