Radians to Arcminutes
An instant radians-to-arcminutes converter, with the formula and a reference table below.
| Radians | Arcminutes |
|---|---|
| 1 rad | 3437.746771 ′ |
| 2 rad | 6875.493542 ′ |
| 3 rad | 10313.240312 ′ |
| 5 rad | 17188.733854 ′ |
| 10 rad | 34377.467708 ′ |
| 25 rad | 85943.66927 ′ |
| 50 rad | 171887.338539 ′ |
| 100 rad | 343774.677078 ′ |
How to use
- Enter a value in the Radians field.
- The Arcminutes figure appears immediately — no button to press.
- Typing in the Arcminutes field converts back to Radians the same way.
- Use the reference table for the values that come up most often.
Radians to Arcminutes formula
To convert radians to arcminutes, multiply by 3437.74677.
′ = rad × 3437.74677
Why this factor: the radian and the arcminute are both defined against the degree, so dividing one definition by the other gives 3437.74677 directly. Both definitions are set out in full below.
To go the other way, divide by 3437.74677 — or use the Arcminutes to Radians converter, which is the same calculation reversed.
Worked example
Start with 45 rad. Multiply by 3437.74677 to get 154698.604685 ′.
45 rad × 3437.74677 = 154698.604685 ′
The converter above does this for any value you type, in either direction.
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.
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.
Radians vs Arcminutes
The radian is an SI unit while the arcminute is a specialized 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 arcminutes are in a radian?
One radian equals 3437.74677 arcminutes.
What is the formula to convert radians to arcminutes?
Multiply the number of radians by 3437.74677. To reverse it, divide by 3437.74677 instead.
How do I convert arcminutes back to radians?
Divide by 3437.74677, which is the same as multiplying by 0.000290888209.
How many arcminutes are in 10 radians?
10 rad works out to 34377.467708 ′.
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 radian defined?
A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.