A degree is pi/180 radians.
Degrees to Arcseconds Converter — deg to arcsec
Convert Degree (deg) to Arcsecond (arcsec) using the exact conversion factor (1 degree = 3,600 arcsecond). See the formula, worked examples, conversion table, history, and common uses.
Degrees to Arcseconds converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
One arcsecond is 1/3600 degree.
Result = input x 0.01745329252 / 4.84813681e-6.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Degrees to Arcseconds
Degree and Arcsecond are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Degree is most often used for navigation and cartography (latitude/longitude).
Formula
arcseconds = degrees × 3600
This factor comes from each unit's defined relationship to the category's base unit: 1 degree equals 0.0174532925199 base units, and 1 arcsecond equals 0.0000048481368111 base units, so dividing one by the other gives the direct degree-to-arcsecond factor of 3600.
Simple example
1 deg × 3600 = 3,600 arcsec
1 degree = 3,600 arcseconds.
Real-world example
90 deg × 3600 = 324,000 arcsec
90 degrees = 324,000 arcseconds.
Conversion table
| Degree (deg) | Arcsecond (arcsec) |
|---|---|
| 0 deg | 0 arcsec |
| 30 deg | 108,000 arcsec |
| 45 deg | 162,000 arcsec |
| 90 deg | 324,000 arcsec |
| 180 deg | 648,000 arcsec |
| 360 deg | 1,296,000 arcsec |
Reverse conversion: Arcsecond to Degree
1 arcsec × 0.0002777777778 = 0.0002777778 deg
1 arcsecond = 0.0002777778 degrees.
degrees = arcseconds × 0.000277777777778
For a page dedicated to this direction, see Arcsecond to Degree.
Understanding the Degree
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
Where it's used: Used worldwide for navigation, geography, and everyday angle measurement.
Uses of the Degree today
- Navigation and cartography (latitude/longitude)
- Construction and surveying
- Everyday angle measurement (protractors, sports)
History of the Degree
The 360-degree circle traces to ancient Babylonian astronomy, whose base-60 (sexagesimal) number system made 360 — divisible by many small numbers — a practical choice for dividing a circle. The convention passed through Greek astronomy (Hipparchus, Ptolemy) into common use.
Historical origin. Degree was not the invention of a single named person; it developed through the process described above.
Understanding the Arcsecond (arcsec)
One arcsecond is 1/3600 degree.
Degree — sources
- NIST Special Publication 811 — Lists the degree among non-SI units accepted for use with SI.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many arcseconds are in 1 degree?
1 degree equals 3,600 arcseconds, using the exact defined conversion factor rather than an estimate.
How do I convert degree to arcsecond?
Multiply the degree value by 3600. The converter above does this instantly to whatever precision you set.
How do I convert arcsecond back to degree?
Use the reverse factor: 1 arcsecond equals 0.0002777778 degrees. You can also use the swap control in the converter above to flip the direction instantly.
What is a degree?
Degree (deg) measures angle. A degree is 1/360 of a full rotation, a division dating to Babylonian base-60 astronomy. It is classified as a Non-SI unit accepted for use with SI.
What is a arcsecond?
Arcsecond (arcsec) is a unit of angle.
Is the degree to arcsecond conversion exact?
Yes. Both degree and arcsecond are defined by fixed standards rather than physical artifacts, so the factor of 3600 used above is exact to as many digits as you choose to display.
Where is the degree still used today?
Used worldwide for navigation, geography, and everyday angle measurement.