Angle Unit Converter

Formula or method

Output = input × source angle factor ÷ destination angle factor, through radians. One turn = 360° = 2π rad = 400 gon. One degree is 60 arcminutes or 3,600 arcseconds.

How to use this calculator

1. Enter the Value to convert. The interface starts with 1; replace it with your measurement or quantity. Blank, nonnumeric and out-of-range values cannot produce a result.
2. Select From unit for the source unit. Match the complete label, including square/cubic units, decimal/binary prefixes or the gallon system when applicable.
3. Select To unit for the destination unit, then read Converted value with its unit label.
4. Try the worked example with its stated source and destination units. Results show at most eight fractional digits; very small nonzero values use scientific notation. Check the page limitations before interpreting the output.

Worked example

Select degree (°) → radian (rad), then enter 180. Compute 180 × π/180 = π rad, displayed as 3.14159265 rad. A negative input of −90° gives −1.57079633 rad.

Understanding the result

The sign and number of full turns are preserved. A 450° input is 1.25 turns, not automatically reduced to 90°. Arcminutes and arcseconds describe angles, not elapsed time.

Limitations and assumptions

• Signed angles and zero are accepted. There is no wrapping into a 0–360° interval or compass-bearing interpretation.
• π is evaluated with floating-point arithmetic; output is rounded to at most eight decimal places, not a symbolic multiple of π.

Frequently asked questions

Sources

• NIST SP 811: quantity-specific conversion factors
• NIST SP 330: non-SI units accepted with the SI