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Gradians to Degrees Converter

Enter an angle in gradians to convert to degrees and radians.

Result

33.75°
0.5890 rad

How it is calculated

A full circle is 400 gradians (gon) or 360 degrees, so the tool uses degrees = gon × 0.9 and radians = gon × π / 200. gon is the angle in gradians. Degrees are shown with two decimals and the degree sign, radians with four decimals. There is no range limit: negative angles and angles above 400 gon are converted as they are, without wrapping around to 0–360, so 450 gon returns 405.00°, not 45°. Anything that is not a number returns no result. Results are rounded for display only, so a long decimal in the input can show a rounded last digit.

Worked example

A surveying instrument reads 37.5 gon. Degrees: 37.5 × 0.9 = 33.75°. Radians: 37.5 × 3.14159 / 200 = 0.5890 rad. As a check, 37.5 gon is 37.5% of a right angle, and 33.75 is 37.5% of 90, so both agree.

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Common mistakes

  • Dividing by 0.9 instead of multiplying. One gon is smaller than one degree, so the degree value is always 10% less than the gon value.
  • Confusing gon with grad as a unit on a calculator display. Many scientific calculators label the third angle mode GRAD; it is the same gradian, not a different unit.
  • Expecting angles to wrap to a single turn. The tool gives 405° for 450 gon; subtract 360 yourself if you need the equivalent within one revolution.
  • Reading a surveying bearing in degrees-minutes-seconds as a decimal degree. The tool takes decimal gon only.
  • Using the radian output for a degree-mode calculation, or the reverse, which is the commonest cause of wrong trigonometry results.

Sources

About this calculator

The gradian (gon) is an alternative angle unit that divides a full right angle into 100 equal parts instead of 90, making a complete circle equal to 400 gon. The conversion is a fixed ratio: 1 gon = 0.9 degrees (since 400 gon = 360°), and the same value can also be expressed in radians using the standard π/180 relationship applied to the degree equivalent.

Gradians were designed to simplify decimal calculations in land surveying and civil engineering — a right angle of exactly 100 gon avoids the fractional awkwardness of 90°. They still appear on many surveying instruments, in French and other European engineering traditions, and as a selectable angle mode on scientific calculators alongside degrees and radians.

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  • Editorial team

    Before you convert, check which angle mode your instrument is really in: a total station or calculator left in degree mode will show a right angle as 90, not 100. For a mental check, take a tenth off the gon value; 100 gon is 90 degrees. The tool gives decimal degrees only, so 33.75 is 33 degrees 45 minutes. What instrument or field do you meet gon in?

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