Common Distance Calculation Mistakes

Mistake One: Squaring After Adding

Adding the changes and then squaring the total. For a 3 and 4 case that gives 49 instead of the correct 25. Square each difference first, then add.

Mistake Two: Dropping a Term

In three dimensions, calculating as if it were two dimensional leaves the z change out entirely, which always understates the distance unless z happens to be equal.

Mistake Three: Rounded Unit Factors

Using 1 mile as 1.6 kilometres loses about 9 metres per mile. Since every unit is exactly defined, there is never a reason to use the rounded figure.

Mistake Four: Confusing the Nautical and Statute Mile

They differ by roughly 1.15 percent. Using the wrong one in a navigation or aviation context produces a systematic error in every figure derived from it.

Mistake Five: Early Rounding

Rounding the squared differences before adding them. The error is then carried into the square root, and for small differences the relative error can be surprisingly large.

Mistake Six: Expecting Travel Distance to Match

The straight line is a lower bound. Any real route involves obstacles, so planning around the straight line figure systematically underestimates journeys.