📐 Angle Converter
Convert between degrees, radians, gradians, turns and arc units instantly.
What is this tool?
The Angle Converter is a free online tool that instantly converts between all common units of angle measurement. Whether you are working on a trigonometry problem, programming a rotation in a game, or aligning a satellite dish, this converter handles the math for you with precision. Angles are fundamental in mathematics, physics, engineering, and computer graphics. There are several ways to express an angle, each useful in different contexts. Degrees are the most intuitive for everyday use, dividing a full circle into 360 equal parts. Radians are the standard unit in higher mathematics because they simplify many formulas in calculus. Gradians divide a circle into 400 parts and are popular in surveying. Turns represent a fraction of a full rotation, which is convenient in computer animation. Arcminutes and arcseconds subdivide degrees for applications requiring extreme precision, such as astronomy and optics. This converter supports all six units and converts in both directions simultaneously. Simply type a value in any field and every other field updates instantly. All calculations are performed locally in your browser, so there is no delay and your data never leaves your device.How it works
The converter uses exact mathematical relationships between angle units. The fundamental basis is that one complete rotation equals 360 degrees, which also equals 2π radians (approximately 6.283185), 400 gradians, 1 turn, 21,600 arcminutes, or 1,296,000 arcseconds. When you enter a value in any field, the tool first converts it to degrees as the common intermediary unit, then converts from degrees to all other units. The conversion factors are: 1 degree = π/180 radians ≈ 0.017453, 1 degree = 1.11111 gradians, 1 degree = 0.002778 turns, 1 degree = 60 arcminutes, and 1 degree = 3600 arcseconds. These relationships are exact (except for the decimal approximation of π), ensuring results are accurate to the full precision of JavaScript floating-point arithmetic. The interface updates all fields in real time as you type. No buttons to press, no page reloads, and no data sent to any server.How to use
- Enter an angle value in any input field.
- Watch all other fields update instantly.
- Click any field to edit it directly.
- Use the swap button to reverse conversion direction.
- Copy any result with one click.
Frequently Asked Questions
Frequently Asked Questions
How accurate is this angle converter?
The converter uses full double-precision floating-point math, giving you about 15 significant digits of accuracy. The conversion factors are exact, so the only limitation is the inherent precision of JavaScript numbers.
Why do I need radians instead of degrees?
Radians are the natural unit for calculus and many physics formulas. In calculus, the derivatives of trigonometric functions are only clean when the angle is in radians. Most programming libraries for graphics also use radians internally.
What are gradians used for?
Gradians (also called gon or grade) divide a circle into 400 units instead of 360. They are mainly used in surveying and some European engineering traditions because they make right angles come out to exactly 100 units, simplifying certain field calculations.
Can I convert arcseconds for astronomy?
Yes. One arcsecond is 1/3600 of a degree. Astronomers use arcseconds to describe the apparent size of distant objects, and this converter handles the very small numbers accurately.
Tips & Advice
Angle conversion is straightforward once you memorize the key relationship: 360 degrees equals 2π radians. For quick mental math, remember that 1 radian is about 57.3 degrees. If you work with 3D graphics or game development, most APIs accept radians, so keeping a converter handy saves time. When dealing with very small angles (arcseconds), be aware that floating-point precision can introduce tiny rounding errors in the last few digits. For most practical applications, rounding to 6 decimal places gives perfectly clean results.
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