Turns to Gradians (turn to grad)
1 turn equals 400 gradians exactly.
How to convert turns to gradians
To convert turns to gradians, multiply the number of turns by 400. This factor is exact. To go the other way, multiply gradians by 0.0025.
gradians = turns × 400
Example: 10 turns = 4,000 gradians.
About these units
Turn (turn)
One full revolution, 360 degrees or 2π radians.
A turn is the simplest angle to define: the whole way around, back to the starting direction. It also goes by cycle and revolution, and it equals 2π radians, 360 degrees, or 400 gradians. In the International System of Quantities, rotation is a plain count of revolutions, the angle divided by 2π radians, and it can be negative or exceed one.
Measuring in turns is older than it might seem. Percentage protractors marked in hundredths of a turn have existed since 1922, and in 1962 the astronomer Fred Hoyle proposed the terms centiturn, milliturn, and microturn. A 1974 German standard, DIN 1315, suggested the symbol pla, from the Latin for full angle. Some HP calculators, such as the HP Prime of 2013, accept tr as an angle unit. In CSS, 1turn equals 360deg, so a rule can rotate an element by 1.75turn. Binary angular measurement in computing also treats a full turn as the value 1, which lets integer overflow wrap an angle around for free.
The turn is the reference unit for angle on this site.
Sources: Wikipedia: Turn (angle); MDN Web Docs: CSS <angle>; NIST Guide to the SI, Appendix B.8 (angle conversion factors)
Gradian (grad)
One 400th of a full turn, so a right angle is exactly 100 gradians. Used in surveying in parts of Europe, also called the gon.
The gradian came out of the French Revolution as part of the push to make measurement rational. It was first called the grade, and it divides the right angle into 100 parts, so a full turn is 400 grads and one grad is 0.9 degree. In northern Europe the word grad already meant an ordinary degree, which caused confusion, so the name gon was adopted, first regionally and later internationally. Gon is the symbol given in ISO 31-1, Annex B.
The link to the meter explains the appeal. The meter was originally set at one ten-millionth of a quarter of Earth's meridian, so one gon of arc along the surface spans about 100 kilometers and one centigon about 1 kilometer. Surveyors, mainly in Europe, still use it, along with some mining and geology work, and it is legally recognized in the European Union and Switzerland. It is not part of the SI, and the SI Brochure does not mention it. Many scientific calculators of the 1970s through the 1990s offered a gon mode, though some recent models have dropped it.
1 gradian = 0.0025 turns (exactly).
Sources: Wikipedia: Gradian; NIST Guide to the SI, Appendix B.8 (angle conversion factors); MDN Web Docs: CSS <angle>
Related conversions
- Gradians to turns (reverse)
- Turns to degrees
- Turns to radians
- Turns to arcminutes
- Turns to arcseconds
- Degrees to gradians
- Radians to gradians
- Arcminutes to gradians
- Arcseconds to gradians
See all angle units.