Gradians Conversion

Protractors are often used to measure angle

The gradian is a unit used to measure angle. Use one of the conversion calculators below to convert to another unit of measure, or read on to learn more about gradians.

Gradian Conversion Calculators

Choose a unit of angle to convert to.

Gradian Definition and Usage

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.

Background and Origin

Gradians originated in 1793 in post-revolutionary France and were initially part of the metric system. There are thus 100 grads in a right angle. Because of this, grads are sometimes called a metric degree.

Uses

Gradians currently have some specialized uses in certain fields such as surveying and mining. They are otherwise an abandoned unit of measurement in favor of radians and degrees, which are much more widely used.

Gradians Measurement Conversion Table

Common gradian values and equivalent imperial and metric angle measurements
gradians radians milliradians degrees minutes of arc seconds of arc revolutions circles mils (NATO)
1g 0.015708 rad 15.707963 mrad 0.9° 54' 3,240" 0.0025 r 0.0025 cir 16 mil
2g 0.031416 rad 31.415927 mrad 1.8° 108' 6,480" 0.005 r 0.005 cir 32 mil
3g 0.047124 rad 47.12389 mrad 2.7° 162' 9,720" 0.0075 r 0.0075 cir 48 mil
4g 0.062832 rad 62.831853 mrad 3.6° 216' 12,960" 0.01 r 0.01 cir 64 mil
5g 0.07854 rad 78.539816 mrad 4.5° 270' 16,200" 0.0125 r 0.0125 cir 80 mil
6g 0.094248 rad 94.24778 mrad 5.4° 324' 19,440" 0.015 r 0.015 cir 96 mil
7g 0.109956 rad 109.955743 mrad 6.3° 378' 22,680" 0.0175 r 0.0175 cir 112 mil
8g 0.125664 rad 125.663706 mrad 7.2° 432' 25,920" 0.02 r 0.02 cir 128 mil
9g 0.141372 rad 141.371669 mrad 8.1° 486' 29,160" 0.0225 r 0.0225 cir 144 mil
10g 0.15708 rad 157.079633 mrad 540' 32,400" 0.025 r 0.025 cir 160 mil
11g 0.172788 rad 172.787596 mrad 9.9° 594' 35,640" 0.0275 r 0.0275 cir 176 mil
12g 0.188496 rad 188.495559 mrad 10.8° 648' 38,880" 0.03 r 0.03 cir 192 mil
13g 0.204204 rad 204.203522 mrad 11.7° 702' 42,120" 0.0325 r 0.0325 cir 208 mil
14g 0.219911 rad 219.911486 mrad 12.6° 756' 45,360" 0.035 r 0.035 cir 224 mil
15g 0.235619 rad 235.619449 mrad 13.5° 810' 48,600" 0.0375 r 0.0375 cir 240 mil
16g 0.251327 rad 251.327412 mrad 14.4° 864' 51,840" 0.04 r 0.04 cir 256 mil
17g 0.267035 rad 267.035376 mrad 15.3° 918' 55,080" 0.0425 r 0.0425 cir 272 mil
18g 0.282743 rad 282.743339 mrad 16.2° 972' 58,320" 0.045 r 0.045 cir 288 mil
19g 0.298451 rad 298.451302 mrad 17.1° 1,026' 61,560" 0.0475 r 0.0475 cir 304 mil
20g 0.314159 rad 314.159265 mrad 18° 1,080' 64,800" 0.05 r 0.05 cir 320 mil

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