# Meters and feet

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## Overview

Meter/feet conversion is a deeper subject than you probably think.

For one thing, there are different definitions of a foot. For another, the size of the numbers we deal with in maps requires that we use high-precision conversion factors and not simple rule-of-thumb factors you may be used to.

Also see Projection.

## When is a Foot not a Foot?

There are different definitions of "foot". Two in particular we deal with:

• "standard", or international foot = 0.3048 meters
• US survey foot = 1200/3937 meters

US survey feet are used in MOST (but not all) state plane systems. The difference (about 2 feet per million) is enough to matter in precision GPS and map projection, especially when the coordinates are large. In the example given below the error is over 26 feet.

When in doubt, use US survey feet.

## Conversion Factors

USE THESE! Do NOT use simplified or rounded versions. These are rounded to the nearest billionth; all listed decimals are significant.

• US Survey Feet:
• 1 US survey foot = 0.304800610 meters
• 1 US survey foot = 1200/3937 meters
• 1 meter = 3.280833333 US survey feet
• 1 meter = 3937/1200 US survey feet
• International Feet:
• 1 international foot = 0.3048 meters
• 1 international foot = 381/1250 meters
• 1 meter = 3.280839895 international feet
• 1 meter = 1250/381 international feet
• Between the two:
• 1 international foot = 0.99999799989839999 US survey feet
• 1 US survey foot = 1.0000020013083362 international feet

So, to convert international feet to US survey feet, multiply by 0.99999799989839999. To convert US survey feet to international feet, multiply by 1.0000020013083362.

## Why So Much Precision?

Here is a real-world example illustrating the hazards of rounding.

On a raster translation project, we recieved MRSID data which had been projected into feet at a conversion factor of 3.28.

The origin of one of the SID files was (2109603, 12936516). This is in Texas, the numbers are large.

Divide by their factor (3.28) to get the original meters and you get: (643171.65, 3944059.76). Then multiply by a slightly more accurate 3.2808: (2110117.55, 12939671.26).

That's 515 feet off in X and 3155 feet off in Y! The total offset is 3196 feet!

A more accurate factor for survey feet is 3.280833333. Do the same thing from our more accurate version, and the difference between 3.2808 and 3.280833333 is: (2110138.99, 12939802.73) - which is 21 feet off in X and 131 feet off in Y.... total offset is 133ft.

More generally, you can generate an error factor thus:

```error = rightFactor / wrongFactor - 1.0;
```

Multiply this error factor by your coordinates and you'll get some idea how far off you'll be.

The error in 3.2808 is 0.0000101600219458 and the error in 3.28 is a whopping 0.00025406493902435656. Sure, that's only 2 ten-thousandths, but when you multiply it by a number over ten million, it matters a LOT - thousands of feet. Makes it hard to find your truck, a consumer, or a pole.

Note that using the wrong type of feet - e.g. international rather than survey - would, in this example, result in an error of over 26 feet.