Convert Gradians to Arcseconds - Angle Converter
This converter translates angles measured in gradians (also called grads or gon) into arcseconds using an exact mathematical relationship. Gradians subdivide the right angle into 100 parts and the full circle into 400 gradians; arcseconds are the sexagesimal subdivision of degrees (1° = 60′ = 3600″).
The conversion here is exact and intended for professional contexts (surveying, geodesy, navigation, astronomy) where traceability and instrument resolution matter. Where applicable, verify results against instrument calibration certificates and follow national metrology guidelines for measurement uncertainty.
Use the simple input to convert a single value; consult the methodology and FAQs for the exact factor, recommended rounding, and notes on instrument limits and regulatory traceability.
Governance
Record 9550751d04bf • Reviewed by Fidamen Standards Committee
Interactive Converter
Convert between gradian and arcsecond with precision rounding.
Quick reference table
| Gradian | Arcsecond |
|---|---|
| 1 grad | 3,240 arcsec |
| 5 grad | 16,200 arcsec |
| 10 grad | 32,400 arcsec |
| 25 grad | 81,000 arcsec |
| 50 grad | 162,000 arcsec |
| 100 grad | 324,000 arcsec |
Methodology
Start from the fundamental relationships: 1 full circle = 400 gradians = 360 degrees, and 1 degree = 3600 arcseconds. Combine these to derive the exact factor between gradians and arcseconds.
Because the relationships above are exact by definition, the arithmetic conversion is exact: 1 gradian = (9/10) degree = 0.9° = 3240 arcseconds. For conversion use the integer factor 3240 or its reciprocal depending on direction.
When applying results in practice, choose rounding consistent with instrument resolution and the intended use: laboratory reporting should follow NIST/ISO traceability and report uncertainty; field work typically rounds to the nearest instrument least-count (see FAQs and citations).
Worked examples
Example 1: 12.5 gradians → 12.5 × 3240 = 40,500 arcseconds.
Example 2: 1,000 arcseconds → 1,000 ÷ 3240 ≈ 0.3086419753 gradians (round to required precision).
F.A.Q.
What is the exact conversion factor between gradians and arcseconds?
Exactly 1 gradian = (9/10) degree and 1 degree = 3600 arcseconds, so 1 gradian = 0.9° = 0.9 × 3600 = 3240 arcseconds. The reciprocal is 1 arcsecond = 1/3240 gradian (≈ 0.00030864197530864197 gradian).
Is this conversion exact or approximate?
The mathematical relationship is exact because it derives from the definitions of the units. Any approximation arises only from decimal rounding when displaying or reporting values.
How should I choose rounding or significant figures?
Match rounding to the resolution of your measurement device and the uncertainty you can substantiate. For high-precision lab work, keep enough digits to encompass instrument uncertainty and report uncertainty per NIST/ISO guidance. For field surveying, round to the instrument least-count (for example, a device with 1 arcsecond resolution need not report fractional arcseconds).
What instrument limits or calibration steps should I consider?
Verify the instrument's least-count and calibration certificate. Ensure angular sensors or theodolites have current calibration and that you document traceability to a national metrology institute when required. Follow manufacturer procedures for periodic calibration and use appropriate environmental controls to reduce systematic error.
Can I convert bearings or directions that cross the 0/360 (wrap-around) boundary?
Yes. Convert the numeric angle value using the factor shown, then apply modular arithmetic as required for wrap-around (e.g., normalize to the desired range such as 0–400 gradians or 0–360 degrees) so directional semantics are preserved.
Which professional standards or references cover these units and traceability?
Guidance on units, traceability, and reporting of measurement uncertainty is available from national metrology bodies and standards organizations. See NIST guidance and national geodetic services for traceability and reporting practices; refer to the citations below for authoritative resources.
What are common applications for converting gradians to arcseconds?
Applications include surveying and civil engineering (where gradians are sometimes used for bearings), cartography, geodetic computations, and astronomy when mixing sexagesimal and decimal angular units. Always maintain consistent units across computations to avoid transcription errors.
Sources & citations
- NIST — Guide for the Use of the International System of Units (SI) and related guidance — https://www.nist.gov/pml/weights-and-measures/si-brochure
- NOAA National Geodetic Survey — Geodesy and coordinate reference resources — https://geodesy.noaa.gov
- MIT OpenCourseWare — mathematics and physics course materials (reference for angular measures and conversions) — https://ocw.mit.edu
- ISO 80000-3:2019 — Space and time — https://www.iso.org/standard/64974.html
- NIST SP 811 — Guide for the Use of the International System of Units — https://www.nist.gov/pml/special-publication-811
Further resources
Related tools
External guidance
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: 9550751d04bfWhat changed (latest)
v1.0.0 • 2025-11-25 • 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 • 2025-11-25 • 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 25, 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 • 2025-11-25 • 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: d6a98bf5460f