Gradian Conversion Calculator
Enter a value in gradians below to convert to another unit of angle.
What Is a Gradian?
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A gradian is a unit used to measure angle.
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.
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.
How Much 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.[1]
This unit simplifies the measurements of right angles, as 90° is equal to 100 gradians.
| Gradians | Degrees |
|---|---|
| 0 grad | 0° |
| 100 grad | 90° |
| 200 grad | 180° |
| 300 grad | 270° |
| 400 grad | 360° |
How to Convert Gradians
To convert gradians to another unit of angle, you need to multiply the value by a conversion factor. A conversion factor is a numerical value used to change the units of a measurement without changing the value.[2]
You can find the conversion factors for gradians in the conversion table below.
Then, multiply the angle measurement by the conversion factor to find the equivalent value in the desired unit of measurement.
gradians × conversion factor = result
You can also use a calculator, such as one of the converters below, for the conversion.
Gradian Conversion Table
| 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 | 9° | 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 |
Gradian Conversion Calculators
You can also convert angle using one of our gradian converters below.
References
- 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
- National Institute of Standards & Technology, Unit Conversion, https://www.nist.gov/pml/owm/metric-si/unit-conversion