Convert Radians to Arcminutes
1 radian is 3,437.75 ′. One radian is exactly 3437.74677078 arcminutes.
One radian is 3437.7468 arcminutes. To convert radians to arcminutes, multiply by 3437.7468; to go the other way, divide by 3437.7468 or multiply by 2.9089 × 10^-4. 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. The angle subtending an arc equal to the radius.
Factor checked against the defining standard · How we check
- Radians × 3437.7468
1 * 3437.74683,437.747 ′
1 radian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians (as entered) | 1 rad | — |
| degrees | 57.29577951 ° | × 57.2957795131 |
| gradians | 63.66197724 gon | × 63.6619772368 |
| arcminutes | 3,437.746771 ′ | × 3,437.74677078 |
| arcseconds | 206,264.8062 ″ | × 206,264.806247 |
| turns | 0.1591549431 turn | × 0.159154943092 |
| milliradians | 1,000 mrad | × 1,000 |
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 radians to arcminutes? The converter and the working
- 1.Take the measurement in radians.
- 2.Multiply by 3437.7468 — that is how many arcminutes fit in one radian.
- 3.To go back the other way, divide by 3437.7468, or multiply by 2.9089 × 10^-4.
Worked example: 25 radians to arcminutes
- Formula
- rad × 3437.7468 = ′
- Arithmetic
- 25 × 3437.7468 = 85,943.67 ′
- Answer
- 25 rad = 85,943.67 ′
The factor is rounded for display; the figure above is computed from the full value.
Radians to arcminutes conversion table
| Radians | Arcminutes |
|---|---|
| 1 rad | 3,437.75 ′ |
| 2 rad | 6,875.49 ′ |
| 3 rad | 10,313.24 ′ |
| 4 rad | 13,750.99 ′ |
| 5 rad | 17,188.73 ′ |
| 6 rad | 20,626.48 ′ |
| 7 rad | 24,064.23 ′ |
| 8 rad | 27,501.97 ′ |
| 9 rad | 30,939.72 ′ |
| 10 rad | 34,377.47 ′ |
| 12 rad | 41,252.96 ′ |
| 15 rad | 51,566.2 ′ |
| 20 rad | 68,754.94 ′ |
| 25 rad | 85,943.67 ′ |
| 50 rad | 171,887.34 ′ |
| 100 rad | 343,774.68 ′ |
| 200 rad | 687,549.35 ′ |
| 300 rad | 1,031,324.03 ′ |
| 500 rad | 1,718,873.39 ′ |
| 1000 rad | 3,437,746.77 ′ |
| 2000 rad | 6,875,493.54 ′ |
| 5000 rad | 17,188,733.85 ′ |
| 10000 rad | 34,377,467.71 ′ |
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.
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.
How many arcminutes are in a radian?
One radian is 3437.7468 arcminutes. Going the other way, one arcminute is 2.9089 × 10^-4 radians. 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 a radian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Radians to arcminutes. Rule Calculator. https://rulecalculators.com/convert/radian-to-arcminute
- MLA
- "Convert Radians to arcminutes." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/radian-to-arcminute.
- Chicago
- Rule Calculator. "Convert Radians to arcminutes." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/radian-to-arcminute.
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Questions people actually ask
- How many arcminutes are in a radian?
- 3437.7468. 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.
- How do I convert arcminutes back to radians?
- Divide by 3437.7468, or multiply by 2.9089 × 10^-4 — they are the same operation.
Other angle conversions
Arcminutes to radians — the same conversion the other way.