Working with angles in different units? Our free angle converter instantly transforms degrees to radians, radians to degrees, and converts between gradians, turns, and other angle units. Whether you're a student learning trigonometry, an engineer calculating rotations, a programmer working with graphics, or a physicist analyzing angular motion, this tool provides accurate, instant conversions without complexity. With support for all major angle units and precise decimal handling, you'll never need to manually calculate angle conversions again.
An angle converter is a computational tool that transforms angle measurements from one unit of angular measure to another. Angles can be measured in multiple units depending on the field and application: degrees (common in everyday use and basic geometry), radians (standard in advanced mathematics and physics), gradians (also called gons, proposed metric system unit), and turns (complete rotations). The converter applies mathematical conversion factors to accurately translate between these units. For example, since a full circle is 360 degrees and also 2π radians, the conversion factor between degrees and radians is π/180. Understanding these relationships is crucial for anyone working with angles in mathematics, science, engineering, or computer programming.
Multiple Unit Support — Convert between degrees, radians, gradians, turns, arcminutes, and arcseconds. Instant Results — Get conversions immediately as you type or paste values. Bidirectional Conversion — Convert from any supported unit to any other supported unit. Precision Handling — Maintains decimal precision for accurate scientific and engineering calculations. Negative Angle Support — Correctly handles clockwise (negative) and counterclockwise (positive) angles. Common Angle Presets — Quick access to frequently used angles like 90°, 180°, 360°. History Tracking — Keep track of recent conversions for reference. Copy Results — One-click copying of converted values. Mobile Friendly — Works perfectly on phones and tablets. Free & Unlimited — No registration, no limits, completely free to use.
Using our angle converter is straightforward: Enter your angle value in the input field. You can type a number or paste from another source. Select the current unit of your angle from the dropdown menu. Choose from degrees (°), radians (rad), gradians (gon), turns, arcminutes, or arcseconds. Choose your desired output unit from the second dropdown. The tool will automatically convert your input to this unit. The converted value appears instantly in the results area. For precise values, the tool displays multiple decimal places. Click the copy button to copy the result to your clipboard for use in your calculations or documents. The entire process takes seconds, and you can perform unlimited conversions.
Students and Educators — Converting between degrees and radians when learning trigonometry. Checking homework answers involving angle calculations. Converting angles for drawing geometric figures. Engineers and Designers — Converting rotation specifications between different systems. Calculating angular velocity and acceleration in dynamics. Converting bearing angles in navigation and surveying. Programmers and Developers — Converting user input in degrees to radians for trigonometric functions. Working with graphics APIs that use radians for rotations. Converting angles in game physics engines. Scientists and Researchers — Converting experimental data between different angle units. Standardizing angle measurements across different datasets. Working with angular measurements in physics experiments. Trades and Craftspeople — Converting angles for cutting materials at specific bevels. Setting up machinery with precise angular settings. Converting between different measurement systems in international projects.
Mathematical Accuracy — Our converter uses precise conversion factors with π calculated to sufficient precision for any practical application. No rounding errors that plague manual calculations. Time Saving — Instant conversions eliminate the need to remember formulas or use calculators. Complete unit coverage in one tool. Educational Value — The converter helps students understand relationships between different angle units. Seeing equivalent values reinforces concepts about circular measure. Professional Reliability — Engineers and scientists can trust the precision for critical calculations. No ambiguity about conversion factors. Accessibility — Available on any device with a web browser. No software installation required. Free Forever — Unlike paid calculation apps, our tool is completely free with no hidden fees or premium tiers.
Mathematics Students — Anyone learning trigonometry, pre-calculus, or calculus who needs to convert between degrees and radians. Engineering Students — Civil, mechanical, and electrical engineering students working with angular measurements in different contexts. Physics Students — Students studying rotational motion, waves, and angular momentum. Professional Engineers — Mechanical, civil, and software engineers working with rotational systems, navigation, or graphics. Programmers — Developers working with computer graphics, game development, scientific computing, or any code involving angles. Surveyors — Professionals converting between different angle measurement systems in the field. Architects — Designers working with angular specifications in different unit systems. Machinists — Tradespeople setting up angles on machinery requiring precise conversions. Hobbyists — Anyone with DIY projects involving angle measurements and conversions.
Getting started takes under 30 seconds: Open the angle converter in your web browser on any device. Clear the example value in the input field. Enter your angle value or paste it from another source. Select your current unit (degrees, radians, gradians, etc.) from the first dropdown. Choose your target conversion unit from the second dropdown. View your converted result instantly. The value updates automatically as you change inputs. Copy the result using the copy button. Paste the converted value into your document, calculator, or code. That's it! You can perform unlimited conversions, experimenting with different units and values.
Know Your Context — Degrees are standard in everyday life; radians in advanced math and physics. Choose the appropriate unit for your specific application. Double-Check Units — Always verify you're converting FROM the correct unit and TO the correct unit. Common mistakes involve swapping input and output units. Keep Precision — For chained calculations, maintain full precision until the final step. Don't round intermediate angle values. Understand Sign Conventions — Positive angles are counterclockwise; negative angles are clockwise. Maintain the correct sign for your application. Learn Key Conversions — Memorize these common conversions: 90° = π/2 rad, 180° = π rad, 360° = 2π rad. Verify Reasonableness — Check that your converted result makes sense. A degree value should be about 57 times larger than the equivalent radian value. Use Appropriate Precision — Don't report more decimal places than justified by your input precision. The tool shows many digits, but use what's meaningful for your work. Consider Coterminal Angles — Angles differing by full rotations (360° or 2π rad) are equivalent. The tool can help verify coterminal relationships.
Degrees and radians are both units for measuring angles but use different scales. A full circle is 360 degrees or 2π radians (approximately 6.28318 radians). One degree equals π/180 radians (about 0.01745 radians), while one radian equals 180/π degrees (about 57.2958 degrees). Degrees are more intuitive and commonly used in everyday applications, navigation, and basic geometry. Radians are preferred in advanced mathematics, physics, and calculus because they simplify formulas and make derivatives cleaner. When using trigonometric functions in programming and scientific calculations, radians are typically the default unit.
To convert degrees to radians, multiply the degree value by π/180 (approximately 0.0174533). The formula is: radians = degrees × (π/180). For example: 90° × (π/180) = π/2 ≈ 1.5708 radians. 180° × (π/180) = π ≈ 3.1416 radians. 360° × (π/180) = 2π ≈ 6.2832 radians. Our angle converter performs this calculation automatically. Simply enter your degree value, select 'degrees' as the input unit, and choose 'radians' as the output unit. The tool instantly provides the converted value.
To convert radians to degrees, multiply the radian value by 180/π (approximately 57.2958). The formula is: degrees = radians × (180/π). For example: π/2 radians × (180/π) = 90°. π radians × (180/π) = 180°. 2π radians × (180/π) = 360°. Common conversions to remember: π/6 radians = 30°, π/4 radians = 45°, π/3 radians = 60°, π/2 radians = 90°. Our converter handles any value instantly, including decimal and fractional radian measurements.
Use radians instead of degrees in these scenarios: Advanced Mathematics - Calculus derivatives and integrals of trigonometric functions are simpler with radians. The derivative of sin(x) is cos(x) only when x is in radians. Physics Calculations - Angular velocity, angular acceleration, and rotational dynamics equations assume radians. Programming - Most programming languages (Python, JavaScript, C++, Java) use radians for trigonometric functions like sin(), cos(), and tan(). Engineering - Structural analysis, signal processing, and wave equations typically use radians. Higher Mathematics - Complex analysis, Fourier transforms, and differential equations use radians. However, continue using degrees for: Navigation and surveying, everyday angle measurements, basic geometry education, architectural drawings.
Gradians (also called gons or grads) are an alternative angle measurement where a right angle equals 100 gradians, and a full circle equals 400 gradians. This system was proposed as part of metric system decimalization but never became widely adopted. In gradians: 90° = 100 gon, 180° = 200 gon, 360° = 400 gon. Gradians are rarely used in practice but appear in some surveying equipment in certain European countries. Most scientific, engineering, and everyday applications use degrees or radians. The gradian system's advantage would be easier mental arithmetic (base-10), but the widespread familiarity with degrees and mathematical elegance of radians have made gradians obsolete for most purposes.
Arcminutes and arcseconds are subdivisions of degrees used for precise angle measurements, particularly in astronomy and navigation. One degree equals 60 arcminutes (60 arcmin), and one arcminute equals 60 arcseconds (60 arcsec). Therefore: 1 degree = 60 arcminutes = 3600 arcseconds. This sexagesimal (base-60) system is similar to time measurement (hours, minutes, seconds). In astronomy: The Sun and Moon appear about 30 arcminutes across in the sky. A telescope's resolution might be measured in arcseconds. Star positions are often given in degrees, arcminutes, and arcseconds. Navigation: Latitude and longitude use degrees with decimal or degrees-minutes-seconds (DMS) format. For example: 40 degrees 42 minutes 51 seconds North equals 40.714 degrees. Our converter can handle these precise subdivisions.
A turn (also called a revolution, full circle, or cycle) represents one complete rotation around a circle, equal to 360 degrees or 2π radians. The turn is useful in contexts involving rotation and periodic motion. Common turn fractions: 1/2 turn = 180° = π radians (straight angle). 1/4 turn = 90° = π/2 radians (right angle). 1/8 turn = 45° = π/4 radians. 1/12 turn = 30° = π/6 radians. Turns are commonly used in: Mechanical engineering - gear ratios and rotation calculations. Physics - angular frequency and periodic motion. Navigation - bearing changes and course corrections. Our converter supports turns as an input unit alongside degrees, radians, and gradians.
Yes, our angle converter handles negative angles correctly. Negative angles represent clockwise rotation from the positive x-axis, while positive angles represent counterclockwise rotation. For example: -90° = 270° (both point downward). -180° = 180° (both point left). -360° = 0°/360° (complete full rotation back to start). Negative angles are commonly used in: Trigonometry - describing clockwise rotations. Physics - angular displacement and velocity directions. Computer graphics - rotation transformations. Engineering - describing direction of rotation. When converting negative angles, simply enter the negative value with the minus sign. The converter preserves the sign and provides accurate conversions to all supported units.
Avoid these common angle conversion mistakes: Confusing input/output units - Double-check which unit you're converting FROM versus TO. Calculator mode - Ensure your calculator is in the correct mode (DEG vs RAD) before calculations. Precision loss - Rounding intermediate values can cause significant errors in chained calculations; keep full precision until final result. Direction confusion - Remember that positive angles are counterclockwise; negative angles are clockwise. Mixing angular units in formulas - Never mix degrees and radians in the same calculation without conversion. Forgetting π - When converting, the factor π/180 or 180/π is crucial. Approximation errors - Using 3.14 instead of π can cause noticeable errors for large angles. Sign errors - Negative angles represent clockwise rotation; don't drop the sign unless specifically meaning to find the coterminal positive angle.