Degree to Second Converter
Enter the value that you want to convert degree (°) to second (") or second to degree.Also written as ° to " conversion.
1 degree = 3599.9971200 second
Formula: second = degree value × 3599.9971200
° to " — degree to second
10 degree = 35999.97120 second
Popular Degree Converters:
Why Convert Degree to Second?
What is Degree?
Dating back to ancient Babylonian astronomy, the degree divides a full rotation into 360 equal parts.
The Babylonians used a base-60 number system and observed that the sun moved approximately one degree per day across the sky over a year. The 360° circle became universal in navigation, surveying, architecture, and education. Degrees remain the standard angle unit in everyday life — from compass bearings and map coordinates to smartphone screen rotation and camera field-of-view specifications.
What is Second?
Second (") is a unit of degree measurement. 1 second is equal to 0.0002778 degree.
Why Angle Conversions Matter
Angle conversions bridge the gap between everyday measurement (degrees) and mathematical computation (radians). A mechanical engineer designing a robotic arm needs radians for inverse kinematics. A pilot reads compass headings in degrees. A surveyor might work in gradians. Game developers convert between degrees (artist-friendly) and radians (GPU shaders) hundreds of times per frame. Understanding these conversions is essential across STEM fields, navigation, and digital media production.
degree to second metric conversion table
| 0.01 ° | = | 35.99997 " |
| 0.1 ° | = | 359.99971 " |
| 1 ° | = | 3599.99712 " |
| 2 ° | = | 7199.99424 " |
| 3 ° | = | 10799.99136 " |
| 4 ° | = | 14399.98848 " |
| 5 ° | = | 17999.98560 " |
| 6 ° | = | 21599.98272 " |
| 7 ° | = | 25199.97984 " |
| 8 ° | = | 28799.97696 " |
| 9 ° | = | 32399.97408 " |
| 10 ° | = | 35999.97120 " |
| 11 ° | = | 39599.96832 " |
| 12 ° | = | 43199.96544 " |
| 13 ° | = | 46799.96256 " |
| 14 ° | = | 50399.95968 " |
| 15 ° | = | 53999.95680 " |
| 16 ° | = | 57599.95392 " |
| 17 ° | = | 61199.95104 " |
| 18 ° | = | 64799.94816 " |
| 19 ° | = | 68399.94528 " |
| 20 ° | = | 71999.94240 " |
| 30 ° | = | 107999.91360 " |
| 40 ° | = | 143999.88480 " |
| 50 ° | = | 179999.85600 " |
| 60 ° | = | 215999.82720 " |
| 70 ° | = | 251999.79840 " |
| 80 ° | = | 287999.76960 " |
| 90 ° | = | 323999.74080 " |
| 100 ° | = | 359999.71200 " |
| 200 ° | = | 719999.42400 " |
| 300 ° | = | 1079999.13600 " |
| 400 ° | = | 1439998.84800 " |
| 500 ° | = | 1799998.56000 " |
| 600 ° | = | 2159998.27200 " |
| 700 ° | = | 2519997.98400 " |
| 800 ° | = | 2879997.69600 " |
| 900 ° | = | 3239997.40800 " |
| 1000 ° | = | 3599997.12000 " |
How to Convert ° to " (Degree to Second)?
We can convert degree to second by using an example.
Example:
Convert 20 Degree to Second?
We know 1 Degree = 3599.9971200 second; 1 Second = 0.0002778 degree.
20 degree = ___"
20 × 3599.9971200 = 71999.94240 " (we know 1 degree = 3599.9971200 second)
Answer:
20 degree = 71999.94240 second
How to Convert Degrees to Arcseconds (Step-by-Step)
One degree contains 3600 arcseconds (60 arcminutes × 60 arcseconds per arcminute). To convert:
- Write down the angle in degrees.
- Multiply the degree value by 3600.
- The result is the angle in arcseconds (″).
- For DMS format: separate whole degrees, multiply decimal by 60 for minutes, then decimal of minutes by 60 for seconds.
Degrees to Arcseconds Quick Reference
| Degree | Second |
|---|---|
| 1° | 3600″ |
| 0.1° | 360″ |
| 0.01° | 36″ |
| 0.001° | 3.6″ |
| 0.0001° | 0.36″ |
| 15° | 54000″ |
Solved Examples
Question 1: Convert 0.05 degrees to arcseconds.
Solution:
Arcseconds = Degrees × 3600
= 0.05 × 3600
= 180
Answer: 0.05° = 180 arcseconds
Question 2: Express 2.5° in DMS (degrees, minutes, seconds) format.
Solution:
Whole degrees: 2°
Remainder: 0.5° × 60 = 30′
No remaining decimal in minutes.
Answer: 2.5° = 2° 30′ 0″
Question 3: Convert 45.7625° to DMS format.
Solution:
Whole degrees: 45°
Decimal: 0.7625° × 60 = 45.75′
Whole minutes: 45′
Remaining: 0.75′ × 60 = 45″
Answer: 45.7625° = 45° 45′ 45″
Question 4: Stellar parallax of Proxima Centauri is 0.7687″. What fraction of a degree?
Solution:
Degrees = Arcseconds ÷ 3600
= 0.7687 / 3600
= 0.0002135°
Answer: 0.7687″ = 0.000214° (incredibly tiny angle)
Practice Questions
Try solving these on your own to test your understanding:
- Convert 0.25° to arcseconds. (Answer: 900″)
- Express 73.1547° in DMS. (Answer: 73° 9′ 17″)
- How many arcseconds in a full circle? (Answer: 1,296,000″)
- Convert 0.0028° to arcseconds. (Answer: 10.08″)
- A telescope resolves 0.5 arcseconds. What is this in degrees? (Answer: 0.000139°)
Arcseconds in Astronomy and Stellar Distances
The parsec (parallax-arcsecond) is defined as the distance at which a star shows 1 arcsecond of parallax. Proxima Centauri, the nearest star, has a parallax of only 0.77 arcseconds (distance: 1.3 parsecs = 4.24 light-years). Telescope resolution measured in arcseconds determines what details can be observed — atmospheric turbulence limits ground-based telescopes to about 1 arcsecond resolution without adaptive optics.
Arcseconds in GPS and Geodesy
High-precision GPS receivers report positions to 0.0001° (0.36 arcseconds), corresponding to about 11 meters accuracy. Survey-grade GPS achieves centimeter accuracy — fractions of an arcsecond. At the equator, 1 arcsecond of longitude = 30.87 meters; 1 arcsecond of latitude = 30.72 meters everywhere. This makes arcseconds a practical unit for expressing positioning accuracy.
Key Takeaways
- Multiply degrees by 3600 to get arcseconds (1° = 3600″).
- 1 arcsecond ≈ 31 meters on Earth's surface.
- DMS format: degrees° minutes′ seconds″ (e.g., 45° 30′ 15″).
- Telescope resolution is measured in arcseconds.
- The parsec distance unit is defined using arcsecond parallax.
- High-precision GPS works at sub-arcsecond accuracy.
Degree to Second Conversion Formula
second = degree × 3599.9971200
1 degree = 3599.9971200 second
1 second = 0.0002778 degree
Reverse: degree = second × 0.0002778
Frequently Asked Questions
How many second are in 1 degree?
There are 3599.9971200 second in 1 degree. To convert degree to second, multiply the value by 3599.9971200.
How do I convert degree to second?
Multiply your degree value by 3599.9971200 to get the equivalent in second. For example, 5 degree = 5 × 3599.9971200 = 17999.98560 second.
How do I convert second to degree?
Multiply your second value by 0.0002778 to get the equivalent in degree. Alternatively, divide by 3599.9971200.
What is 10 degree in second?
10 degree is equal to 35999.97120 second.
What is 100 degree in second?
100 degree is equal to 359999.71200 second.