How to Convert Radians to Arcminutes (rad to ′)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert radians into arcminutes by hand, with examples and a quick-reference table.
The conversion
To convert radians to arcminutes, multiply the value by 3,437.7467707849. To go the other way, divide by the same number (or multiply by 0.0002908882). For a quick estimate, multiply by about 3,400.
Arcminutes = radians × 3,437.7467707849
Worked examples
- 3 rad = 10,313.24 ′
- 12.5 rad = 42,971.83 ′
- 75 rad = 257,831.01 ′
Radians to Arcminutes table
| Radians | Arcminutes |
|---|---|
| 1 rad | 3,437.75 ′ |
| 2 rad | 6,875.49 ′ |
| 5 rad | 17,188.73 ′ |
| 10 rad | 34,377.47 ′ |
| 20 rad | 68,754.94 ′ |
| 25 rad | 85,943.67 ′ |
| 50 rad | 171,887.34 ′ |
| 100 rad | 343,774.68 ′ |
| 250 rad | 859,436.69 ′ |
| 500 rad | 1,718,873.39 ′ |
| 1,000 rad | 3,437,746.77 ′ |
Common questions
Is rad to ′ 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 Arcminutes to Radians 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.
Rounding the factor too early
Using 3 instead of 3.28 for feet per metre introduces an error of almost 9% before you have started.
Mixing similar-sounding units
US and imperial gallons, pints and tons are different sizes, and decimal kilobytes differ from binary kibibytes.
Background
Unit conversion is simply multiplication by a fixed ratio. The ratio between two units of the same quantity never changes, so once you know it you can convert any value in either direction.
Singapore adopted the metric system in the 1970s, replacing imperial units and traditional Chinese measures in most official uses. Metric units are now standard in schools, trade and government, but older units survive in property, markets and imported goods.
Many conversion factors are exact by definition. The inch has been defined as exactly 2.54 centimetres since 1959, and the pound as exactly 0.45359237 kilograms, so conversions involving them can be as precise as you need.
For any value, use the Radians to Arcminutes Converter or browse all angle converters.
Run your own numbers: Radians to Arcminutes Converter