One milliradian is 0.001 radians.
Milliradians to Arcseconds Converter — mrad to arcsec
Convert Milliradian (mrad) to Arcsecond (arcsec) using the exact conversion factor (1 milliradian = 206.2648062 arcsecond). See the formula, worked examples, and conversion table.
Milliradians to Arcseconds 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 arcsecond is 1/3600 degree.
Result = input x 0.001 / 4.84813681e-6.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Milliradians to Arcseconds
Milliradian and Arcsecond 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 milliradian is 0.001 radians, and one arcsecond is 1/3600 degree.
Formula
arcseconds = milliradians × 206.264806247
This factor comes from each unit's defined relationship to the category's base unit: 1 milliradian equals 0.001 base units, and 1 arcsecond equals 0.0000048481368111 base units, so dividing one by the other gives the direct milliradian-to-arcsecond factor of 206.264806247.
Simple example
1 mrad × 206.2648062 = 206.2648062 arcsec
1 milliradian = 206.2648062 arcseconds.
Real-world example
90 mrad × 206.2648062 = 18,563.83256 arcsec
90 milliradians = 18,563.83256 arcseconds.
Conversion table
| Milliradian (mrad) | Arcsecond (arcsec) |
|---|---|
| 0 mrad | 0 arcsec |
| 30 mrad | 6,187.944187 arcsec |
| 45 mrad | 9,281.916281 arcsec |
| 90 mrad | 18,563.83256 arcsec |
| 180 mrad | 37,127.66512 arcsec |
| 360 mrad | 74,255.33025 arcsec |
Reverse conversion: Arcsecond to Milliradian
206.2648062 arcsec × 0.004848136811 = 0.9999999998 mrad
206.2648062 arcseconds = 0.9999999998 milliradians.
milliradians = arcseconds × 0.0048481368111
For a page dedicated to this direction, see Arcsecond to Milliradian.
Understanding the Milliradian (mrad)
One milliradian is 0.001 radians.
Understanding the Arcsecond (arcsec)
One arcsecond is 1/3600 degree.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many arcseconds are in 1 milliradian?
1 milliradian equals 206.2648062 arcseconds, using the exact defined conversion factor rather than an estimate.
How do I convert milliradian to arcsecond?
Multiply the milliradian value by 206.2648062. The converter above does this instantly to whatever precision you set.
How do I convert arcsecond back to milliradian?
Use the reverse factor: 1 arcsecond equals 0.0048481368 milliradians. You can also use the swap control in the converter above to flip the direction instantly.
What is a milliradian?
Milliradian (mrad) is a unit of angle.
What is a arcsecond?
Arcsecond (arcsec) is a unit of angle.
Is the milliradian to arcsecond conversion exact?
Yes. Both milliradian and arcsecond are defined by fixed standards rather than physical artifacts, so the factor of 206.2648062 used above is exact to as many digits as you choose to display.