Degrees to Gradians Converter

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

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Results in Gradians:
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1° = 1.111111g

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How to Convert Degrees to Gradians

To convert a measurement in degrees to a measurement in gradians, multiply the angle by the following conversion ratio: 1.111111 gradians/degree.

Since one degree is equal to 1.111111 gradians, you can use this simple formula to convert:

gradians = degrees × 1.111111

The angle in gradians is equal to the angle in degrees multiplied by 1.111111.

For example, here's how to convert 5 degrees to gradians using the formula above.
gradians = (5° × 1.111111) = 5.555556g
conversion scale showing degrees and equivalent gradians angle values

How Many Gradians Are in a Degree?

There are 1.111111 gradians in a degree, which is why we use this value in the formula above.

1° = 1.111111g

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

What Is a Degree?

A degree is a measure of angle equal to 1/360th of a revolution, or circle.[1] 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 arcminutes and arcseconds as an alternative to using the decimal form. Arcminutes and arcseconds are expressed using the prime (′) and double-prime (″) characters, respectively, although a single-quote and double-quote are often used for convenience.

One arcminute is equal to 1/60th of a degree, and one arcsecond is equal to 1/60th of an arcminute.

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.

Learn more about degrees.

What Is a Gradian?

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.[2]

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.

In the expressions of units, the slash, or solidus (/), is used to express a change in one or more units relative to a change in one or more other units.

Learn more about gradians.

Degree to Gradian Conversion Table

Table showing various degree measurements converted to gradians.
Degrees Gradians
1.1111g
2.2222g
3.3333g
4.4444g
5.5556g
6.6667g
7.7778g
8.8889g
10g
10° 11.11g
11° 12.22g
12° 13.33g
13° 14.44g
14° 15.56g
15° 16.67g
16° 17.78g
17° 18.89g
18° 20g
19° 21.11g
20° 22.22g
21° 23.33g
22° 24.44g
23° 25.56g
24° 26.67g
25° 27.78g
26° 28.89g
27° 30g
28° 31.11g
29° 32.22g
30° 33.33g
31° 34.44g
32° 35.56g
33° 36.67g
34° 37.78g
35° 38.89g
36° 40g
37° 41.11g
38° 42.22g
39° 43.33g
40° 44.44g

References

  1. Collins Dictionary, Definition of 'degree', https://www.collinsdictionary.com/us/dictionary/english/degree
  2. 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

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