What is Angle Converter?
An angle converter is a tool that instantly converts between different units of angular measurement including degrees, radians, gradians, arcminutes, arcseconds, and turns. Whether you are working in mathematics, physics, engineering, navigation, or astronomy, this converter provides accurate angle conversions across all standard units.
Steps:
- Enter the angle value you want to convert in the input field.
- Select the source unit (the unit you are converting from).
- Select the target unit (the unit you want to convert to).
- The converted result appears instantly along with the formula used.
- Export the result as PDF, Excel, or CSV if needed.
Formula
Angle conversion factors (base unit: degree):
1 Degree (°) = 1°
1 Radian (rad) = 57.29578°
1 Gradian (grad) = 0.9°
1 Arcminute (′) = 1/60°
1 Arcsecond (″) = 1/3600°
1 Turn = 360°
Use Cases
- Mathematics: converting between degrees and radians for trigonometry and calculus.
- Navigation: converting GPS coordinates between decimal degrees and DMS format.
- Surveying: converting between degrees and gradians for land measurement.
- Astronomy: using arcseconds and arcminutes for celestial coordinate measurements.
Key Benefits
- Convert instantly between degrees, radians, gradians, arcminutes, and arcseconds.
- Get precise angle calculations for mathematics, engineering, and navigation.
- Switch effortlessly between scientific, imperial, and metric angle units.
Pro Tips
- Use radians for calculus and physics — most formulas assume radian measure.
- Remember: 180° = π rad = 200 grad = 10,800 arcmin = 648,000 arcsec = 1/2 turn.
- For GPS work, convert decimal degrees to DMS by multiplying the decimal part by 60.
- In surveying, gradians simplify calculations because a right angle is exactly 100 grad.
Common Mistakes to Avoid
- Confusing degrees with radians — always check which unit your calculator or formula expects.
- Forgetting that 1 radian ≈ 57.3°, not 57.3 degrees exactly (it is an irrational number).
- Mixing up arcminutes (′) with minutes of time — they are different units despite similar names.
Key Terms Explained
- Degree: A unit of angle equal to 1/360 of a full rotation, the most commonly used angle unit
- Radian: The SI unit of angle, defined as the angle subtended by an arc equal in length to the radius
- Gradian: A unit dividing a right angle into 100 parts, used in surveying and some European countries
- Arcminute: An angular measurement equal to 1/60 of a degree, used in astronomy and navigation
Example
Converting 90° to radians: 90 × π/180 = π/2 ≈ 1.571 rad. Converting 1 radian to degrees: 1 × 180/π ≈ 57.296°. Converting 100 grads to degrees: 100 × 0.9 = 90°.