Arcminutes to Radians
Convert arcminutes to radians instantly — one arcminute is 0.000290888 radians.
| Arcminutes | Radians |
|---|---|
| 1 ′ | 0.000291 rad |
| 2 ′ | 0.000582 rad |
| 3 ′ | 0.000873 rad |
| 5 ′ | 0.001454 rad |
| 10 ′ | 0.002909 rad |
| 25 ′ | 0.007272 rad |
| 50 ′ | 0.014544 rad |
| 100 ′ | 0.029089 rad |
How to use
- Enter a value in the Arcminutes field.
- The Radians figure appears immediately — no button to press.
- Typing in the Radians field converts back to Arcminutes the same way.
- Use the reference table for the values that come up most often.
Arcminutes to Radians formula
To convert arcminutes to radians, multiply by 0.000290888209.
rad = ′ × 0.000290888209
Why this factor: the arcminute and the radian are both defined against the degree, so dividing one definition by the other gives 0.000290888209 directly. Both definitions are set out in full below.
To go the other way, divide by 0.000290888209 — or use the Radians to Arcminutes converter, which is the same calculation reversed.
Worked example
Take 30 ′ and multiply by the factor 0.000290888209: the result is 0.008727 rad.
30 ′ × 0.000290888209 = 0.008727 rad
The converter above does this for any value you type, in either direction.
What is an arcminute?
An arcminute is one sixtieth of a degree, used where degrees are too coarse.
Definition: Exactly 1/60 degree. Symbol is the prime (′).
Where it is used: Navigation and latitude (one arcminute of latitude is one nautical mile), astronomy, and optometry.
What is a radian?
A radian is the angle that subtends an arc equal in length to the circle's radius — the natural unit of angle.
Definition: A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.
Where it is used: Calculus and trigonometry, physics, and every standard programming library's sin, cos and tan.
Worth knowing: Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
Arcminutes vs Radians
The arcminute is a specialized unit while the radian is an SI unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many radians are in an arcminute?
One arcminute equals 0.000290888209 radians.
What is the formula to convert arcminutes to radians?
Multiply the number of arcminutes by 0.000290888209. To reverse it, divide by 0.000290888209 instead.
How do I convert radians back to arcminutes?
Divide by 0.000290888209, which is the same as multiplying by 3437.74677.
How many radians are in 10 arcminutes?
10 ′ works out to 0.002909 rad.
Is there anything to watch out for with radians?
Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
How is the arcminute defined?
Exactly 1/60 degree. Symbol is the prime (′).