Gradians to Degrees Conversion

Enter the angle in gradians below to get the value converted to degrees.

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Results in Degrees:
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1g = 0.9°
1g = 0° 54′ 0″
Do you want to convert degrees to gradians?

How to Convert Gradians to Degrees

conversion scale showing gradians and equivalent degrees angle values

To convert a gradian measurement to a degree measurement, multiply the angle by the conversion ratio. One gradian is equal to 0.9 degrees, so use this simple formula to convert:

degrees = gradians × 0.9

The angle in degrees is equal to the gradians multiplied by 0.9.

For example, here's how to convert 5 gradians to degrees using the formula above.
5g = (5 × 0.9) = 4.5°

Gradians and degrees are both units used to measure angle. Keep reading to learn more about each unit of measure.

Gradians

A gradian is equal to 1/400 of a revolution or circle, or 9/10°. The grad, or gon, is more precisely defined as π/200, or 1.570796 × 10-2 radians.[1]

This unit simplifies the measurements of right angles, as 90° is equal to 100 gradians.

Right angles in gradians
GradiansDegrees
0 grad
100 grad90°
200 grad180°
300 grad270°
400 grad360°

A gradian is sometimes also referred to as a grad, gon, or grade. Gradians can be abbreviated as g, and are also sometimes abbreviated as gr or grd. For example, 1 gradian can be written as 1g, 1 gr, or 1 grd.

Degrees

A degree is a measure of angle equal to 1/360th of a revolution, or circle.[2] The number 360 has 24 divisors, making it a fairly easy number to work with. There are also 360 days in the Persian calendar year, and many theorize that early astronomers used 1 degree per day.

The degree is an SI accepted unit for angle for use with the metric system. A degree is sometimes also referred to as a degree of arc, arc degree, or arcdegree. Degrees can be abbreviated as °, and are also sometimes abbreviated as deg. For example, 1 degree can be written as 1° or 1 deg.

Degrees can also be expressed using minutes and seconds as an alternative to using the decimal form. Minutes and seconds are expressed using the prime (′) and double-prime (″) characters, although a single-quote and double-quote are often used for convenience.

One minute is equal to 1/60th of a degree and one second is equal to 1/60th of a minute.

Protractors are commonly used to measure angles in degrees. They are semi-circle or full-circle devices with degree markings allowing a user to measure an angle in degrees. Learn more about how to use a protractor or download a printable protractor.

Gradian to Degree Conversion Table

Gradian values converted to degrees in decimal and minutes and seconds values
Gradians Degrees (decimal) Degrees (minutes & seconds)
1g 0.9" 0° 54′ 0″
2g 1.8" 1° 48′ 0″
3g 2.7" 2° 42′ 0″
4g 3.6" 3° 36′ 0″
5g 4.5" 4° 30′ 0″
6g 5.4" 5° 24′ 0″
7g 6.3" 6° 18′ 0″
8g 7.2" 7° 12′ 0″
9g 8.1" 8° 6′ 0″
10g 9" 9° 0′ 0″
11g 9.9" 9° 54′ 0″
12g 10.8" 10° 48′ 0″
13g 11.7" 11° 42′ 0″
14g 12.6" 12° 36′ 0″
15g 13.5" 13° 30′ 0″
16g 14.4" 14° 24′ 0″
17g 15.3" 15° 18′ 0″
18g 16.2" 16° 12′ 0″
19g 17.1" 17° 6′ 0″
20g 18" 18° 0′ 0″
21g 18.9" 18° 54′ 0″
22g 19.8" 19° 48′ 0″
23g 20.7" 20° 42′ 0″
24g 21.6" 21° 36′ 0″
25g 22.5" 22° 30′ 0″
26g 23.4" 23° 24′ 0″
27g 24.3" 24° 18′ 0″
28g 25.2" 25° 12′ 0″
29g 26.1" 26° 6′ 0″
30g 27" 27° 0′ 0″
31g 27.9" 27° 54′ 0″
32g 28.8" 28° 48′ 0″
33g 29.7" 29° 42′ 0″
34g 30.6" 30° 36′ 0″
35g 31.5" 31° 30′ 0″
36g 32.4" 32° 24′ 0″
37g 33.3" 33° 18′ 0″
38g 34.2" 34° 12′ 0″
39g 35.1" 35° 6′ 0″
40g 36" 36° 0′ 0″

References

  1. Ambler Thompson and Barry N. Taylor, Guide for the Use of the International System of Units (SI), National Institute of Standards and Technology, https://physics.nist.gov/cuu/pdf/sp811.pdf
  2. Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/degree