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"Skyhawk 872ND, airport at your 12 o'clock in 15 miles."

"Baron 981K, traffic, 2 o'clock 5 miles, opposite direction, a Piper southbound, 1000 feet below you."

Does ATC use nautical miles or statute miles?

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ATC uses nautical miles, this is because it's the ICAO standard documented in Annex 5 - Units of Measurement to be used in Air and Ground Operations, which states that Nautical Miles are to be used for distance and Knots for speed as an alternative non-SI measurement. Kilometers are actually the primary distance measurement because they are the SI standard, however nautical miles are so entrenched they've kept them and there's no termination date.

The ICAO annex is hard to find because everyone wants you to buy it, however the standards have been copied into this CAAS document word for word if you want some light bedtime reading.

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Broadcast weather METARs use statute miles. Navigational information, such as that from ATC, would use nautical miles.
Nautical miles are used for navigation, mainly because a nautical mile is one minute of a degree on the surface of Earth's geoid.(basically one minute of latitude.)
Kilometers and statute miles are each a fixed distance unit, nautical miles are not a fixed straight line distance but are a fixed fraction of the earth's circumference. Very useful for long range navigation and triangulation, 60 miles to each degree and exactly 21600 nautical miles per circumnavigation.

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    $\begingroup$ I don't think the nautical mile is defined the way you're talking about anymore. It's exactly 1852 meters nowadays. $\endgroup$ – Erin Anne Jul 4 '18 at 20:28
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    $\begingroup$ METARs don't use statute miles everywhere, internationally it's usually kilometers. In any case if it's statute miles it says SM after. $\endgroup$ – GdD Jul 4 '18 at 20:29
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    $\begingroup$ The question was about statute miles vs nautical miles, clearly Km are Km, at every station that uses miles the METAR uses statute miles, the station is considered a 5 statute mile radius, the "vicinity" is 10 statute miles, and up to 30 statute miles for "distant".(DSNT is only found in remarks section) The one exception is for lightening which uses NM, though I don't know why. And wind speed is in knots, because aircraft speed is generally in knots. $\endgroup$ – Max Power Jul 4 '18 at 21:54
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    $\begingroup$ The meter originally was the same concept as the NM. It was originally defined as 100 km per gradian latitude, the gradian being the original metric unit of angle. In both cases, it was realized the Earth is not a sphere and the measurements kept being refined anyway, so they were decoupled. $\endgroup$ – user71659 Jul 4 '18 at 22:24
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    $\begingroup$ @Max, even if it was true (I doubt, although it may be partly), it is not anymore. NM is considered a fixed unit of distance (and ultimately defined via SI, as everything nowadays). $\endgroup$ – Zeus Jul 5 '18 at 0:44

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