How to convert degrees to gradians
To convert a measurement in degrees to gradians, multiply the value by 1.111111. The conversion factor comes from the relationship between both units and the radian.
For example, to convert 5 ° to gradians: 5 × 1.111111 = 5.555556 gon.
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.
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.
When you need to convert degrees to gradians
Surveyors and civil engineers working with European instruments encounter gradians (gon), where a right angle is a clean 100 gon. Converting familiar degrees to gradians is needed when reading total-station output or cadastral plans that use the decimal grade system.
Degrees to gradians worked examples
Here are some common values converted:
1 ° = 1.111111 gon 5 ° = 5.555556 gon 10 ° = 11.111111 gon 50 ° = 55.555556 gon 100 ° = 111.111111 gon
Frequently asked questions
How many gradians are in one degree?
One degree (°) equals 1.111111 gradians (gon). Multiply any value in degrees by 1.111111 to convert to gradians.
How do I convert degrees to gradians?
Multiply the value in degrees by 1.111111. For example, 5 ° × 1.111111 = 5.555556 gon.
How do I convert gradians to degrees?
Multiply the value in gradians by 0.9, or divide by 1.111111. Use the swap button on the converter above to reverse the direction.
Is the degree to gradian 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 degrees to gradians?
The formula is: gon = ° × 1.111111. This comes from the definition of both units relative to the radian.