Convert Gradians to Microradians
Convert Gradians (grad) to Microradians (µrad) instantly and accurately.
Conversion Formula
µrad = grad × 15707.96327
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 Microradians
A microradian (µrad) is one millionth of a radian (10⁻⁶ rad ≈ 0.206265 arcseconds). It is the standard unit for small angles in precision optics and structural monitoring. A 1 µm wavelength beam from a 1 mm aperture has a diffraction-limited half-angle divergence of ~1 µrad. Atmospheric seeing for ground-based telescopes is typically 2.4-9.7 µrad (0.5-2 arcseconds). Autocollimators resolve angular deviations to 0.05-1 µrad for machine tool alignment. Building tilt monitoring tracks µrad/day. 1 µrad ≈ 0.2063″ = 0.2063 arcseconds.
Quick Reference Table
| Gradians (grad) | Microradians (µrad) |
|---|---|
| 1 grad | 15708 µrad |
| 2 grad | 31415.9 µrad |
| 5 grad | 78539.8 µrad |
| 10 grad | 157080 µrad |
| 25 grad | 392699 µrad |
| 50 grad | 785398 µrad |
| 100 grad | 1570800 µrad |