Angle Converter

How it converts

Worked example

1 radian = 1 × 57.2958 ÷ 1 = 57.2958 degree.

Quick reference

• 1 degree = 0.01745 radian = 1.11111 gradian = 59.9999 arcmin = 3600 arcsec = 0.00278 revolution
• 1 radian = 57.2958 degree = 63.662 gradian = 3437.74 arcmin = 206264.6 arcsec = 0.15915 revolution

Second worked example

45 degree = 45 × 1 ÷ 57.29577951 = 0.785398 radian.

Common values

Worked out with the same factors the converter uses.

• 30 degree = 0.523599 radian = 33.3333 gradian = 0.0833333 revolution
• 45 degree = 0.785398 radian = 50 gradian = 0.125 revolution
• 60 degree = 1.0472 radian = 66.6667 gradian = 0.166667 revolution
• 90 degree = 1.5708 radian = 100 gradian = 0.25 revolution
• 180 degree = 3.14159 radian = 200 gradian = 0.5 revolution
• 270 degree = 4.71239 radian = 300 gradian = 0.75 revolution
• 360 degree = 6.28319 radian = 400 gradian = 1 revolution

Common mistakes

• Leaving a scientific calculator in DEG mode for an angle in radians, or the reverse. sin 30 is 0.5 only when the 30 is in degrees; sin of 30 radians is −0.988.
• Reading a gradian as a degree. A full turn is 400 gradians, so 1 gradian = 0.9°.
• Counting arcminutes and arcseconds in hundreds. They go by 60: 1° = 60 arcmin = 3600 arcsec, so 0.5° is 30 arcmin, not 50.

Learn the method

• The Built-In Unit Converter — A Tour for Exam-Style Conversions
• Dimensional Analysis — The Unit-Conversion Method That Never Fails

About this converter

One of the unit converters in the Chemistry Calculator Suite, alongside its chemistry, physics and maths tools. Nothing is behind a login and no value you type is sent anywhere — the conversion runs in your own browser.

The Angle converter above is the live tool — it converts right here on the page. The link under it opens the full suite with this set already selected.

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