DIY Cost Tools
Angle Converter
CONVERSION CALCULATOR
Convert angles between degrees, radians, gradians, turns, arcminutes, and arcseconds.
How it works
All measurements are converted through radians. One full turn equals 2π radians, 360 degrees, or 400 gradians.
Conversion formula
Radians = degrees × π ÷ 180. Degrees = radians × 180 ÷ π.
Worked example
180 degrees equals π radians, approximately 3.14159265359.
Important limits
- Angle units are dimensionless ratios expressed with different scales.
- Displayed decimal radians approximate values that may be exact multiples of π.
- Arcminutes and arcseconds are angular units, not units of time.
Frequently asked questions
How many radians are in a full circle?
A full turn contains 2π radians.
How many arcseconds are in one degree?
One degree contains 60 arcminutes or 3,600 arcseconds.
Interpreting angle conversions
Choose the unit that matches the source measurement before converting. Degrees are common in construction and navigation, radians are standard in higher mathematics and programming, gradians divide a full turn into 400 parts, and turns express rotation as a fraction of one revolution. A full turn equals 360 degrees, 2π radians, or 400 gradians.
Keep extra decimal places while calculating and round only the displayed result. Small rounding differences matter when an angle is used across a long distance, such as laying out a roof, ramp, or survey line. For direction or bearing work, also confirm whether the source uses clockwise rotation, counterclockwise rotation, or a compass bearing.
Review notes
Factors follow the standard 360-degree, 2π-radian, and 400-gradian full turn. Last reviewed September 30, 2026.