📐 Angle Conversion Calculator
Convert angles between degrees, radians, gradians, arcminutes, arcseconds, and turns.
Ideal for trigonometry, navigation, surveying, and robotics where precise angle conversions matter.
180 Degrees (°) equals
3.141593 Radians (rad)
Other Units
Degrees (°)
180
Gradians (gon)
200
Arcminutes (′)
10,800
Arcseconds (″)
648,000
Turns (rev)
0.5
How to Use This Calculator
Enter the angle
Type the angle magnitude in any supported unit. Decimals are welcome for precise measurements.
Pick source and target units
Select the unit you have and the unit you need—degrees, radians, gradians, arcminutes, arcseconds, or turns.
Copy the results
Review the main conversion and optional equivalents for quick reference in calculations or reports.
Formula
Radians = Degrees × π / 180
Degrees = Radians × 180 / π
Arcminutes = Degrees × 60, Arcseconds = Degrees × 3,600, Turns = Degrees ÷ 360, Gradians = Degrees × 10 / 9.
Use the formula breakdown to confirm the calculation logic or perform the conversion manually if needed.
Full Description
Angle conversions show up in geometry, navigation plotting, astronomy charts, and motion control systems. Many formulas expect radians, while surveying and navigation tools rely on degrees or arcminutes. Converting accurately keeps those formulas consistent.
This calculator handles the most common angular units and preserves precision across multiple decimal places. Use the quick list to see alternative units instantly, helping you cross-check manuals or collaborate with teams that prefer a different unit system.
Because the converter uses direct mathematical relationships, it avoids rounding errors typical of repeated manual conversions. Copy the results into spreadsheets, simulation tools, or CAD software with confidence.
Frequently Asked Questions
Why is π (pi) used in angle conversions?
Radians measure angles based on the arc length of a unit circle, so converting between degrees and radians requires π. The formulas ensure the ratio stays exact.
What is a turn?
A turn (sometimes called a revolution) represents a full circle, equal to 360° or 2π radians.
Are negative angles supported?
Yes. Negative values simply indicate direction (e.g., clockwise rotation). The converter preserves the sign during conversions.
Can I convert bearings or compass headings?
Yes. Enter the heading in degrees and convert to the desired unit. Remember that navigation often uses degrees with 0–360°, so wrap values accordingly.