General
Angle Converter Calculator
Convert angles between degrees, radians, gradians, and turns with this easy-to-use calculator.
Reviewed by the calculator.uk.com Team · Last reviewed 13 July 2026 · Our methodology
Enter an angle value and select units to see the conversion result
Related to Angle Converter Calculator
The Angle Converter Calculator is a versatile tool that allows you to convert angles between different units of measurement: degrees, radians, gradians, and turns. The calculator uses precise mathematical formulas to ensure accurate conversions between these different angular units.
Conversion Formulas
• Degrees to Radians: rad = deg × (π/180)
• Radians to Degrees: deg = rad × (180/π)
• Degrees to Gradians: grad = deg × (10/9)
• Gradians to Degrees: deg = grad × (9/10)
• Degrees to Turns: turn = deg ÷ 360
• Turns to Degrees: deg = turn × 360
The calculator first converts the input angle to degrees as an intermediate step, then converts it to the desired output unit using these mathematical relationships. This two-step process ensures consistent and accurate results across all possible conversion combinations.
Different angle units serve various purposes in mathematics, engineering, and everyday applications. Understanding these units helps in choosing the most appropriate one for your needs.
Common Angle Units
• Degrees (°): Most commonly used unit, where a full circle is 360°
• Radians (rad): Used in calculus and advanced mathematics, where a full circle is 2π radians
• Gradians (grad): Used in surveying, where a full circle is 400 gradians
• Turns: Used to measure full rotations, where one turn equals 360°
1. Why are there different units for measuring angles?
Different angle units evolved to serve specific purposes. Degrees are intuitive for everyday use, radians are natural for calculus and mathematical analysis, gradians are useful in surveying and engineering, and turns are convenient for measuring complete rotations.
2. Which angle unit should I use?
The choice depends on your application. Use degrees for general purposes and basic geometry, radians for calculus and advanced mathematics, gradians for surveying work, and turns when dealing with rotational measurements.
3. Why do mathematicians prefer radians?
Radians are preferred in mathematics because they provide a natural relationship between the angle and the arc length on a circle. This makes many mathematical formulas simpler and eliminates the need for conversion factors in calculus.
4. What is the advantage of using gradians?
Gradians divide a right angle into 100 parts, making decimal calculations easier in surveying and engineering applications. This decimal division makes it particularly useful for calculations involving slopes and grades.
5. What is the scientific source for this calculator?
The conversions rely on the basic geometric identity that a full turn equals 360 degrees, 2π radians, or 400 gradians, relationships fixed by definition rather than measurement. The radian is the SI-derived unit for plane angle, while degrees and gradians are non-SI units accepted for use alongside it, and none of the ratios between them changes with precision or context.