One arcsecond is 1/3600 degree.
Arcseconds to Milliradians Converter — arcsec to mrad
Convert Arcsecond (arcsec) to Milliradian (mrad) using the exact conversion factor (1 arcsecond = 0.0048481368 milliradian). See the formula, worked examples, and conversion table.
Arcseconds to Milliradians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
One milliradian is 0.001 radians.
Result = input x 4.84813681e-6 / 0.001.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Arcseconds to Milliradians
Arcsecond and Milliradian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: One arcsecond is 1/3600 degree, and one milliradian is 0.001 radians.
Formula
milliradians = arcseconds × 0.0048481368111
This factor comes from each unit's defined relationship to the category's base unit: 1 arcsecond equals 0.0000048481368111 base units, and 1 milliradian equals 0.001 base units, so dividing one by the other gives the direct arcsecond-to-milliradian factor of 0.0048481368111.
Simple example
1 arcsec × 0.004848136811 = 0.0048481368 mrad
1 arcsecond = 0.0048481368 milliradians.
Real-world example
90 arcsec × 0.004848136811 = 0.436332313 mrad
90 arcseconds = 0.436332313 milliradians.
Conversion table
| Arcsecond (arcsec) | Milliradian (mrad) |
|---|---|
| 0 arcsec | 0 mrad |
| 30 arcsec | 0.1454441043 mrad |
| 45 arcsec | 0.2181661565 mrad |
| 90 arcsec | 0.436332313 mrad |
| 180 arcsec | 0.872664626 mrad |
| 360 arcsec | 1.745329252 mrad |
Reverse conversion: Milliradian to Arcsecond
0.0048481368 mrad × 206.2648062 = 0.9999999977 arcsec
0.0048481368 milliradians = 0.9999999977 arcseconds.
arcseconds = milliradians × 206.264806247
For a page dedicated to this direction, see Milliradian to Arcsecond.
Understanding the Arcsecond (arcsec)
One arcsecond is 1/3600 degree.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many milliradians are in 1 arcsecond?
1 arcsecond equals 0.0048481368 milliradians, using the exact defined conversion factor rather than an estimate.
How do I convert arcsecond to milliradian?
Multiply the arcsecond value by 0.004848136811. The converter above does this instantly to whatever precision you set.
How do I convert milliradian back to arcsecond?
Use the reverse factor: 1 milliradian equals 206.2648062 arcseconds. You can also use the swap control in the converter above to flip the direction instantly.
What is a arcsecond?
Arcsecond (arcsec) is a unit of angle.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
Is the arcsecond to milliradian conversion exact?
Yes. Both arcsecond and milliradian are defined by fixed standards rather than physical artifacts, so the factor of 0.004848136811 used above is exact to as many digits as you choose to display.