Convert Gradians to Arcminutes
Convert Gradians (grad) to Arcminutes (′) instantly and accurately.
Conversion Formula
′ = grad × 54
About Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
About Arcminutes
An arcminute (′) is 1/60 of a degree - π/10,800 rad ≈ 2.909 × 10⁻⁴ rad. One arcminute of latitude equals exactly one nautical mile (1,852 m), which is the origin of the nautical mile unit. The Moon and Sun both subtend ~30 arcminutes in apparent diameter - the coincidence exploited in total solar eclipses. Human 20/20 visual acuity resolves letters 5 arcminutes tall at 6 m. Binocular and telescope apparent fields of view are quoted in arcminutes. 1′ = π/10,800 rad ≈ 0.01667° ≈ 290.9 µrad.
Quick Reference Table
| Gradians (grad) | Arcminutes (′) |
|---|---|
| 1 grad | 54 ′ |
| 2 grad | 108 ′ |
| 5 grad | 270 ′ |
| 10 grad | 540 ′ |
| 25 grad | 1350 ′ |
| 50 grad | 2700 ′ |
| 100 grad | 5400 ′ |