Gradian to Second of Arc Conversion Chart
| Gradian (grad) | Second of arc (arcsec) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.0003 grad | 0.972 arcsec | One Arcsecond Baseline Astronomical Parallax in Gradians | 0.0003 × 3240 = 0.972 arcsec |
| 0.001 grad | 3.24 arcsec | High-Precision Electronic Theodolite Angular Tolerance | 0.001 × 3240 = 3.24 arcsec |
| 0.01 grad | 32.4 arcsec | Centesimal Centigrad Geodetic Triangulation Precision | 0.01 × 3240 = 32.4 arcsec |
| 0.05 grad | 162 arcsec | Half Centigrad Topographic Offset in Arcseconds | 0.05 × 3240 = 162 arcsec |
| 0.1 grad | 324 arcsec | One-Tenth Gradian Cadastral Station Misclosure Arc | 0.1 × 3240 = 324 arcsec |
| 0.5 grad | 1620 arcsec | Half Gradian Centesimal Deflection in Arcseconds | 0.5 × 3240 = 1620 arcsec |
| 1 grad | 3240 arcsec | Exact International Definition of 3,240 Arcseconds in Gradian | 1 × 3240 = 3240 arcsec |
| 2 grad | 6480 arcsec | Two Gradians Land Surveying Traverse Displacement | 2 × 3240 = 6480 arcsec |
| 5 grad | 16200 arcsec | Five Gradians Topographic Mapping Sector Coverage | 5 × 3240 = 16200 arcsec |
| 10 grad | 32400 arcsec | Ten Gradians Decimal Metric Sector in Arcseconds | 10 × 3240 = 32400 arcsec |
| 20 grad | 64800 arcsec | Twenty Gradians Centesimal Vector in Arcseconds | 20 × 3240 = 64800 arcsec |
| 50 grad | 162000 arcsec | Half Right Angle Fifty Gradians Metric Octant Arcseconds | 50 × 3240 = 162000 arcsec |
| 100 grad | 324000 arcsec | Perpendicular Right Angle Exactly 324,000 Arcseconds | 100 × 3240 = 324000 arcsec |
| 200 grad | 648000 arcsec | Straight Semicircle Angle Exactly 648,000 Arcseconds | 200 × 3240 = 648000 arcsec |
| 400 grad | 1296000 arcsec | Full Geometric Circle Revolution Exactly 1,296,000 Arcseconds | 400 × 3240 = 1296000 arcsec |
Gradian to Second of arc Formula & Unit Definitions
The conversion from gradians to seconds of arc is governed by the exact integer ratio of 3,240 (1 grad = 3,240 arcsec). To convert gradians into seconds of arc, multiply the gradian value by 3,240. Conversely, to convert seconds of arc into gradians, divide the arcsecond value by 3,240 (or multiply by ~0.000308642).
Quick Estimation: Multiply gradians by 3,240 (or multiply by 54 to get arcminutes, then multiply by 60). Also note that 1 centigrad (0.01 grad) equals exactly 32.4 arcseconds, and 1 milligon equals exactly 3.24 arcseconds. For example: 0.1 grad = 324 arcsec; 1 grad = 3,240 arcsec; 100 grad = 324,000 arcsec.
Gradian Unit (grad / gon)
Centesimal Metric Division- Creator & Origin: French Revolutionary metric commission (1790s) to create a decimal circle.
- Standard Definition: Defined as exactly 1/400 of a complete circle (100 grad = 1 right angle).
- Everyday Focus: Tunnel theodolites, railway superelevation curves, total stations, and European cadastre.
Second of Arc (arcsec / ″)
Fine Sexagesimal Division (1/3,600°)- Creator & Origin: Ptolemy's Almagest and Bessel's 19th-century astronomical measurements.
- Standard Definition: Defined as exactly 1/3,600 of a degree (3,240 arcsec = 1 grad, 1,296,000 arcsec = 1 circle).
- Everyday Focus: Stellar parallax, telescope optical tracking, satellite attitude determination, and laser metrology.
Frequently Asked Questions
Q.How many seconds of arc are in one gradian?
One gradian equals exactly 3,240 seconds of arc (1 grad = 54 × 60 = 3,240 arcsec).
Q.What is the reverse conversion from arcseconds to gradians?
To convert back, use the Second of Arc to Gradian Converter where 1 arcsec equals 1/3,240 grad.
Q.How many arcseconds is 100 gradians (right angle)?
100 gradians equals exactly 324,000 arcseconds (90 × 3,600).
Q.How many arcseconds is 1 centigrad (0.01 grad)?
0.01 grad equals exactly 32.4 arcseconds.
Q.What formula converts gradians to seconds of arc?
Multiply the gradian value by 3,240: Arcseconds = Gradians × 3,240.