My stabilized camera platform has 0.5 mrad of residual jitter. Will that smear my 2 arcsecond resolution astronomical images?

0.5 × 206.265 = 103 arcseconds of jitter. That's 50× the camera's 2 arcsecond resolution — the jitter would completely smear the image. You'd need jitter below 0.01 mrad (≈2 arcseconds) to avoid degrading resolution.

Why does 1 mrad equal 206.265 arcseconds specifically?

One radian = 180/π degrees × 3,600 arcseconds/degree = 206,264.8 arcseconds. Dividing by 1,000 gives 206.265 arcseconds per milliradian. This constant connects the radian (natural mathematical unit) with arcseconds (practical astronomical unit).

A satellite attitude sensor reports 0.2 mrad pointing error. Is that acceptable for imaging at 1 arcsecond ground resolution?

0.2 × 206.265 = 41.3 arcseconds of error — far more than the 1 arcsecond resolution target. The attitude error would degrade images by a factor of 40×. Acceptable error would be under 0.005 mrad.

How many arcseconds is one scope click (0.1 mrad)?

0.1 × 206.265 = 20.6 arcseconds. At 1,000 m, each click moves the point of impact 10 cm — equivalent to 20.6 arcseconds of angular adjustment.

Milliradians to Arcseconds Converter

Enter a value to instantly convert between angle units.

From

Precision4 dp

1 Milliradian = 206.2648 Arcsecond

Key Formulas

Degree → Radian

rad = ° × 0.0174533

Radian → Degree

° = rad × 57.2958

Degree → Gradian

grad = ° × 1.11111

Gradian → Degree

° = grad × 0.9

Formula

arcseconds = mrad × 206.2648

Precision optical instruments — telescope mounts, astronomical cameras, adaptive optics systems — specify angular resolution and pointing accuracy in arcseconds. Military and tactical optics use milliradians. When an astronomer integrates a tracking telescope with a fire-control-grade stabilizer, or when a satellite imaging system must verify that its mrad-specified pointing jitter does not exceed the instrument's arcsecond resolution limit, this conversion is the check. The factor 206.265 is the number of arcseconds per milliradian, equal to the number of arcseconds in one radian (206,265) divided by 1,000.

Source: ISO 80000-3:2019 (Quantities and units — Space and time)

Last reviewed: 2026-06-11 · see our methodology

Frequently Asked Questions

Real-World Examples

1 mrad — 206.265 arcseconds, the same constant used in the parsec definition (1 arcsecond of parallax = 1 parsec). 1 mrad/1000 = 1 radian/206,265 arcseconds.

1 mrad = 206.265 ″

0.00485 mrad — exactly 1 arcsecond. A telescope with 1 arcsecond resolution is sensitive to 0.00485 mrad of platform jitter.

0.00485 mrad = 1 ″

5 mrad — 1,031 arcseconds, the pointing error of a stabilized gimbal verified against the camera's 0.5 arcsecond sensor resolution.

5 mrad = 1031.3 ″

0.1 mrad — 20.63 arcseconds, a scope click's angular equivalent expressed for comparison with arcsecond-rated star chart coordinates.

0.1 mrad = 20.627 ″

degrees to radians radians to degrees degrees to gradians gradians to degrees

Milliradians to Arcseconds Converter

Key Formulas

Formula

Frequently Asked Questions

Real-World Examples

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