How to Convert Arcminutes to Radians (′ to rad)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert arcminutes into radians by hand, with examples and a quick-reference table.
The conversion
To convert arcminutes to radians, multiply the value by 0.0002908882. To go the other way, divide by the same number (or multiply by 3,437.7467707849). Because the factor is tiny, scientific notation keeps the numbers manageable.
Radians = arcminutes × 0.0002908882
Worked examples
- 3 ′ = 0.000873 rad
- 12.5 ′ = 0.003636 rad
- 75 ′ = 0.021817 rad
Arcminutes to Radians table
| Arcminutes | Radians |
|---|---|
| 1 ′ | 0.000291 rad |
| 2 ′ | 0.000582 rad |
| 5 ′ | 0.001454 rad |
| 10 ′ | 0.002909 rad |
| 20 ′ | 0.005818 rad |
| 25 ′ | 0.007272 rad |
| 50 ′ | 0.014544 rad |
| 100 ′ | 0.029089 rad |
| 250 ′ | 0.072722 rad |
| 500 ′ | 0.145444 rad |
| 1,000 ′ | 0.290888 rad |
Common questions
Is ′ to rad exact?
The factors used here are the internationally defined values where they exist; results are rounded for display only.
How do I convert back?
Use the Radians to Arcminutes converter.
Mistakes to avoid
Forgetting squared and cubed units
Area and volume factors are the length factor squared or cubed, so 1 m² is about 10.76 sq ft, not 3.28.
Dropping the units
A bare number without a unit is easy to misread later. Always write the unit with the result.
Multiplying when you should divide
Converting to a smaller unit gives a bigger number, and converting to a larger unit gives a smaller one. If your answer moves the wrong way, you have inverted the factor.
Background
Writing the units next to every number while you work is the simplest way to avoid mistakes. If the units do not cancel to leave the one you want, the calculation is set up wrongly.
A conversion table is handy for common values, but a calculator is faster and avoids interpolation errors for anything in between.
For everyday use, three or four significant figures are usually enough. Engineering, science and trade documents may need more, and rounding should happen only at the end of a calculation.
For any value, use the Arcminutes to Radians Converter or browse all angle converters.
Run your own numbers: Arcminutes to Radians Converter