Convert Radians to Arcminutes
Radians to arcminutes is the conversion you need when an angle comes out of math or code in radians and you want it in arcminutes — the fine unit where each degree is split into 60 parts. One radian is approximately 3437.7468 arcminutes, so the arcminute number always comes out much larger.
Radians to Arcminutes conversion table
| Radians (rad) | Arcminutes (′) |
|---|---|
| 1 | 3,437.746771 |
| 2 | 6,875.493542 |
| 3 | 10,313.240312 |
| 5 | 17,188.733854 |
| 10 | 34,377.467708 |
| 20 | 68,754.935416 |
| 50 | 171,887.338539 |
| 100 | 343,774.677078 |
| 500 | 1,718,873.385392 |
| 1,000 | 3,437,746.770785 |
The formula
To convert radians to arcminutes, multiply the angle in radians by 3437.7468:
arcminutes = radians × 3437.7468
A worked example
Say you have 0.5 radian and want it in arcminutes:
0.5 × 3437.7468 = 1718.8734 arcminutes
So half a radian is about 1718.8734 arcminutes.
Why it's an approximation
The factor 3437.7468 is a rounded value. Here's where it comes from: one radian is about 57.29578 degrees, and each degree splits into 60 arcminutes, so a radian is roughly 57.29578 × 60 arcminutes. Because that degree figure depends on pi — which is irrational and never ends — the arcminute total never resolves to a clean number, so any figure you write down is rounded. 3437.7468 is precise enough for almost anything.
When you'll use it
Taking an angle from math or code, where sin, cos, and tan expect radians, into the arcminutes used for fine measurements in astronomy, optics, and navigation.
Frequently asked questions
How many arcminutes are in a radian?
About 3437.7468 arcminutes. It's a rounded figure — the value depends on pi, which never ends, so 3437.7468 is the practical number to use.
What is an arcminute?
It's one 60th of a degree, used where you need finer angles than whole degrees — astronomy, optics, and navigation. Since one radian is roughly 57.3 degrees, and each degree holds 60 arcminutes, a radian is thousands of arcminutes.
Is the radians to arcminutes conversion exact?
No. The value depends on pi, which is irrational, so 3437.7468 is rounded for everyday use. More decimal places give you more precision if you need it.