Measuring accuracy of latitude and longitude?

  • I have latitude and longitude as 19.0649070739746 and 73.1308670043945 respectively.

    In this case both coordinates are 13 decimal places long, but sometimes I also get coordinates which are 6 decimal places long.

    Do fewer decimal points affect accuracy, and what does every digit after the decimal place signify?

    The answers here are good. I thought I would add to the answer by relating how the digits in longitude are affected by latitude. The charts given above can have the longitude adjusted by multiplying the value in the table by Cos(latitude)

    There are several charts in this thread and they can appear in almost any sequence. I can speak to the one in my answer: although I made a conscious decision not to include this information (any reference to trigonometry risks scaring off people who otherwise have the background to understand everything else), it's a great point and reminds us to make quantitative statements when we can. +1.

    If you consider the two common data types of "float32" and "float64", these give about 7 and 16 decimal digits of precision, respectively, here's a rule of thumb: the former gives you about a meter of precision, the latter give you a nanometer of precision. In other words, using floats with latitude and longitude, with a single precision I can distinguish the lat/lng position of adjacent chairs in a conference room. With double precision, I can distinguish the lat/lng position of adjacent mitochondria in a skin cell on the scalp of the person sitting in one of those chairs.

    Plase cite the coordinate system, seems WGS84, the default, but important to be explicit about it.. No discussion make sense without a CRS.

    What kind of coordinate measurement accuracy are you asking for? 1) About instrumental accuracy, 2) about cartographic accuracy, 3) about analytical accuracy, etc., etc. : -) ...

  • whuber

    whuber Correct answer

    10 years ago

    Accuracy is the tendency of your measurements to agree with the true values. Precision is the degree to which your measurements pin down an actual value. The question is about an interplay of accuracy and precision.

    As a general principle, you don't need much more precision in recording your measurements than there is accuracy built into them. Using too much precision can mislead people into believing the accuracy is greater than it really is.

    Generally, when you degrade precision--that is, use fewer decimal places--you can lose some accuracy. But how much? It's good to know that the meter was originally defined (by the French, around the time of their revolution when they were throwing out the old systems and zealously replacing them by new ones) so that ten million of them would take you from the equator to a pole. That's 90 degrees, so one degree of latitude covers about 10^7/90 = 111,111 meters. ("About," because the meter's length has changed a little bit in the meantime. But that doesn't matter.) Furthermore, a degree of longitude (east-west) is about the same or less in length than a degree of latitude, because the circles of latitude shrink down to the earth's axis as we move from the equator towards either pole. Therefore, it's always safe to figure that the sixth decimal place in one decimal degree has 111,111/10^6 = about 1/9 meter = about 4 inches of precision.

    Accordingly, if your accuracy needs are, say, give or take 10 meters, than 1/9 meter is nothing: you lose essentially no accuracy by using six decimal places. If your accuracy need is sub-centimeter, then you need at least seven and probably eight decimal places, but more will do you little good.

    Thirteen decimal places will pin down the location to 111,111/10^13 = about 1 angstrom, around half the thickness of a small atom.

    Using these ideas we can construct a table of what each digit in a decimal degree signifies:

    • The sign tells us whether we are north or south, east or west on the globe.
    • A nonzero hundreds digit tells us we're using longitude, not latitude!
    • The tens digit gives a position to about 1,000 kilometers. It gives us useful information about what continent or ocean we are on.
    • The units digit (one decimal degree) gives a position up to 111 kilometers (60 nautical miles, about 69 miles). It can tell us roughly what large state or country we are in.
    • The first decimal place is worth up to 11.1 km: it can distinguish the position of one large city from a neighboring large city.
    • The second decimal place is worth up to 1.1 km: it can separate one village from the next.
    • The third decimal place is worth up to 110 m: it can identify a large agricultural field or institutional campus.
    • The fourth decimal place is worth up to 11 m: it can identify a parcel of land. It is comparable to the typical accuracy of an uncorrected GPS unit with no interference.
    • The fifth decimal place is worth up to 1.1 m: it distinguish trees from each other. Accuracy to this level with commercial GPS units can only be achieved with differential correction.
    • The sixth decimal place is worth up to 0.11 m: you can use this for laying out structures in detail, for designing landscapes, building roads. It should be more than good enough for tracking movements of glaciers and rivers. This can be achieved by taking painstaking measures with GPS, such as differentially corrected GPS.
    • The seventh decimal place is worth up to 11 mm: this is good for much surveying and is near the limit of what GPS-based techniques can achieve.
    • The eighth decimal place is worth up to 1.1 mm: this is good for charting motions of tectonic plates and movements of volcanoes. Permanent, corrected, constantly-running GPS base stations might be able to achieve this level of accuracy.
    • The ninth decimal place is worth up to 110 microns: we are getting into the range of microscopy. For almost any conceivable application with earth positions, this is overkill and will be more precise than the accuracy of any surveying device.
    • Ten or more decimal places indicates a computer or calculator was used and that no attention was paid to the fact that the extra decimals are useless. Be careful, because unless you are the one reading these numbers off the device, this can indicate low quality processing!

    "...can indicate low quality processing" may be a little unfair. Perhaps "...can indicate low quality _presentation_" is fairer.

    @martin That's a good point. But when the presentation is low quality that suggests the analysis may be lacking, too. Let's be careful to take that as intended: an *indication* is only a flag, not a blanket indictment.

    Is this accuracy applies to both Latitude and Longitude? I'm aware that the vertical and horizontal circumference of Earth is slightly different.

    For Longitude values the accuracy/precision question only starts to make an order of magnitude difference from the answer given here at 85 Degrees Latitude and higher. At 90 Degrees the question is irrelevant. See the Wiki Page at - link

    Excellent answer. Regarding "A nonzero hundreds digit tells us we're using longitude, not latitude!" - hopefully it is obvious to the reader that the opposite does not hold. For example, `+/- 0 to 90` degrees is valid for both longitude and latitude, but `+/- 0 to 180 degrees` is valid only for longitude.

    We recently bought 24 acres of land and we're having to verify a lot of survey work on it for some boundary locations, wetlands RPA boundaries, and so on. (Once we know about where things are, then we'll be having surveyors do the official work for permits and such - we'll save a lot of time on a lot that large if they don't have to look for pins and nails.) You have no idea what a big help this is for us! For example, we had trouble pinpointing the back boundary and corners. Now we know one marker is within 30-40' of the back corner. (Which makes it likely it is the back corner marker.)

    Important to cite the coordinate system (!), all discussion is about WGS84... is it? Please show in the answer.

    @Peter (1) I believe you are referring to the *datum* rather than the coordinate system and (2) it doesn't matter: the answer remains completely the same, because the flattening of the earth is tiny (only about 1/300) compared to the order-of-magnitude statements made here.

    @whuber sometimes, even in nowadays, we use e. g. UTM-SIRGAS, that is other system and other datum, example... And about "order-of-magnitude statements" , well, you post 6...10.. so meters to microns ;-)

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