Convert Gradians to Arcminutes - Angle Converter
This converter converts gradians (gon) to arcminutes (′) using the fixed geometric relationship between circle subdivisions. Gradians partition a full circle into 400 units; arcminutes partition a degree into 60 minutes.
Use this tool for surveying, mapping, geodesy, education, or any situation where you need a precise, reproducible unit conversion. Results are exact arithmetically (no empirical approximation) — apply rounding only to match instrument resolution or reporting requirements.
Governance
Record eff216b4528d • Reviewed by Fidamen Standards Committee
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Methodology
A full circle equals 400 gradians and also equals 360 degrees. Therefore one gradian is 1/400 of a circle, which equals 360/400 = 9/10 degrees.
Because one degree equals 60 arcminutes, multiply the gradian value by 9/10 and then by 60 to convert to arcminutes. That reduces to a single conversion factor: 1 gradian = 54 arcminutes.
When converting measured values, consider instrument resolution and uncertainty. Report converted values to a precision consistent with the original measurement (for example, if a theodolite reads to 0.01 gon, convert and round to a precision that reflects that resolution).
Worked examples
Example 1: 1 grad → arcminutes: 1 × 54 = 54 arcminutes.
Example 2: 2.5 grad → arcminutes: 2.5 × 54 = 135 arcminutes.
Example 3 (inverse): 270 arcminutes → gradians: 270 / 54 = 5 gradians.
F.A.Q.
What is a gradian (gon)?
A gradian, also called a gon, is an angular unit where a full circle equals 400 gradians. It is commonly used in surveying and civil engineering in some countries and contexts.
Why is the conversion factor exactly 54?
Because 1 gradian = 9/10 degree and 1 degree = 60 arcminutes, so 1 gradian = 0.9 × 60 = 54 arcminutes. This is a fixed geometric relationship, not an empirical approximation.
How should I handle rounding after conversion?
Round converted results to reflect the resolution and uncertainty of the original measurement. For example, if the instrument reports to 0.01 gon, convert then round so the reported arcminutes do not imply more precision than the original reading supports.
Is the gradian an SI unit?
The gradian is not a base SI unit. Conventional angular units such as the degree are widely accepted for use with the SI; references on unit usage and conventions are published by standards organizations and NIST.
Are there practical limits or calibration considerations?
Yes. Surveying instruments (theodolites, total stations, GNSS-based attitude sensors) have finite resolution and systematic errors. Always check instrument calibration certificates and apply appropriate uncertainty propagation when reporting converted values.
Can I convert large arrays of values programmatically?
Yes. Use the exact factor 54 to convert numerically: arcminutes = grads × 54. For batch conversions, propagate numeric precision consistent with your data type and rounding policy.
Sources & citations
- NIST Special Publication 811 — Guide for the Use of the International System of Units (SI) — https://www.nist.gov/pml/special-publication-811
- ISO standard information — quantities and units (angle guidance reference) — https://www.iso.org
- National Geodetic Survey (NOAA) — geodetic and surveying resources — https://www.ngs.noaa.gov
- MIT OpenCourseWare — mathematics and trigonometry resources — https://ocw.mit.edu
- ISO 80000-3:2019 — Space and time — https://www.iso.org/standard/64974.html
Further resources
Related tools
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: eff216b4528dWhat changed (latest)
v1.0.0 • 2025-11-22 • 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 • 2025-11-22 • 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 22, 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 • 2025-11-22 • 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: 7dd8649de543