Convert Arcminutes to Radians
1 arcminute is 0.0002909 rad. One arcminute is exactly 0.000290888208666 radians.
One arcminute is 2.9089 × 10^-4 radians. To convert arcminutes to radians, multiply by 2.9089 × 10^-4; to go the other way, divide by 2.9089 × 10^-4 or multiply by 3437.7468. The relation is exact but the figure is not: it is a rounding of a number that does not terminate, and it follows from NIST Special Publication 811. A sixtieth of a degree.
Factor checked against the defining standard · How we check
- Arcminutes × 2.9089 × 10^-4
1 * 0.00029090 rad
1 arcminute in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 0.0002908882087 rad | × 0.000290888208666 |
| degrees | 0.01666666667 ° | × 0.0166666666667 |
| gradians | 0.01851851852 gon | × 0.0185185185185 |
| arcminutes (as entered) | 1 ′ | — |
| arcseconds | 60 ″ | × 60 |
| turns | 0.0000462962963 turn | × 0.0000462962962963 |
| milliradians | 0.2908882087 mrad | × 0.290888208666 |
Factors are entered by hand from NIST Special Publication 811 rather than derived from a units library, so the ones that terminate are exact rather than rounded.
How do you convert arcminutes to radians? The converter and the working
- 1.Take the measurement in arcminutes.
- 2.Multiply by 2.9089 × 10^-4 — that is how many radians fit in one arcminute.
- 3.To go back the other way, divide by 2.9089 × 10^-4, or multiply by 3437.7468.
Worked example: 25 arcminutes to radians
- Formula
- ′ × 2.9089 × 10^-4 = rad
- Arithmetic
- 25 × 2.9089 × 10^-4 = 0.01 rad
- Answer
- 25 ′ = 0.01 rad
The factor is rounded for display; the figure above is computed from the full value.
Arcminutes to radians conversion table
| Arcminutes | Radians |
|---|---|
| 1 ′ | 0.0002909 rad |
| 2 ′ | 0.0005818 rad |
| 3 ′ | 0.0008727 rad |
| 4 ′ | 0.001164 rad |
| 5 ′ | 0.001454 rad |
| 6 ′ | 0.001745 rad |
| 7 ′ | 0.002036 rad |
| 8 ′ | 0.002327 rad |
| 9 ′ | 0.002618 rad |
| 10 ′ | 0.002909 rad |
| 12 ′ | 0.003491 rad |
| 15 ′ | 0.004363 rad |
| 20 ′ | 0.01 rad |
| 25 ′ | 0.01 rad |
| 50 ′ | 0.01 rad |
| 100 ′ | 0.03 rad |
| 200 ′ | 0.06 rad |
| 300 ′ | 0.09 rad |
| 500 ′ | 0.15 rad |
| 1000 ′ | 0.29 rad |
| 2000 ′ | 0.58 rad |
| 5000 ′ | 1.45 rad |
| 10000 ′ | 2.91 rad |
What is an arcminute?
A sixtieth of a degree. A nautical mile was defined as one arcminute of latitude, which is why the two units keep appearing together on charts.
What is a radian?
The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
How many radians are in an arcminute?
One arcminute is 2.9089 × 10^-4 radians. Going the other way, one radian is 3437.7468 arcminutes. Both figures come from the same defined relation rather than from a measurement, which is why they are the same today as they were in 1959.
Every angle unit here
The whole group — 7 units with their symbols and the size of each one in radians — is on the conversion index, along with every pair it makes. The table above already gives each of them relative to an arcminute.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Arcminutes to radians. Rule Calculator. https://rulecalculators.com/convert/arcminute-to-radian
- MLA
- "Convert Arcminutes to radians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/arcminute-to-radian.
- Chicago
- Rule Calculator. "Convert Arcminutes to radians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/arcminute-to-radian.
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Questions people actually ask
- How many radians are in an arcminute?
- 2.9089 × 10^-4. The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
- How do I convert radians back to arcminutes?
- Divide by 2.9089 × 10^-4, or multiply by 3437.7468 — they are the same operation.
Other angle conversions
Radians to arcminutes — the same conversion the other way.