Second of Arc to Gradian Conversion Chart
| Second of arc (arcsec) | Gradian (grad) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.972 arcsec | 0.0003 grad | One Arcsecond Baseline Astronomical Parallax in Gradians | 0.972 × 0.000309 = 0.0003 grad |
| 3.24 arcsec | 0.001 grad | High-Precision Electronic Theodolite Angular Tolerance | 3.24 × 0.000309 = 0.001 grad |
| 32.4 arcsec | 0.01 grad | Centesimal Centigrad Geodetic Triangulation Precision | 32.4 × 0.000309 = 0.01 grad |
| 162 arcsec | 0.05 grad | Half Centigrad Topographic Offset in Arcseconds | 162 × 0.000309 = 0.05 grad |
| 324 arcsec | 0.1 grad | One-Tenth Gradian Cadastral Station Misclosure Arc | 324 × 0.000309 = 0.1 grad |
| 1620 arcsec | 0.5 grad | Half Gradian Centesimal Deflection in Arcseconds | 1620 × 0.000309 = 0.5 grad |
| 3240 arcsec | 1 grad | Exact International Definition of 3,240 Arcseconds in Gradian | 3240 × 0.000309 = 1 grad |
| 6480 arcsec | 2 grad | Two Gradians Land Surveying Traverse Displacement | 6480 × 0.000309 = 2 grad |
| 16200 arcsec | 5 grad | Five Gradians Topographic Mapping Sector Coverage | 16200 × 0.000309 = 5 grad |
| 32400 arcsec | 10 grad | Ten Gradians Decimal Metric Sector in Arcseconds | 32400 × 0.000309 = 10 grad |
| 64800 arcsec | 20 grad | Twenty Gradians Centesimal Vector in Arcseconds | 64800 × 0.000309 = 20 grad |
| 162000 arcsec | 50 grad | Half Right Angle Fifty Gradians Metric Octant Arcseconds | 162000 × 0.000309 = 50 grad |
| 324000 arcsec | 100 grad | Perpendicular Right Angle Exactly 324,000 Arcseconds | 324000 × 0.000309 = 100 grad |
| 648000 arcsec | 200 grad | Straight Semicircle Angle Exactly 648,000 Arcseconds | 648000 × 0.000309 = 200 grad |
| 1296000 arcsec | 400 grad | Full Geometric Circle Revolution Exactly 1,296,000 Arcseconds | 1296000 × 0.000309 = 400 grad |
Second of arc to Gradian Formula & Unit Definitions
The conversion from seconds of arc to gradians is governed by the exact rational factor of 1/3,240 (1 arcsec = 1/3,240 grad ≈ 0.000308642 grad). To convert arcseconds to gradians, divide the arcsecond value by 3,240 (or multiply by ~0.000309). Conversely, to convert gradians into arcseconds, multiply by 3,240.
Quick Estimation: Divide arcseconds by 3,240 (or divide arcseconds by 3.24 to find the angle in milligons). For example: 3.24 arcsec = 0.001 grad (1 mgon); 32.4 arcsec = 0.01 grad; 324 arcsec = 0.1 grad; 3,240 arcsec = 1 grad.
Second of Arc (arcsec / ″)
Fine Sexagesimal Division (1/3,600°)- Creator & Origin: Ptolemaic base-60 geometry and Bessel's stellar parallax distance triangulation.
- Standard Definition: Defined as exactly 1/3,600 of an angular degree (1/3,240 of a gradian).
- Everyday Focus: Astronomical resolving power, optical seeing, collimator test benches, and space geodesy.
Gradian Unit (grad / gon)
Centesimal Metric Division- Creator & Origin: Conceived during French metric reforms to establish base-10 circular angles.
- Standard Definition: Defined as 1/400 of a circle (1 grad = 3,240 arcsec, 100 grad = 90°).
- Everyday Focus: Alpine railway gradients, civil boundary surveys, theodolite angles, and CAD coordinates.
Frequently Asked Questions
Q.How many gradians are in one second of arc?
One second of arc equals exactly 1/3,240 gradian (approximately 0.000308642 grad or gon).
Q.What is the reverse conversion from gradians to arcseconds?
To convert back, use the Gradian to Second of Arc Converter where 1 grad equals 3,240 arcsec.
Q.How many gradians is 3,240 arcseconds?
3,240 arcseconds equals exactly 1 gradian (1 gon).
Q.How many gradians is 324,000 arcseconds (90 degrees)?
324,000 arcseconds equals exactly 100 gradians (100 gon).
Q.How do you convert arcseconds to gradians?
Divide the number of arcseconds by 3,240: Gradians = Arcseconds / 3,240.