Angle Converter
Convert between different angle units including degrees, radians, gradians, turns, arcminutes, and arcseconds. Quick and accurate angle conversions for mathematical and engineering applications.
Conversion Settings
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Conversion Result
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Enter a value and click "Convert" to start
About Angle Units
Degrees (°): Most common unit, 360° in a full circle
Radians (rad): Mathematical unit, 2π radians in a full circle
Gradians (grad): 400 gradians in a full circle
Turns: Complete rotations, 1 turn = full circle
Arcminutes ('): 1/60 of a degree
Arcseconds ("): 1/3600 of a degree
About Angle Converter
A precise angle converter that handles conversions between major angular measurement units including degrees, radians, gradians, turns, arcminutes, and arcseconds. This essential tool provides accurate angle conversions for mathematical calculations, engineering applications, navigation, and scientific work with instant results and proper decimal precision.
Why use a Angle Converter?
Essential for mathematical calculations, engineering designs, navigation systems, and scientific research where different angular units are used. Prevents conversion errors in trigonometric calculations, astronomy observations, surveying work, and engineering projects while supporting both academic and professional angle conversion needs.
Who is it for?
Essential for mathematicians, engineers, surveyors, astronomers, students, and navigators who need accurate angle conversions. Also valuable for game developers, 3D modelers, architects, and anyone working with rotational measurements, trigonometry, or geometric calculations that require different angular units.
How to use the tool
Enter your angle value in the input field
Select the source angle unit (degrees, radians, gradians, turns, arcminutes, or arcseconds)
Choose your target angle unit for conversion
View the converted angle with appropriate decimal precision
Copy the result for use in calculations, formulas, or engineering work
Frequently Asked Questions
How do I convert angle units?
Enter the source value, pick the 'from' and 'to' units, and the result appears instantly. Supports degrees (°), radians (rad), gradians (grad), turns, arcminutes ('), arcseconds ("). Copy the converted value to clipboard. Conversion runs entirely in your browser — values never leave the device. Decimal precision is configurable; default shows 4-6 significant figures, appropriate for most use cases. For scientific work needing more precision, increase the decimal places in the settings.
What angle units does this converter support?
degrees (°), radians (rad), gradians (grad), turns, arcminutes ('), arcseconds ("). The set covers SI base and derived units, common imperial/US-customary units, and domain-specific units where relevant. SI prefixes (k, M, G, m, μ, n) apply where applicable. For any unit not in the list that you need converted, mention it via feedback — the unit set evolves based on user requests.
How accurate is the angle conversion?
Conversions use exact internationally-defined factors where they exist — no rounding loss at the math level. Radians are dimensionless (a ratio of arc length to radius). 1 rad = 180/π ≈ 57.2958°. 1° = π/180 ≈ 0.01745 rad. Conversions are exact (π is irrational, so output precision matters). Output precision is bounded by the displayed decimal places (configurable, typically 4-6 by default). For extreme precision needs (scientific publications), increase the displayed decimals to match your significant-figure requirements.
What's the formula to convert degrees to radians?
rad = ° × π/180. Engineering / CAD (degrees), physics calculations (radians), GPS coordinates (degrees, with decimal or arcminute/second sub-divisions), astronomy (arcseconds for precise positions). For other angle-unit pairs, the tool applies the appropriate exact conversion factor automatically — no manual formula needed. The conversion preserves precision to the displayed decimal places; choose precision to match your downstream use (engineering specs typically need 3-4 significant figures; scientific work may need more).
What's the key accuracy caveat for angle conversion?
**Radians (SI unit) vs degrees vs gradians** — three competing systems. A full circle is 360° = 2π rad ≈ 6.2832 rad = 400 grad = 1 turn. Radians are the SI unit and the basis for physics/math formulas (trigonometric functions in calculators and programming languages default to radians). Degrees are the everyday human-readable unit. Gradians (400 per circle) are used in some surveying and military contexts. **Arcminutes and arcseconds** subdivide a degree: 1° = 60' = 3,600" — used in astronomy and navigation.
What's a common real-world use case for angle conversion?
Engineering / CAD (degrees), physics calculations (radians), GPS coordinates (degrees, with decimal or arcminute/second sub-divisions), astronomy (arcseconds for precise positions).
What angle units are commonly confused?
**Degrees vs radians** — formulas in code (Math.sin, etc.) default to radians; user inputs are usually degrees. **Gradians ('grad')** — 400 per circle; rare except in some European surveying.
How do I handle very large or very small angle values?
Use SI prefixes for clean scaling: kilo (10³), mega (10⁶), giga (10⁹), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹). For values beyond standard prefixes, the tool displays results in scientific notation (e.g. 1.23e+15) for readability. Radians are dimensionless (a ratio of arc length to radius). 1 rad = 180/π ≈ 57.2958°. 1° = π/180 ≈ 0.01745 rad. Conversions are exact (π is irrational, so output precision matters). For data interchange to other tools, copy the raw value; for human readers, use the precision that matches the context.
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