Fidamen

Convert Radians to Arcminutes - Angle Converter

This converter turns an angle measured in radians into arcminutes (sometimes written as minutes of arc). Radians are the SI-compatible angular measure used in mathematics and many physics formulas; arcminutes are a sexagesimal subdivision of degrees commonly used in surveying, astronomy, and optical specifications.

Use this tool when you need a rapid, reliable conversion with clear guidance on how the value was computed, how to report significant figures, and what instrument/measurement limits may affect the meaningful precision of the result.

Updated Nov 3, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record 404595f5a010 • Reviewed by Fidamen Standards Committee

Interactive Converter

Convert between radian and arcminute with precision rounding.

Quick reference table

RadianArcminute
RAD 1.00 rad3,437.7468 arcmin
RAD 5.00 rad17,188.7339 arcmin
RAD 10.00 rad34,377.4677 arcmin
RAD 25.00 rad85,943.6693 arcmin
RAD 50.00 rad171,887.3385 arcmin
RAD 100.00 rad343,774.6771 arcmin

Methodology

We follow the standard relationship between radians and degrees and the sexagesimal subdivision of degrees: 1 radian = 180/pi degrees, and 1 degree = 60 arcminutes. This chain gives the exact factor 1 radian = 10800 / pi arcminutes.

Where relevant, recommended practices from national measurement authorities and metrology guidance are used to describe numeric precision and reporting. For practical work (surveying, astronomy, optics), compare the computed precision to instrument resolution and environmental limitations before reporting results.

Key takeaways

Conversion factor (exact): 1 radian = 10800 / π arcminutes.

For engineering and lab reporting, match rounding to instrument resolution (for example, typical theodolite Vernier readings or CCD plate scales).

Consult national metrology guidance for traceability and calibration requirements when angle measurements are part of regulated or high-accuracy workflows.

Worked examples

1 radian → 1 * (10800 / π) ≈ 3437.7468 arcminutes

0.1 radian → 0.1 * (10800 / π) ≈ 343.7747 arcminutes

2π radians → 2π * (10800 / π) = 21600 arcminutes (which equals 360 degrees)

F.A.Q.

What is the exact mathematical relationship between radians and arcminutes?

Exactly: 1 radian = 10800 / π arcminutes. Numerically 1 radian ≈ 3437.7467707849397 arcminutes.

How many decimal places should I keep when converting?

Keep as many digits as needed to remain above the instrument or method uncertainty. For casual use 4–6 significant figures is common; for precision surveying or astronomy, match the value to your calibration certificate or sensor resolution and report uncertainty alongside the converted value.

Why are radians considered 'dimensionless' in SI but still used as angles?

In SI, the radian is defined as the ratio of two lengths (arc length divided by radius) and therefore technically dimensionless. Practically, it is treated as an angular unit to avoid confusion and to ensure correct interpretation in formulas.

Can I convert directly to arcseconds from radians?

Yes. Since 1 arcminute = 60 arcseconds, multiply arcminutes by 60. Combined: arcseconds = radians * (10800 / π) * 60 = radians * (648000 / π).

Are there regulatory or calibration guidance I should follow when reporting these conversions?

For traceable, high-accuracy angle measurements consult national metrology guidance and calibration providers. Agencies such as NIST and national geodetic services publish best practices and calibration standards relevant to surveying, optics, and instrumentation.

How do instrument limits affect the meaningful precision of a converted value?

If a sensor or instrument reports angles to the nearest 0.01 degree, converting that reading to arcminutes doesn't increase information—rounding should reflect the original instrument resolution and stated uncertainty. Always propagate uncertainty when conversions are part of measurement chains.

Sources & citations

Further resources

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: 404595f5a010

What changed (latest)

v1.0.0 • 2025-11-03 • 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 3, 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 • 2025-11-03 • 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: e5f29bb35507