Angle Converter
Degree
Definition: A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees.
History/origin: The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun advanced roughly one degree in the sky each day.
Current use: Degrees are widely used in geometry, trigonometry, geography (latitude and longitude), astronomy, and everyday engineering applications.
Second of arc
Definition: A second of arc, arcsecond (arcsec), or second arc, denoted by the symbol ", is a unit of angular measurement equal to 1/60 of an arcminute, or 1/3600 of a degree.
History/origin: Like the arcminute, the arcsecond is derived from the ancient Babylonian sexagesimal system. It was later formalized by Greek mathematicians like Ptolemy and Hipparchus for charting stars.
Current use: Arcseconds are widely used in astronomy to measure the apparent sizes of and distances between objects in the sky. They are also essential in high-precision GPS and geomatics.
Degree to Second of arc Conversion Table
| Degree [deg] | Second of arc [sec] |
|---|---|
| 0.01 deg | 35.99999712 sec |
| 0.1 deg | 359.9999712 sec |
| 1 deg | 3599.999712 sec |
| 2 deg | 7199.999424 sec |
| 3 deg | 10799.999136 sec |
| 5 deg | 17999.99856 sec |
| 10 deg | 35999.99712 sec |
| 20 deg | 71999.99424 sec |
| 50 deg | 179999.9856 sec |
| 100 deg | 359999.9712 sec |
| 1000 deg | 3599999.71200002 sec |
How to Convert Degree to Second of arc
1 deg = 3599.999712 sec
1 sec = 0.00027778 deg
Example: convert 15 deg to sec:
15 deg = 15 × 3599.999712 sec = 53999.99568 sec
Did You Know?
- A full circle is divided into 360 degrees. This system likely originated from ancient Babylonians who used a base-60 number system.
- An arcsecond is extremely small—just 1/3600th of a degree! Astronomers use it to measure parallax and the precise positions of distant stars.