## Accuracy of Longitude/Latitude Coordinates

### #1

Posted 03 February 2010 - 01:59 PM

In the military I remember that they used grid coordinates where an 8 digit coordinate was accurate to 10 meter, 10 digit to 1 meter. But I have no clue as to what size box our cache coordinates are giving us.

Thanks for any info you guys might be able to give me on this.

### #2

Posted 03 February 2010 - 02:07 PM

1st - the coordinates are decimal minutes not degrees - so the measurement is to the thousands of a minute.

2nd - longitude lines converge the closer you get to the poles so that distance varies by where you are at on the globe. Figure 4 to 7 feet for most areas around the US.

3rd - The area between coords may be a square but the coords themselves always lead to a singular point.

This post has been edited by **StarBrand**: 03 February 2010 - 02:07 PM

### #3

Posted 03 February 2010 - 02:07 PM

microvision, on Feb 3 2010, 01:59 PM, said:

In the military I remember that they used grid coordinates where an 8 digit coordinate was accurate to 10 meter, 10 digit to 1 meter. But I have no clue as to what size box our cache coordinates are giving us.

Thanks for any info you guys might be able to give me on this.

Actually the co-ordinates given on a cache page or read off a gps gives you a point. For a square you would need four different sets of co-ordinates. Now if your asking about accuracy of the readings, a 20-40 foot circle of uncertainty is not uncommon.

### #4

Posted 03 February 2010 - 02:27 PM

StarBrand, on Feb 3 2010, 05:07 PM, said:

1st - the coordinates are decimal minutes not degrees - so the measurement is to the thousands of a minute.

2nd - longitude lines converge the closer you get to the poles so that distance varies by where you are at on the globe. Figure 4 to 7 feet for most areas around the US.

3rd - The area between coords may be a square but the coords themselves always lead to a singular point.

Thanks StarBrand,

Good point about the decimal minutes. I meant to say minutes and not degrees.

Also it is good to know about the varying of the longitude lines. I knew they did not form exact squares with the latitude lines but did not know how much they varied within the US.

Interesting about the coords being a point. I have trouble thinking in anything but grid coordinates. But if the cache coords are for a single point then that means when the CO first finds the coords for his cache there is a good chance that the cache is not exactly on that point and his GPS unit is rounding to the nearest point (lets ignore the fact that his unit is going to have some measurement error for the moment). So knowing the area between the coords that form that almost square would be helpful in knowing what kind of rounding error we are starting out with. Do you know what the distance between the coordinates is assuming they are to the thousandths of a minute?

### #5

Posted 03 February 2010 - 02:50 PM

microvision, on Feb 3 2010, 03:27 PM, said:

StarBrand, on Feb 3 2010, 05:07 PM, said:

1st - the coordinates are decimal minutes not degrees - so the measurement is to the thousands of a minute.

2nd - longitude lines converge the closer you get to the poles so that distance varies by where you are at on the globe. Figure 4 to 7 feet for most areas around the US.

3rd - The area between coords may be a square but the coords themselves always lead to a singular point.

Thanks StarBrand,

Good point about the decimal minutes. I meant to say minutes and not degrees.

Also it is good to know about the varying of the longitude lines. I knew they did not form exact squares with the latitude lines but did not know how much they varied within the US.

Interesting about the coords being a point. I have trouble thinking in anything but grid coordinates. But if the cache coords are for a single point then that means when the CO first finds the coords for his cache there is a good chance that the cache is not exactly on that point and his GPS unit is rounding to the nearest point (lets ignore the fact that his unit is going to have some measurement error for the moment). So knowing the area between the coords that form that almost square would be helpful in knowing what kind of rounding error we are starting out with. Do you know what the distance between the coordinates is assuming they are to the thousandths of a minute?

In the case of UTM or MGRS, the coordinates DO refer to the square to the right and up of the given coordinate set regardless of the number be it 2 4 6 8 or 10 digit... you are correct that they represent smaller and smaller (divisible by 10 squares). Lat and long represent single points as stated by others...

You can always program in DD MM.mmm and switch units to UTM for navigating... if it helps you. Just watch the datum if you try to relate to a UTM grid map... get the right one.

Doug

### #6

Posted 03 February 2010 - 02:52 PM

jholly, on Feb 3 2010, 02:07 PM, said:

microvision, on Feb 3 2010, 01:59 PM, said:

In the military I remember that they used grid coordinates where an 8 digit coordinate was accurate to 10 meter, 10 digit to 1 meter. But I have no clue as to what size box our cache coordinates are giving us.

Thanks for any info you guys might be able to give me on this.

Actually the co-ordinates given on a cache page or read off a gps gives you a point. For a square you would need four different sets of co-ordinates. Now if your asking about accuracy of the readings, a 20-40 foot circle of uncertainty is not uncommon.

### #7

Posted 03 February 2010 - 02:52 PM

jholly, on Feb 3 2010, 05:07 PM, said:

microvision, on Feb 3 2010, 01:59 PM, said:

In the military I remember that they used grid coordinates where an 8 digit coordinate was accurate to 10 meter, 10 digit to 1 meter. But I have no clue as to what size box our cache coordinates are giving us.

Thanks for any info you guys might be able to give me on this.

Actually the co-ordinates given on a cache page or read off a gps gives you a point. For a square you would need four different sets of co-ordinates. Now if your asking about accuracy of the readings, a 20-40 foot circle of uncertainty is not uncommon.

Thanks JHolly,

I understand that you are correct about the coordinates giving a point but that means if you zoom up enough on a map you would see it is covered with a grid of points with gray area all around. If you happen to be in that gray area I image that your GPSr will round or jump to the nearest point it can read to which will give us some error. So knowing the distance between those points is useful. I understand that the unit will have error as well depending on how many satellites are around, etc. But even if the unit was perfect there would still be some rounding error for most coordinates assuming they did not just happen to be on top of one of those points.

### #8

Posted 03 February 2010 - 02:54 PM

As you move towards the poles the latitude remains constant but the longitude gets smaller until at the poles it is zero feet.

This post has been edited by **webscouter.**: 03 February 2010 - 02:55 PM

### #9

Posted 03 February 2010 - 02:57 PM

### #11

Posted 03 February 2010 - 03:03 PM

StarBrand, on Feb 3 2010, 05:57 PM, said:

Outstanding StarBrand! Outstanding! Thanks very much. That is exactly what I was looking for. Looks like for where I live the distance between 0.001 minutes is only about 4.5 feet. So worst case the rounding error would be about 2 feet. Not worth worrying about but good to know.

Thanks again.

### #12

Posted 03 February 2010 - 03:04 PM

webscouter., on Feb 3 2010, 05:54 PM, said:

As you move towards the poles the latitude remains constant but the longitude gets smaller until at the poles it is zero feet.

Thanks Webscouter. Looks like for where I am at a thousandths of a minute is about 4.5 feet.

### #13

Posted 03 February 2010 - 03:06 PM

microvision, on Feb 3 2010, 04:27 PM, said:

Important part in purple

I'll answer the last first with a link to this portion of my FAQ. The difference between a latitude line is constant anywhere on the globe. If it increases or decreases 0.001 minutes (e.g., from N 42° 20.000 to N 42° 20.001) the distance is a constant 6.074 feet. According to the grid I linked, since Boston is around N 42 20.000, W 071° 04.000, you would look for 42 degrees going down and go over to the column labeled "20" to see that the distance between W 071° 04.000 and W 071° 04.001 would be about 4.49 feet.

**So, movement of the GPS one click up or down is somewhere between 4˝ and 6 feet. That's the precision of the device.**

Let's take a look at the rounding you're talking about. I believe I know where you're coming from. Look at this diagram:

You're worried that the cache might be in that dotted line square instead of exactly where the cross-hairs are. Believe me GPS devices are NOT that accurate. They usually are off by about 20-30 feet. The difference you're talking about is a square that is only somewhere around 4x6 feet.

**The device is MUCH more precise than it is accurate.**

================

I think you're over-thinking it. The GPS device has an error of accuracy of about 20 feet. But if it was a completely accurate and precise device that showed you down to the millimeter where the cache was, it wouldn't really be any challenge. A better way to think of it is that the hider's GPS is taking a pretty good estimate that the cache is within 20 feet of the coordinates being displayed when the cache is placed. The seeker's GPS will try to match those coordinates, and when it says it's RIGHT AT THE CACHE, the cache may actually be somewhere around 20 feet away. If both the hider and the seekers are 20 feet off in the opposite directions, the cache could be 40 feet away from the real-life coordinates.

So, when you get down to less than 30 feet from the cache, put your GPS down and think of a 10-yard-line in football. Then look around in that radius to see if there's any place where you'd hide a cache.

### #14

Posted 03 February 2010 - 03:07 PM

### #15

Posted 03 February 2010 - 03:07 PM

### #16

Posted 03 February 2010 - 03:13 PM

microvision, on Feb 3 2010, 04:07 PM, said:

Your settings changed - I forget how to change them back but I will look them up - seems to me it is found under the "my controls" link at the top of the page. - checking..........

### #17

Posted 03 February 2010 - 03:58 PM

Markwell, on Feb 3 2010, 03:06 PM, said:

**So, movement of the GPS one click up or down is somewhere between 4˝ and 6 feet. That's the precision of the device.**

Let's take a look at the rounding you're talking about. I believe I know where you're coming from. Look at this diagram:

You're worried that the cache might be in that dotted line square instead of exactly where the cross-hairs are. Believe me GPS devices are NOT that accurate. They usually are off by about 20-30 feet. The difference you're talking about is a square that is only somewhere around 4x6 feet.

**The device is MUCH more precise than it is accurate.**

It is nice to see that someone understands the difference between precision and accuracy! The GPS does not lead to a point, but rather a rectangle 4x6 feet!

### #18

Posted 04 February 2010 - 08:46 AM

StarBrand, on Feb 3 2010, 06:13 PM, said:

microvision, on Feb 3 2010, 04:07 PM, said:

Your settings changed - I forget how to change them back but I will look them up - seems to me it is found under the "my controls" link at the top of the page. - checking..........

Thanks for letting me know my settings changed StarBrand. That got me looking to fix the problem on my end. Turns out if you go to the top right of a topic there is a box labeled "Options", in it there are "Display Modes" and that is where one can change the way a topic is listed. For some reason mine switched from standard to outline on its own. But I now have it back to standard so all is good.

### #20

Posted 04 February 2010 - 10:37 AM

Markwell, on Feb 3 2010, 04:07 PM, said:

Well, I understand a lot about navigation, and I for one appreciated both the pretty picture and the faq...

Keep up the good work... Come to think, I like most of your stuff... I keep a file of such things on the computer...

Thanks.

Doug

### #21

Posted 04 February 2010 - 01:32 PM

Same basic picture as last time. However, the dotted square of 4x6 is now highlighted, and is to scale. I've also added the scale concentric circles of 20 feet and 30 feet to show how much error is typically on a standard GPS.

So the error in the accuracy of the GPS is far greater than the error in the precision of the displayed coordinates. That is by design. I know that the GPS units that were constructed pre-2000 had the capacity to be accurate to the same scale we are now, but selective availability limited the accuracy to around 300 feet. The units like the Magellan 315 only had precision on the display out to 2 decimals of minutes (N 41° 20.06 W 071° 04.75). That was fine because they were more precise than they were accurate. When SA was turned off May 1 2000, the units were more accurate than they were precise, and that's a problem.

- I could tell you that I'm about 1.72 meters tall. If you looked at me from a kilometer away, that would be good enough because you couldn't tell the difference between someone that was 1.7 meters tall and 1.8 meters tall.
- If you were right next to me, and I told you I was 1.7272 meters tall and someone else was 1.7275 meters tall you wouldn't know the difference. Again, I'm giving you more precision than you need.
- If you were right next to me, and I told you I was 1.7 meters tall and someone else was 1.7 meters tall they could be anywhere from 1.65 meters to 1.74 - that's about 3˝ inches difference in the empirical system. That's less precision than accuracy needs, and so it's faulty.

### #22

Posted 06 February 2010 - 12:41 PM

In other words the "6 feet" example you give remains constant, but the "4 feet" measurement you depict depends on your position north (for example) of the equator. So you cold possibly end up with a 6 foot X 1 foot target zone if you go far enough North.

Correct me if I am wrong.

When I first started researching my GPS for hunting I seem to recall finding a website that gave the equation to use to figure the "width"of the longitude "square" based on your location. I believe I found it on a "Surveying" website.

Did I mention I hate math??? lol if your using this in reference to caching, your accuracy will be dependent on the accuracy of the lister.

This post has been edited by **NeecesandNephews**: 06 February 2010 - 12:43 PM

### #23

Posted 06 February 2010 - 01:18 PM

NeecesandNephews, on Feb 6 2010, 03:41 PM, said:

In other words the "6 feet" example you give remains constant, but the "4 feet" measurement you depict depends on your position north (for example) of the equator. So you cold possibly end up with a 6 foot X 1 foot target zone if you go far enough North.

When I first started researching my GPS for hunting I seem to recall finding a website that gave the equation to use to figure the "width"of the longitude "square" based on your location. I believe I found it on a "Surveying" website.

I believe the Longitude equation constant you are looking for is Cosine (Latitude).

At the Equator (0 Degrees Latitude) Cosine 0 = 1 (6 times 1 = 6 feet spacing per .001 minute Longitude)

At either Pole (90 Degrees Latitude) Cosine 90 = 0 (6 times 0 = 0 feet spacing per .001 minute Longitude)

At 60 Degrees Latitude Cosine 60 = .5 (6 times .5 = 3 feet spacing per .001 minute Longitude)

At 40 Degrees Latitude Cosine 40 = .766 (6 times .766 = 4.596 feet spacing per .001 minute Longitude)

The Latitude spacing does remain a 6 foot constant anywhere on Earth.

### #24

Posted 07 February 2010 - 09:55 AM

NeecesandNephews, on Feb 6 2010, 02:41 PM, said:

You are indeed correct. This portion of my FAQ was mentioned earlier. The original poster is in somewhere near Boston, which is why I used N 41 20.056 W 071 04.753 as the basis. That would put the difference between longitude lines at somewhere around 4.59 feet. Farther north, the longitude lines get closer until at exact point of the true north pole, the longitude lines conversion on a single point and the distance is exactly 0. Farther south, they spread apart until when you're at the equator the rectangle would be a square of 6.076 feet both in separation of a single 0.001 of minutes.

I continued on the example I had used previously of Boston, so the rectangle would be about 4x6 (actually 4.59x6.076 - but I gave a rough approximation).

But the whole POINT was that the accuracy of the point is not so cumbersome as the precision of the device, which is much worse than the accuracy (hence my picture).

This post has been edited by **Markwell**: 07 February 2010 - 09:58 AM