Angle Converter 📐
Free online angle converter. Convert degrees to radians, radians to degrees, and 16 angle units instantly. Includes degree radian calculator with formulas.
📐 Conversion Formula
Common Angle Conversions
Quick Angle Conversions
Radian to Degree
× (180/π)
1 rad = 57.3°
Degree to Radian
× (π/180)
180° = π rad
Circle = 360°
= 2π radians
Full rotation
1° = 60'
= 3600"
Minutes & Seconds
Converter Performance Metrics
How to Use Angle Converter
Step 1: Enter Angle Value
Type the angle value you want to convert in the "From" field. The converter accepts any positive or negative number including decimals. For example, enter 90 for 90 degrees or 3.14159 for π radians depending on your selected unit.
Step 2: Select Source Unit
Choose the unit of your input angle from the "From" dropdown. Options include degrees, radians, gradians, revolutions and 16+ other angle units. Select the unit that matches your angle measurement.
Step 3: Select Target Unit
Pick the unit you want to convert to from the "To" dropdown. The conversion happens automatically in real-time as you change units. The formula used for conversion is displayed below for educational reference.
Step 4: Use Results
View the converted result in the "To" field. Click Copy to copy the result to clipboard, Swap to reverse conversion direction, or Reset to start over. All calculations are instant and accurate for mathematics and engineering.
Understanding Angle Measurement
What are Degrees and Radians?
Degree (°) is the most common angle unit dividing a circle into 360 equal parts. One degree = 1/360 of full rotation. Radian (rad) is the SI unit measuring angle by arc length on unit circle. One radian is angle where arc length equals radius. Full circle = 360° = 2π radians ≈ 6.28318 radians.
Conversion Formulas: Degree to Radian: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \). Radian to Degree: \( \text{degrees} = \text{radians} \times \frac{180}{\pi} \approx \text{radians} \times 57.29578 \). Key values: \( 180° = \pi \text{ rad} \), \( 90° = \frac{\pi}{2} \text{ rad} \), \( 45° = \frac{\pi}{4} \text{ rad} \), \( 60° = \frac{\pi}{3} \text{ rad} \), \( 30° = \frac{\pi}{6} \text{ rad} \).
Common Angle Units Explained
Degree (°): Divides circle into 360 equal parts. Historical origins from Babylonian base-60 number system and approximate 360 days/year. Subdivided into 60 arcminutes (') per degree, 60 arcseconds (") per arcminute. Common in navigation, geography, surveying, everyday measurements. Right angle = 90°, straight angle = 180°.
Radian (rad): Natural angle unit in mathematics. Angle subtended by arc equal to radius. Simplifies calculus, trigonometry—derivatives/integrals cleaner. \( 2\pi \) radians = 360°, π radians = 180°. No subdivision—expressed as decimals or fractions of π. Essential in physics, engineering, computer graphics, advanced mathematics.
Gradian/Gon (grad): Metric angle unit dividing circle into 400 equal parts. Right angle = 100 grad. Used in surveying, civil engineering in some countries. More decimal-friendly than degrees. 100 grad = 90°. Each grad divided into 100 centigrads. Less common than degrees or radians.
Common Use Cases
📚 Mathematics & Trigonometry
Convert between degrees and radians for trigonometric functions. Calculators may use radians, textbooks use degrees. Sine, cosine, tangent calculations require correct angle mode. Essential for calculus, physics problems, and understanding trigonometric identities across different unit systems.
🗺️ Navigation & Geography
Convert latitude, longitude, bearings, azimuths for navigation. GPS uses degrees-minutes-seconds (DMS) format. Aviation, maritime navigation use various angle formats. Convert compass bearings (0-360°) to mathematical angles. Essential for maps, surveying, and location-based applications.
💻 Programming & Game Development
Programming languages use radians for trig functions—Python, JavaScript, C++. Game engines rotate objects in degrees but calculations use radians. Convert user-friendly degree input to radian calculations. Critical for 3D graphics, physics simulations, animation, and rotational transforms.
🏗️ Construction & Engineering
Convert roof pitch, slope angles, structural angles. Roof pitch (4:12) to degrees for calculations. Surveying instruments use gradians or degrees. Convert between formats for blueprints, CAD software, construction specifications. Essential for architecture, civil engineering, and building design.
🔭 Astronomy & Physics
Celestial coordinates in degrees-minutes-seconds. Angular separation between stars. Convert telescope pointing angles. Orbital mechanics uses radians. Essential for astrophotography, telescope alignment, satellite tracking, and understanding astronomical measurements and calculations.
🎓 Education & Homework
Students convert angles for geometry, trigonometry, physics homework. Understand relationship between degrees and radians. Practice angle conversions for tests. Verify calculator mode settings (DEG vs RAD). Essential for learning mathematics, solving problems, and developing spatial reasoning skills.