Arcseconds to Gradians (″ to grad)

1 arcsecond equals 0.0003086419753 gradians (rounded).

1 arcsecond = 0.0003086419753 gradians

How to convert arcseconds to gradians

To convert arcseconds to gradians, multiply the number of arcseconds by 0.0003086419753. The factor is rounded to 10 significant digits. To go the other way, multiply gradians by 3,240.

gradians = arcseconds × 0.0003086419753

Example: 10 arcseconds = 0.003086419753 gradians.

About these units

Arcsecond (″)

General & non-SICurrent unit

One sixtieth of an arcminute (1/3,600 degree). Used for tiny angles in astronomy.

An arcsecond is 1/3,600 of a degree, or 1/1,296,000 of a turn. In radians it is π/648,000, about 4.85 millionths, so it covers roughly 4.8 millimeters at a distance of 1 kilometer. The SI Brochure treats it as an alternative name for the second of plane angle, with the symbol as or ″, and counts it among the widely used non-SI units.

Astronomy is where it matters most. The parsec is the distance at which a star shows a parallax of one arcsecond, about 3.26 light-years, so a star's distance in parsecs is the reciprocal of its parallax in arcseconds. The unit also appears in planetary angular diameters, binary star separations, and star motions. For comparison, the Sun's disk is roughly 1,900 arcseconds across. Smaller angles use the prefixes milli- and micro-.

1 arcsecond = 7.716049383×10⁻⁷ turns (approximately).

Sources: BIPM SI Brochure, 9th edition (2019); ESA Gaia: Cosmic distances; NIST Guide to the SI, Appendix B.8 (angle conversion factors)

Gradian (grad)

General & non-SICurrent unit

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

See all angle units.