Degree to Arc Second Converter
Angle · unit-converter
Convert Degree to Arc Second with a fixed input and output unit, step-by-step formula line, and reference tables. All calculations bridge through radians with fixed definitions (360° per turn, 400 grad per turn, 60′ per degree, 60″ per minute, plus practical units like MOA, urad, and NATO 6400 mils per turn).
About Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
About Arc Second
An arc second is 1/60 of an arc minute or 1/3600 of a degree. Common in astronomy and very fine angular resolution.
How to convert degrees to arc seconds
1 degree equals 3600 arc second in this tool (via radian):
1 deg = (0.017453292519943295 rad ÷ 0.00000484813681109536 rad) arcsec = 3600 arcsec
Each degree carries 0.017453292519943295 rad and each arc second 0.00000484813681109536 rad, so one deg equals 0.017453292519943295 ÷ 0.00000484813681109536 arcsec.
Let θ(deg) be the angle in Degree (deg), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(deg) × (0.017453292519943295 / 0.00000484813681109536)
Equivalently, divide by how many deg fit into one arcsec (rad per arcsec divided by rad per deg):
θ(arcsec) = θ(deg) ÷ 0.0002777777777777778
Examples
Example #1: Convert 1 deg to arc second
1 deg = 1 deg × (0.017453292519943295/0.00000484813681109536) arcsec = 3600 arcsec
1 deg = 1 deg ÷ 0.0002777777777777778 = 3600 arcsec
1 deg × (0.017453292519943295/0.00000484813681109536) = 3,600.000000 arcsec
Example #2: Convert 10 deg to arc second
10 deg = 10 deg × (0.017453292519943295/0.00000484813681109536) arcsec = 36000 arcsec
10 deg = 10 deg ÷ 0.0002777777777777778 = 36000 arcsec
10 deg × (0.017453292519943295/0.00000484813681109536) = 36,000.000000 arcsec
Summary
To convert Degree to Arc Second, multiply the value in deg by (0.017453292519943295 rad per deg) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_deg × (0.017453292519943295 / 0.00000484813681109536). Numerically, 1 deg equals 3600 arcsec.
Relationship context
Both Degree and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per deg) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Degree (deg) | Arc Second (arcsec) |
|---|---|
| 0.1 | 360 |
| 1 | 3,600 |
| 2 | 7,200 |
| 3 | 10,800 |
| 4 | 14,400 |
| 5 | 18,000 |
| 6 | 21,600 |
| 7 | 25,200 |
| 8 | 28,800 |
| 9 | 32,400 |
| Degree (deg) | Arc Second (arcsec) |
|---|---|
| 10 | 36,000 |
| 20 | 72,000 |
| 30 | 108,000 |
| 40 | 144,000 |
| 50 | 180,000 |
| 60 | 216,000 |
| 70 | 252,000 |
| 80 | 288,000 |
| 90 | 324,000 |
| 100 | 360,000 |