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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, 2025

Interactive Converter

Convert between radian and arcminute with precision rounding.

Quick reference table

RadianArcminute
1 rad3,437.7468 arcmin
5 rad17,188.7339 arcmin
10 rad34,377.4677 arcmin
25 rad85,943.6693 arcmin
50 rad171,887.3385 arcmin
100 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.

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)

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.

Expert Q&A

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