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Arcminutes to Radians Converter
Convert arcminutes to radians — divide by 3,437.75. Results update as you type; exact factors shown.
One arcminute is 0.0003 radians — see the exact factor, not a rounded rule of thumb.
Convert angle
Direction
Results update as you type
Results
1 ′ in radians
0.0003 rad
Conversion factor—
Reverse conversion—
In radian (base unit)—
Reviewed September 2026. Exact conversion factors from the BIPM SI Brochure and NIST SP 811; The US uses customary units (US gallon, short ton, °F) in daily life; NIST SP 811 gives the exact SI factors.
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About angle conversion
Method
How the arcminutes to radians converter works
Angles convert through the radian. A full turn is 2π radians = 360° = 400 gon = 6,400 NATO mils. A degree is 60 arcminutes, an arcminute 60 arcseconds.
The US uses customary units (US gallon, short ton, °F) in daily life; NIST SP 811 gives the exact SI factors.
Data
Common angle conversions
| From | To | Units |
|---|---|---|
| 1 ′ | 0.0003 rad | arcminute to radians |
| 10 ′ | 0.0029 rad | arcminutes to radians |
| 30 ′ | 0.0087 rad | arcminutes to radians |
| 60 ′ | 0.0175 rad | arcminutes to radians |
| 100 ′ | 0.0291 rad | arcminutes to radians |
| 360 ′ | 0.1047 rad | arcminutes to radians |
| 600 ′ | 0.1745 rad | arcminutes to radians |
| 1,000 ′ | 0.2909 rad | arcminutes to radians |
| 3,437.75 ′ | 1 rad | arcminutes to radians |
| 5,400 ′ | 1.5708 rad | arcminutes to radians |
| 10,800 ′ | 3.1416 rad | arcminutes to radians |
| 21,600 ′ | 6.2832 rad | arcminutes to radians |
Data
Units in this converter and their exact factors
| Unit | Symbol | One unit in radians |
|---|---|---|
| degree | ° | 0.0174532925 radian |
| radian | rad | 1 radian |
| gradian (gon) | gon | 0.0157079633 radian |
| arcminute | ′ | 0.0002908882 radian |
| arcsecond | ″ | 0.0000048481 radian |
| turn (revolution) | rev | 6.2831853072 radian |
| NATO mil (1/6400 turn) | mil | 0.0009817477 radian |
FAQFrequently asked questions about angle conversion
How many radians is one arcminute?
0.000291 rad.
What is 3,437.75 arcminutes?
One radian.
What is 21,600 arcminutes?
A full turn — 2π radians.
Why convert to radians?
Because every trigonometric function in mathematics and software expects them.
What is one arcminute of resolution?
About the limit of unaided human vision — 20/20 acuity.
Sources
Where these figures come from
- BIPM — The International System of Units (SI Brochure, 9th edition) — definitions of the base and derived units.
- NIST Special Publication 811 — Guide for the Use of the International System of Units — the exact conversion factors used here.
- National Institute of Standards and Technology (NIST) — United States's national measurement authority.
Last checked: September 2026. Conversion factors are fixed by definition and do not change with tax years or regulations.