Angle Converter - Free Degrees, Radians, Gradians Converter
Angle Converter
Convert angles between degrees, radians, gradians, and turns. Also convert between decimal degrees and DMS format.
Angle Conversion
DMS ⟷ Decimal Degrees
Conversion Results
Degrees
360° = full circle
Radians
2π rad = full circle
Gradians
400 gon = full circle
Turns
1 turn = full circle
Common Angle References
How to use this calculator
🔄 How to Use the Angle Converter
- Enter an angle value in the input field
- Select the unit you're converting from (degrees, radians, gradians, or turns)
- Click "Convert Angle" to see all conversions
- For DMS conversion, use the dedicated converter below
- View the visual representation of your angle
📐 Angle Units Explained
Degrees (°)
Most common unit. A full circle = 360°. Used in everyday life, navigation, and basic geometry.
Radians (rad)
Used in calculus and physics. A full circle = 2π rad. One radian is the angle where arc length equals radius.
Gradians (gon)
Also called grads. A full circle = 400 gon. Used in surveying and some European countries.
Turns (rev)
Also called revolutions. A full circle = 1 turn. Used in physics for rotational motion.
DMS Format
Degrees, Minutes, Seconds. 1° = 60' = 3600". Used in GPS coordinates and astronomy.
🌟 Common Angle Conversions
Right Angle
90° = π/2 rad = 100 gon = 0.25 turns
Straight Line
180° = π rad = 200 gon = 0.5 turns
Full Circle
360° = 2π rad = 400 gon = 1 turn
One Radian
1 rad ≈ 57.2958° ≈ 63.662 gon
💡 Pro Tips
- • Radians are "natural" units - many formulas are simpler in radians
- • To convert degrees to radians: multiply by π/180
- • To convert radians to degrees: multiply by 180/π
- • Gradians make right angles exactly 100 units
- • Scientific calculators often have DEG/RAD/GRAD modes
- • GPS coordinates use DMS format: e.g., 40°26'46"N
⚠️ Common Mistakes to Avoid
- • Make sure your calculator is in the correct mode (DEG/RAD)
- • Remember: π radians = 180°, not 360°
- • DMS: 1 degree ≠ 100 minutes (it's 60 minutes)
- • Negative angles go clockwise from the reference
- • Angles can be greater than 360° (multiple rotations)
About this calculator
Convert angles between degrees, radians, gradians, and turns. Includes DMS (degrees, minutes, seconds) conversion with visual representation.
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