How to convert gradians to degrees
To convert a measurement in gradians to degrees, multiply the value by 0.9. The conversion factor comes from the relationship between both units and the radian.
For example, to convert 5 gon to degrees: 5 × 0.9 = 4.5 °.
What is a gradian?
A gradian (also called gon or grade) is a unit of plane angle equal to 1/400 of a full turn, so a right angle is exactly 100 gradians. Introduced in France around the time of the French Revolution as part of the push to decimalize all measurement, the gradian divides the quarter circle into a tidy 100 units. It survives mainly in surveying and some European civil engineering.
Common uses of gradians include: Land surveying and geodesy in parts of Europe; Civil engineering slope and grade calculations; Some scientific calculators (GRAD mode); Cadastral (property boundary) measurement.
What is a degree?
A degree is a unit of plane angle equal to 1/360 of a full turn, so a full circle contains exactly 360 degrees. The 360-degree circle traces back to ancient Babylonian astronomers, whose base-60 (sexagesimal) number system made 360 a convenient, highly divisible count for tracking the roughly 365-day solar year. It remains the most widely used angle unit in everyday life.
Common uses of degrees include: Geometry, trigonometry, and school mathematics; Compass bearings and navigation headings; Latitude and longitude coordinates; Camera field of view and lens specifications.
Gradians to degrees worked examples
Here are some common values converted:
1 gon = 0.9 ° 5 gon = 4.5 ° 10 gon = 9 ° 50 gon = 45 ° 100 gon = 90 °
Frequently asked questions
How many degrees are in one gradian?
One gradian (gon) equals 0.9 degrees (°). Multiply any value in gradians by 0.9 to convert to degrees.
How do I convert gradians to degrees?
Multiply the value in gradians by 0.9. For example, 5 gon × 0.9 = 4.5 °.
How do I convert degrees to gradians?
Multiply the value in degrees by 1.111111, or divide by 0.9. Use the swap button on the converter above to reverse the direction.
Is the gradian to degree conversion exact?
Angle conversions are exact. Degrees, gradians and revolutions are defined as exact fractions of a full turn (2π radians).
What is the formula for gradians to degrees?
The formula is: ° = gon × 0.9. This comes from the definition of both units relative to the radian.