Free · Angle conversions
Angle in Radians, Degrees & Arcseconds
Convert angular measurements between radians, degrees and arcseconds with reversible inputs.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Edit a calculated value to solve backwards, or lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A half-turn is 180 degrees, π radians or 648,000 arcseconds. One degree contains 60 arcminutes and 3,600 arcseconds.
radians = degrees × π ÷ 180; arcseconds = degrees × 3600
Worked example
Enter these known values and leave the other values blank.
- Degrees
- 180 deg
- Radians
- 3.14159 rad
- Angular subdivisions
- 648000 arcsec
Assumptions and limitations
- These are plane-angle measurements. Arcseconds are angular units, not seconds of elapsed time.
- The conversion preserves the entered rotation count and sign. It does not normalize angles to a single turn or choose a trigonometric quadrant.
Common questions
Why are π radians equal to 180 degrees?
A full circle contains 2π radians or 360 degrees. Dividing both measures by two gives the half-turn identity used by the converter.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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