Convert Degrees to Arcseconds - Angle Converter
Convert angular values from degrees to arcseconds for high-precision work in astronomy, surveying, microscopy, or optics. This converter uses the exact sexagesimal definitions commonly adopted in scientific and engineering practice.
One degree is defined as 1/360 of a full circle and is subdivided into 60 arcminutes and 60 arcseconds per arcminute. Because those subdivisions are exact integers, the conversion between degrees and arcseconds is an exact integer factor (no empirical calibration required).
Interactive Converter
Convert between degree and arcsecond with precision rounding.
Quick reference table
| Degree | Arcsecond |
|---|---|
| 1 ° | 3,600.001543 arcsec |
| 5 ° | 18,000.007714 arcsec |
| 10 ° | 36,000.015429 arcsec |
| 25 ° | 90,000.038572 arcsec |
| 50 ° | 180,000.077144 arcsec |
| 100 ° | 360,000.154287 arcsec |
Methodology
We base the conversion on the sexagesimal system: 1 degree = 60 arcminutes and 1 arcminute = 60 arcseconds. Multiply degrees by 60 to get arcminutes, and multiply arcminutes by 60 to get arcseconds. The conversion is therefore exact: 1 degree = 3600 arcseconds.
For discipline-level context, this relationship is the same convention used by standards organizations and astronomy references. When reporting high-precision values, account for instrument resolution and rounding rules appropriate to your application (for example, round to instrument least count or report uncertainty alongside the converted value).
Worked examples
Example 1: 1.5° → 1.5 × 3600 = 5400″
Example 2: 0.0002777778° → 0.0002777778 × 3600 ≈ 1″ (useful when converting instrument resolution in degrees to arcseconds)
Key takeaways
Conversion is exact and deterministic: multiply degrees by 3600 to obtain arcseconds.
When using results in experimental or survey reports, pair converted values with measurement uncertainty and note instrument resolution (see FAQs).
Further resources
External guidance
Expert Q&A
What is the exact numeric relationship between degrees and arcseconds?
Exactly 1 degree = 3600 arcseconds, because 1 degree = 60 arcminutes and 1 arcminute = 60 arcseconds.
How do I convert negative angles or angles larger than 360°?
Apply the same multiplication rule to the signed or absolute degree value. For angles larger than 360°, the numeric conversion still uses ×3600; if you need a canonical angle within a circle, reduce modulo 360° first, then convert.
How should I report precision after conversion?
Round according to the least-significant digit of the original measurement or the instrument resolution. For example, if your angle is measured to ±0.01° (36″), report arcseconds with uncertainty (e.g., 36″) rather than implying greater precision.
Does this conversion account for projection, refraction, or instrument calibration?
No. This converter performs only the mathematical unit conversion. Corrections for atmospheric refraction, optical distortion, or calibration offsets must be applied separately using discipline-specific models and calibration data.
How is an arcsecond related to radians?
1 arcsecond = (π / 648000) radians, because 1° = π/180 radians and 1° = 3600″, so 1″ = (π/180) / 3600 = π/648000 radians.
Sources & citations
- NIST — SI Unit Definitions and Conventions — https://www.nist.gov/pml/special-publication-811
- International Astronomical Union (IAU) — Measuring the Sky — https://www.iau.org/public/themes/measuring/
- U.S. Naval Observatory — Astronomical Applications and Conventions — https://aa.usno.navy.mil/
- MIT OpenCourseWare — Astronomy and angular measurement resources — https://ocw.mit.edu/