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).
Governance
Record 10c79d2389ee • Reviewed by Fidamen Standards Committee
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).
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).
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)
F.A.Q.
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/
- ISO 80000-3:2019 — Space and time — https://www.iso.org/standard/64974.html
Further resources
Related tools
External guidance
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: 10c79d2389eeWhat changed (latest)
v1.0.0 • 2025-11-16 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
What changed (latest)
v1.0.0 • 2025-11-16 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Engine
v1.0.0
Data
Baseline (no external datasets)
Content
v1.0.0
UI
v1.0.0
Governance
Last updated: Nov 16, 2025
Reviewed by: Fidamen Standards Committee (Review board)
Credentials: Internal QA
Risk level: low
Reviewer profile (entity)
Fidamen Standards Committee
Review board
Internal QA
Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person
Semantic versioning
- MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
- MINOR: New features or fields that do not change existing outputs for the same inputs.
- PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.
Review protocol
- Verify formulas and unit definitions against primary standards or datasets.
- Run golden-case regression suite and edge-case suite.
- Record reviewer sign-off with credentials and scope.
- Document assumptions, limitations, and jurisdiction applicability.
Assumptions & limitations
- Uses exact unit definitions from the Fidamen conversion library.
- Internal calculations use double precision; display rounding follows the unit's configured decimal places.
- Not a substitute for calibrated instruments in regulated contexts.
- Jurisdiction-specific rules may require official guidance.
Change log
v1.0.0 • 2025-11-16 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: 09f021b1bb63