MOA To MRAD Calculator

MOA and MRAD Conversion Formula

mrad = MOA × π / 10.8; MOA = mrad × 10.8 / π

What the Units Mean

MOA means minute of angle, also called an arcminute. There are 60 angular minutes in one degree. A milliradian is one thousandth of a radian. Both describe angles, so a conversion requires only the angle and its original unit. It does not require a distance or a length measurement. The symbol mrad names the milliradian explicitly and avoids the different meanings of the abbreviation mil.

How the Conversion Works

One degree equals π/180 radians. Dividing by 60 gives π/10,800 radians per angular minute. Multiplying by 1,000 converts radians to milliradians, giving π/10.8 milliradians per MOA. The reverse operation multiplies milliradians by 10.8/π. The calculator uses the full JavaScript value of π and rounds the displayed MOA and milliradian answers to six decimal places.

Worked Example

For 60 MOA, the calculation is 60 × π/10.8 = 17.453293 mrad after rounding. This is exactly one degree, or approximately 0.01745329252 radians. In the reverse direction, 1 mrad corresponds to approximately 3.437747 MOA. Using 3.44 as a shortcut is suitable only when that level of rounding is acceptable.

Choosing the Input

Choose the desired output in Solve for, then enter the angle in the other unit. Zero is valid and converts to zero. A negative value keeps its sign, which is useful for signed angle differences. The converter accepts source values between −1 billion and +1 billion and does not wrap an angle into a single revolution.

Precision and Limitations

The conversion factor is exact when written with π, but an entered measurement may have limited precision. Extra output digits do not add precision to the original measurement. Very small nonzero angles can round to 0.000000 in the main result; the radians result uses significant-digit notation to retain useful small values. This tool converts angular units only. It does not calculate physical offsets, trajectories, equipment settings, or adjustments.

Using the Result

Use the main answer for the selected unit and the supporting rows to check the same angle in degrees and radians. If you need to convert back, use the original unrounded measurement when possible. Repeatedly converting a rounded display value can accumulate small rounding differences. Calculate saves the inputs and result in this browser; Reset clears them.

Reference Table

Sources

National Institute of Standards and Technology. Guide for the Use of the International System of Units (SI), Special Publication 811, 2008 edition, Table 6 and SI prefixes.