Unit Converters
Angle Converter
Convert angle units: degrees, radians, gradians, turns, arcminutes, arcseconds. Perfect for mathematics, engineering, navigation, astronomy, and trigonometry.
Use Angle Converter to get instant results without uploads or sign-ups. Everything runs securely in your browser for fast, reliable output.
Your results will appear here.
About this tool
Angle conversion is fundamental in mathematics, engineering, physics, computer graphics, navigation, and astronomy. Different contexts use different angle units: degrees are intuitive and commonly used in everyday life, radians are standard in calculus and scientific computing, gradians are used in some surveying contexts, and specialized units like arcminutes and arcseconds are used in astronomy and navigation for precise angular measurements.
Our Angle Converter handles all common angle units with precision. Convert between degrees (the 360-based system), radians (based on π and the circle's radius), gradians or gons (the 400-based metric system), turns or revolutions (complete circles), arcminutes and arcseconds (subdivisions of degrees). The calculator uses exact conversion factors and maintains precision for scientific and engineering work.
Understanding angle conversions is essential in numerous applications: programming trigonometric functions (often requiring radians), working with CAD software (which may use different angle modes), navigation and surveying (using degrees, minutes, seconds), astronomy (measuring star positions), computer graphics and game development (rotations and transformations), and physics calculations. For example, a right angle is 90 degrees, π/2 radians, or 100 gradians.
The converter is valuable for students learning trigonometry, programmers working with graphics or physics engines, engineers using CAD software, navigators plotting courses, surveyors measuring land, astronomers calculating celestial positions, and anyone needing to convert between different angular measurement systems. Accurate angle conversions prevent calculation errors and ensure compatibility across different tools and standards.
Usage examples
Right Angle
Convert 90 degrees to radians
90° = 1.5708 rad (π/2)
Complete Circle
Convert 1 turn to degrees
1 turn = 360°
Programming Angle
Convert π radians to degrees
π rad = 180°
Surveying
Convert 100 gradians to degrees
100 grad = 90°
Precise Angle
Convert 1 degree to arcminutes
1° = 60 arcminutes
How to use
- Enter the angle value you want to convert.
- Select the unit you're converting FROM (e.g., degrees).
- Select the unit you're converting TO (e.g., radians).
- Click "Convert" to see the result instantly.
- The converter shows precise results for trigonometry and calculations.
- Useful for programming, CAD, navigation, surveying, and astronomy.
Benefits
- Convert between all common angle units instantly
- Accurate conversions with full precision for π-based calculations
- Essential for trigonometry and calculus
- Useful for programming graphics and physics simulations
- Helps with navigation and surveying calculations
- Perfect for astronomy and celestial measurements
- Simplifies CAD and engineering design work
- Educational tool for mathematics students
- Free alternative to manual conversion calculations
- Prevents errors in scientific computing
- Mobile-friendly for quick reference
- Supports both common and specialized angle units
FAQs
How do I convert degrees to radians?
Multiply degrees by π/180 to get radians. For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians. To convert radians to degrees, multiply by 180/π. This conversion is essential because many programming languages and calculators require radians for trigonometric functions (sin, cos, tan).
What is a radian and why is it used?
A radian is the angle subtended by an arc equal in length to the radius. A complete circle is 2π radians (≈6.2832 rad). Radians are "natural" for calculus because they simplify derivatives: d/dx(sin x) = cos x only when x is in radians. They're standard in advanced mathematics, physics, and programming.
What are gradians and when are they used?
Gradians (also called gons) divide a circle into 400 equal parts, so a right angle is 100 gradians. This metric-inspired system makes some calculations easier. Gradians are used in some European surveying and engineering contexts. 1 gradian = 0.9 degrees, and 400 gradians = 360 degrees = 2π radians.
What are arcminutes and arcseconds?
These are subdivisions of degrees: 1 degree = 60 arcminutes ('), and 1 arcminute = 60 arcseconds ("), so 1 degree = 3,600 arcseconds. They're used for very precise angular measurements in astronomy (star positions), navigation (latitude/longitude), and surveying. For example, a coordinate might be 40° 26' 46" N.
Why do calculators have degree and radian modes?
Trigonometric functions (sin, cos, tan) need to know what unit you're using. In degree mode, sin(90) = 1. In radian mode, sin(90) ≈ 0.894 (since 90 radians ≈ 5156.62 degrees). Most programming uses radians, while human input often uses degrees. Always ensure your calculator/code is in the correct mode.
How many degrees are in π radians?
π radians equals exactly 180 degrees. This is a fundamental relationship: 2π radians = 360 degrees = 1 complete circle. Common angles: π/2 rad = 90°, π/3 rad = 60°, π/4 rad = 45°, π/6 rad = 30°. Memorizing these helps in trigonometry and calculus.
What is a turn or revolution?
A turn (also called revolution or rotation) is one complete circle: 360 degrees or 2π radians. Turns are intuitive for describing rotations. For example, a wheel making 2.5 turns rotates through 900 degrees or 5π radians. Some programming contexts use turns (0 to 1) as a normalized angle measure.
Can I convert DMS (degrees-minutes-seconds) format?
Yes! To convert DMS to decimal degrees: degrees + minutes/60 + seconds/3600. For example, 40° 26' 46" = 40 + 26/60 + 46/3600 ≈ 40.446°. To convert decimal to DMS: the integer part is degrees, multiply the decimal by 60 for minutes, then multiply the remaining decimal by 60 for seconds.
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