Convert arc minutes to degrees and radians first, then check whether the same angle is meaningful at your working radius. The direct answer: 1 arc minute is equal to 1/60 degree, 60 arc-seconds, and 0.0002908882087 rad.
Degree
0.0166666667
Radian
2.908882e-4
At 100 mm
29.09 um
Start with the common question 1 arc minute is equal to what, then convert any arc-minute, degree, arc-second, or radian value and project the angular error to a working radius.
error um = radians x radius mm x 1000.Degree
0.0166666667
Radian
2.908882e-4
At 100 mm
29.09 um
Report Summary
The tool answers the immediate unit question. The report layer explains when the number is useful, when it is insufficient, and how to apply it in a rotary-axis decision.
The conversion is exact
1 arc minute is equal to 1/60 degree, 60 arc-seconds, and pi/10800 radians. NIST SP 811 gives minute (angle) to radian as 2.908882E-04, matching 0.0002908882087 rad.
Evidence: BIPM SI Brochure and NIST SP 811 angle conversion tables
Radians matter for real tolerances
At a 100 mm working radius, 1 arc minute projects to about 29.09 um of linear displacement. At 500 mm, the same angle projects to about 145.44 um.
Evidence: Linear projection = angle in radians x radius
The page should stay canonical
Queries such as arc-minute, 1 arc minute is equal to, 1 arc minute in radians, and arc minute to degree ask for the same conversion cluster. This page answers the equality query directly while keeping one canonical route.
Evidence: OpenSpec alias_merge decision for this change
Conversion is not machine accuracy
The calculator converts units and screens tolerance impact. It does not prove backlash, encoder, thermal, fixture, or load uncertainty under production conditions.
Evidence: NIST TN 1297 uncertainty guidance and ISO 230-2 axis-positioning test scope
Projection is a small-angle screen
At 1 arc minute and 100 mm radius, arc length and chord displacement differ by about 1.026e-4 nm, so the small-angle projection is numerically safe for this conversion. The same formula still does not cover runout, Abbe error, or multi-axis coupling.
Evidence: Radian definition as arc length divided by radius; installation terms remain separate
Acceptance needs repeated direct measurement
ISO 230-2:2014 is useful because it covers accuracy and repeatability of NC axes by direct measurement of individual axes, including rotary axes, with repeated measurements at each position. A catalog conversion alone is not equivalent evidence.
Evidence: ISO 230-2:2014 abstract and scope
The alias phrase 1 arc minute is equal to is answered here with the exact degree, arc-second, and radian identities. It shares the same arc-minute conversion cluster as related radian and degree queries, so the canonical route remains /learn/arc-minute.
Use / Do Not Use
The conversion is exact. The decision context is not exact unless you also know radius, tolerance, and uncertainty contributors.
| Profile | Good fit | Boundary |
|---|---|---|
| Use this page | Unit conversion, RFQ tolerance translation, quick rotary-axis screening, and explaining 1 arc minute in radians. | Works when the question is about angle units or first-pass tolerance impact. |
| Use with caution | Supplier comparison, acceptance planning, and production capability review. | Add backlash, encoder accuracy, repeatability, thermal drift, and load effects. |
| Do not use alone | Final metrology sign-off, warranty acceptance, or safety-critical positioning. | Requires a measurement plan, calibrated instruments, and explicit uncertainty budget. |
Key Numbers
All rows use exact angle identities. Linear projection assumes a 100 mm radius and small-angle geometry.
| Input | Degrees | Radians | Arc-seconds | Linear at 100 mm |
|---|---|---|---|---|
| 1 arc minute | 0.0166666667 deg | 0.0002908882087 rad | 60 arc-sec | 29.09 um |
| 5 arc minutes | 0.0833333333 deg | 0.00145444104 rad | 300 arc-sec | 145.44 um |
| 10 arc minutes | 0.166666667 deg | 0.00290888209 rad | 600 arc-sec | 290.89 um |
| 60 arc minutes | 1 deg | 0.0174532925 rad | 3600 arc-sec | 1745.33 um |
Geometry Boundary
The calculator uses arc length because radians are defined by arc length divided by radius. At 1 arc minute the chord difference is effectively zero for screening, but radius still scales the tolerance impact directly.
| Working radius | Arc length | Chord displacement | Arc-chord difference | Decision use |
|---|---|---|---|---|
| 100 mm | 29.08882 um | 29.08882 um | 1.026e-4 nm | Small-angle arc-length projection is effectively identical to chord displacement for first-pass tolerance screening. |
| 500 mm | 145.44410 um | 145.44410 um | 5.128e-4 nm | Radius multiplies the error directly; the geometry model is still simple, but the tolerance impact is five times larger. |
| 1,000 mm | 290.88821 um | 290.88821 um | 1.026e-3 nm | Use installed-axis measurement when fixture offset, runout, or load deflection is no longer negligible. |
Methodology
The method is intentionally simple and reproducible. It converts units first, then applies linear projection only when a radius is provided.
| Step | Formula | Boundary note |
|---|---|---|
| Normalize | arcmin = input x unit factor | 1 degree = 60 arc-min; 1 arc-min = 60 arc-sec. |
| Convert to degree | degree = arcmin / 60 | This answers the canonical arc minute to degree intent. |
| Convert to radian | radian = degree x pi / 180 = arcmin x pi / 10800 | This explicitly answers 1 arc minute in radians. |
| Project linear error | linear um = radian x radius mm x 1000 | Use only as geometry screening, not as complete machine accuracy. |
Evidence
The page relies on stable unit conventions and measurement guidance. Sources were reviewed on 2026-06-07; supplier-specific installed accuracy is not inferred without dated test evidence.
SI angle relationship
BIPM identifies the radian as the coherent SI unit for plane angle and lists degree, minute, and second under long-standing angle units with explicit radian conversions.
Reviewed 2026-06-07
Stable unit convention
BIPM SI Brochure, 9th edition, updated 20261 arc minute to radian factor
NIST SP 811 Appendix B.8 lists minute (angle) to radian with the multiplier 2.908882E-04, which is the rounded value of pi/10800.
Reviewed 2026-06-07
Direct conversion evidence
NIST SP 811 Appendix B.8Degree, minute, second definitions
NIST SP 330 Section 4 lists 1 degree as pi/180 rad, 1 minute as pi/10800 rad, and 1 second as pi/648000 rad.
Reviewed 2026-06-07
Direct definition evidence
NIST SP 330 Section 4Uncertainty combination
NIST TN 1297 defines expanded uncertainty as U = kuc and notes k is typically 2 to 3; k = 2 is commonly used for about 95% confidence when the normal-distribution assumptions are appropriate.
Reviewed 2026-06-07
Measurement reporting guidance
NIST Technical Note 1297Machine acceptance context
ISO 230-2:2014 covers accuracy and repeatability testing for numerically controlled axes by direct measurement of individual axes, applies equally to linear and rotary axes, and uses repeated measurements at each position.
Reviewed 2026-06-07
Acceptance-test scope
ISO 230-2 standard pageResolution is not accuracy
US Digital explains that rotary encoder accuracy may be specified in degrees, arcminutes, or arcseconds, and that encoder accuracy is only one part of overall motion-system accuracy.
Reviewed 2026-06-07
Terminology boundary
US Digital encoder accuracy white paperEvidence Boundaries
The radian value is exact. The engineering decision becomes conditional once the number is used as a proxy for machine behavior.
| Claim | Trust when | Stop when | Evidence |
|---|---|---|---|
| Exact unit conversion | You need to convert arc-minutes, degrees, arc-seconds, or radians. | You need to certify installed machine accuracy or supplier compliance. | BIPM SI Brochure, NIST SP 811, NIST SP 330 |
| Linear projection at a radius | The radius is known and you only need first-pass displacement impact. | Runout, Abbe offset, fixture deflection, or multi-axis coupling matters. | Radian definition and geometry screening assumption |
| Rotary-axis fit decision | The projected angle is far below tolerance and other errors are budgeted. | The projected value is near the limit or production acceptance is required. | NIST TN 1297 and ISO 230-2 acceptance-test context |
| Supplier comparison | All suppliers report the same metric: accuracy, repeatability, or backlash. | One supplier reports resolution while another reports measured accuracy. | Public evidence often lacks uniform test conditions; verify RFQ terms |
Metric Boundaries
The exact conversion is only useful after the supplier term is clear. Resolution, accuracy, repeatability, and backlash can all be written in arc-minutes while meaning different things.
| Metric | Means | Does not mean | Buying check |
|---|---|---|---|
| Resolution | Smallest commanded or reported increment. | The axis actually lands within that increment after mechanics, control, and load effects. | Ask for accuracy and repeatability in addition to counts, bits, or pulses per revolution. |
| Accuracy | Difference between target/actual angular position and indicated position under a defined test. | Repeatability, backlash, or bidirectional lost motion unless those are separately measured. | Ask for test positions, direction, repeats, load, temperature, and instrument uncertainty. |
| Repeatability | How tightly the axis returns to the same commanded position over repeated moves. | Absolute accuracy against an external reference across the full rotation. | Ask whether repeatability is unidirectional, bidirectional, unloaded, or under process load. |
| Backlash / lost motion | Motion gap or reversal error, often dominant in gear-driven systems. | Encoder resolution or controller interpolation quality. | Ask whether the value is measured at the output table, reducer output, or motor side. |
Acceptance Evidence
Use the lightest evidence that fits the decision. A formula is enough for conversion, but not enough for acceptance near a production limit.
| Decision layer | Evidence needed | Example |
|---|---|---|
| Use conversion only | NIST/BIPM unit identity and your radius/tolerance inputs are enough. | Answering “1 arc minute is equal to what?” or translating an RFQ note into radians. |
| Use conversion plus uncertainty budget | Add backlash, repeatability, encoder, thermal drift, fixture offset, and load terms with uncertainty treatment. | The projected 29.09 um at 100 mm consumes most of a 35 um process allowance. |
| Require acceptance test evidence | Dated direct-measurement report, repeated positions, test direction, environment, load condition, and uncertainty statement. | Supplier claims installed rotary-axis accuracy near your acceptance limit. |
| Mark as needs confirmation / public evidence insufficient | Public catalog omits radius, load, temperature, measurement instrument, or whether the number is accuracy vs resolution. | A page says “1 arc-min precision” without a test method or metric definition. |
Alternatives
A converter is the fastest layer, but final rotary-axis decisions need more evidence than a unit identity.
| Option | Best for | Strength | Limitation |
|---|---|---|---|
| Arc-minute conversion page | Fast unit answer and tolerance screening | Exact formulas, immediate result, alias coverage in one URL | Does not certify installed-axis capability |
| Generic calculator widget | Raw number conversion | Often quick for one field | Usually lacks rotary-axis context and risk boundaries |
| Supplier accuracy table | Component selection | Uses component-specific limits | May mix resolution, repeatability, and accuracy claims |
| Acceptance test report | Final buying decision | Direct evidence under defined conditions | Slower and requires instruments, fixtures, and protocol |
Risk Matrix
These risks are where an exact conversion can still lead to a poor engineering decision.
| Risk | Impact | Mitigation |
|---|---|---|
| Mistaking conversion for capability | High | Use the converter for geometry, then add backlash, repeatability, encoder, thermal, and load terms. |
| Using the wrong radius | Medium | Run the calculator at maximum working radius and worst-case fixture offset. |
| Mixing arc-min and arc-sec specs | High | Normalize every supplier value to arc-seconds or radians before comparison. |
| Treating resolution as accuracy | High | Require separate accuracy, repeatability, and backlash values; do not accept counts-per-rev or bit depth as installed-axis proof. |
| Over-optimizing a coarse process | Medium | If part tolerance is millimeter-class, arc-minute refinements may not improve yield. |
RFQ Checklist
Use these fields when 1 arc minute is close enough to your tolerance that supplier wording can change the buying decision.
| RFQ item | Ask supplier for | Why it matters |
|---|---|---|
| Angular metric | Specify whether the value is accuracy, repeatability, resolution, backlash, or lost motion. | A 1 arc-minute conversion is exact, but those five machine terms are not interchangeable. |
| Test method | Ask for direct-measurement method, positions tested, repeats per position, move direction, and axis load condition. | ISO 230-2 style positioning evidence depends on repeated measurements and defined conditions. |
| Uncertainty statement | Ask whether the report states combined or expanded uncertainty and the coverage factor used. | NIST TN 1297 separates measured value reporting from uncertainty reporting. |
| Working radius | Ask the supplier to translate angular error at your maximum part or fixture radius. | 1 arc minute is about 29.09 um at 100 mm, but about 145.44 um at 500 mm. |
| Unknown public data | Ask for a dated acceptance report when catalog pages do not reveal test radius, load, or temperature. | Public-data gap: many public catalogs do not expose enough conditions for an installed-axis guarantee. |
| Resolution vs accuracy | Ask whether the quoted arc-minute value is command resolution, encoder accuracy, table positioning accuracy, repeatability, or backlash. | Encoder and controller resolution can be much finer than the installed rotary-axis accuracy under load. |
Scenarios
Use these examples to decide whether the converted value is operationally important or just a notation cleanup.
FAQ
Focused answers for conversion, alias intent, supplier comparison, and practical rotary-axis use.
1 arc minute is equal to 1/60 degree, 60 arc-seconds, pi / 10800 radians, 0.0002908882087 radians, and about 29.09 um at a 100 mm working radius.
1 arc minute in radians is pi / 10800 rad, which is approximately 0.0002908882087 rad.
1 arc minute equals 1/60 degree, or approximately 0.0166666667 degrees.
There are 60 arc-seconds in 1 arc minute.
The alias query 1 arc minute is equal to and the canonical query arc-minute share the same conversion intent, so the site keeps them on /learn/arc-minute.
It depends on radius and tolerance. At 100 mm it projects to about 29.09 um, but installed-axis capability also depends on backlash, encoder, repeatability, thermal drift, and load.
Multiply arc minutes by pi / 10800. For example, 5 arc minutes equals 5pi / 10800 rad, or about 0.00145444104 rad.
Multiply radians by 10800 / pi. The calculator supports radian input and returns arc-minutes, degrees, and arc-seconds.
Use any unit for math, but normalize all suppliers to one unit before comparing. Arc-seconds are often clearer for precision rotary-axis claims.
No. Encoder resolution or accuracy is only one term. Coupling, bearing runout, backlash, control tuning, thermal drift, and load can widen installed-axis error.
For 1 arc minute, either is effectively the same for screening. At 100 mm radius, the arc-length and chord-displacement difference is about 1.026e-7 um, far below normal machining tolerance concerns.
For acceptance, ask for repeated direct measurement of the individual axis, the tested positions, direction, environment, load condition, instrument uncertainty, and whether the result is accuracy or repeatability.
It can be too coarse when long working radii or tight micron-level tolerances make the projected linear error exceed the allowed budget.
It is often enough for rough indexing, welding, positioning, and fixturing where the linear tolerance is much larger than the projected angular error.
Ask for angular accuracy, repeatability, backlash, encoder type, test radius, load condition, temperature range, and the acceptance method used to verify the claim.
No. It is a geometry screen based on the angle and radius. It does not include runout, Abbe error, fixture deflection, control error, or thermal effects.
BIPM is the SI authority, while NIST SP 811 and SP 330 provide practical SI guidance and conversion tables commonly used in U.S. engineering contexts.
Reliable public data can be missing for supplier-specific installed accuracy because many catalog pages omit load, radius, temperature, instrument uncertainty, and test protocol.
Mark a claim as needs confirmation when a public page gives an arc-minute number but does not say whether it is resolution, accuracy, repeatability, backlash, the test method, or the test environment.
Next Step
If the converted arc-minute value is close to your process tolerance, move from unit conversion to an uncertainty budget and acceptance test plan before buying the rotary axis.
For broader arc-second feasibility, compare this arc-minute conversion with the arc-second decision guide.