Convert Arcminutes to Turns
Arcminutes to turns is the conversion you need when a small angle in arcminutes has to be read as a fraction of a full rotation — a turn being one complete circle. One arcminute is approximately 0.0000462963 turns, a very small number, because it takes 21,600 arcminutes to make one full turn.
Arcminutes to Turns conversion table
| Arcminutes (′) | Turns (turn) |
|---|---|
| 1 | 0.0000462963 |
| 2 | 0.0000925926 |
| 3 | 0.000139 |
| 5 | 0.000231 |
| 10 | 0.000463 |
| 20 | 0.000926 |
| 50 | 0.002315 |
| 100 | 0.00463 |
| 500 | 0.023148 |
| 1,000 | 0.046296 |
The formula
To convert arcminutes to turns, multiply the number of arcminutes by 0.0000462963 (or divide by 21,600, since 21,600 arcminutes make one turn):
turns = arcminutes × 0.0000462963
A worked example
Say you have 21,600 arcminutes and want it in turns:
21,600 arcminutes = 1 turn
So 21,600 arcminutes is exactly one full turn.
Why it's an approximation
There are exactly 21,600 arcminutes in a turn, so for round values the conversion lands cleanly — 21,600 arcminutes is exactly one turn. The catch is only in the single multiply-by factor: one arcminute is 1/21,600 of a turn, which as a decimal is 0.0000462963, a repeating decimal that gets cut off. Multiplying by that rounded factor can leave a tiny remainder, while dividing by 21,600 keeps clean values exact.
When you'll use it
Expressing a small angle as a fraction of a full rotation, working with a mechanism or motor where positions are counted in turns, or checking how far around a circle a measurement in arcminutes really reaches.
Frequently asked questions
How many arcminutes are in a turn?
Exactly 21,600. A turn is one full circle, which is 360 degrees, and each degree holds 60 arcminutes — so 360 × 60 = 21,600 arcminutes in a turn.
How do I convert arcminutes to turns?
Multiply the number of arcminutes by 0.0000462963, or divide by 21,600. For example, 21,600 arcminutes ÷ 21,600 = 1 turn exactly.
Is the arcminutes to turns conversion exact?
For clean values, yes — 21,600 arcminutes is exactly one turn. The wrinkle is the single multiply-by factor, 0.0000462963, which is a rounded repeating decimal.