Measuring distances in Minecraft can be quite tedious, but with a few simple guidelines you will never make a mistake again!
Official Units of Measure
Distances in Minecraft are quite easy to measure. Officially , Minecraft uses the metric system, and each block is considered to be 1 cubic meter. To measure long distances, then, simply place a torch or other marker object every ten blocks. Place a second marker at each tenth marker to mark 100 m distances, and at ten of these, you have one kilometer. Try placing a sign at each km, just like road signs in the real world.
Using the Imperial System
Some may wish to measure distances in yards and miles instead of meters and kilometers.
So, you can simply consider a block as 1×1×1 yard instead. One mile is exactly 1760 yards. Place your initial markers every 16 blocks, and your double markers at every 11 markers rather than every 10. Thus, a double marker measures 16 × 11 = 176 yards, or 1⁄10 of a mile.
One Mile converts to 1609.344m. To simplify, consider a Mile to be 1610 blocks long. So for every 10 blocks, place a marker. Do this 161 times and you will have about a Mile in total. In Real Life, 1 Mile = 1.6 km & 0.625 Mile = 1 km.
If you press F3, the debug screen will give you your present location in X-Y-Z co-ordinates. Measuring distances between two locations or waypoints is as easy as subtraction, if you walk in a cardinal direction. Otherwise you will need to make use of good old algebra to solve the distance. This is not strictly in-game, but it makes a drastic difference in gameplay, avoiding a lot of frustrated wandering. Note that the X and Z coordinates are horizontal and can be positive or negative (the spawn point will be fairly close to 0, 0), but the Y coordinate represents your altitude, and Y=0 is the bedrock floor of the gameworld.
If the measurement is being taken above ground, and lighting the entire path is not necessary, place the markers as above. When 100 m is reached, the 10 m markers can be removed and reused for the next 100 m run. This allows for the path to be constructed without having to count 100 blocks at a time, while still allowing the markers on the completed path to be easily followed without using too much material.
Volume and Surface Area
The formula for the volume of a cube is s3, where s stands for the measurement of one of the cube's side. Since each side of a normal Minecraft block is 1 meter, this would equal 13, which would result in 1m3. (This works the same for yards, or any other unit of length. So do the rest of these comments.)
The formula for the surface area of a cube is 6s2, where s stands for the measurement of one of the cube's side. Since each side of a normal individual Minecraft block is 1 meter, this would equal 6×12, which would equal 6×1, which would result in 6m2.
As you make something, e.g. a house, bigger in all directions, its surface area increases faster than its length, but not as fast as its volume. The surface area tells you how many blocks you'll need for the outer walls, but your interior furnishings will probably increase according to the volume. Of course, shape matters: An 8×8×1 layer of dirt corresponds to a stack of 64 dirt blocks, but so does a 4×4×4 cube, or a 2×2×16 trench or shaft.
Using the Euclidean Distance Formula
Sometimes the need arises in which you need to measure distances diagonally, which is easy to do with a little algebra. The formula for Euclidean distance (in two dimensions), where d is the distance:
d = sqrt( (x1 - x2)2 + (z1 - z2)2 )
d = Distance in meters x1, z1 = Location number 1, in meters x2, z2 = Location number 2, in meters sqrt(n) = Square root of n (√n)
If this formula looks a bit complicated, don't worry; it should all be much clearer with an example:
Suppose the F3 debug screen shows the following at Location 1:
XYZ: -35.313 / 68.00000 / 97.489
These numbers are coordinates in meters. At Location 2, it shows:
XYZ: 76.793 / 43.00000 / -5.113
Usually, the decimal points can be truncated (ignored), as usually you don't want to cloud your results with where you happen to be standing within each block. In two-dimensional (map) coordinates, we also ignore the elevation (Y value). Hence, those two screens give us the following coordinates:
x1, z1 = -35, 97 x2, z2 = 76, -5
Now we simply plug those numbers in to the distance formula, above:
d = sqrt( (x1 - x2)2 + (z1 - z2)2 ) d = sqrt( (-35 - 76)2 + (97 - -5)2 ) d = sqrt( -1112 + 1022 ) d = sqrt( 12321 + 10404 ) d = sqrt( 22725 ) d = 150.75 m
Considering horizontal (map) distance only, the two locations are 150.75 m apart.
Euclidean Distance in 3 Dimensions (Including Elevation)
The above calculation is correct if you want the "map" distance between two points (i.e., only the North/South (z) and East/West (x) distance). But if you wish to include the elevation (y) in the distance calculation as well, that's very easy to do: Simply add the y coordinates to the above distance formula, as shown in bold text, below:
d = sqrt( (x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2 )
Referencing the above debug screens again, our 3-dimensional coordinates are as follows:
x1, y1, z1 = -35, 68, 97 x2, y2, z2 = 76, 43, -5
Again, solving for d, with differences in bold text:
d = sqrt( (x1 - x2)2 + (y1 - y2)2 + (z1 - z2)2 ) d = sqrt( (-35 - 76)2 + (68 - 43)2 + (97 - -5)2 ) d = sqrt( -1112 + 252 + 1022 ) d = sqrt( 12321 + 625 + 10404 ) d = sqrt( 23350 ) d = 152.81 m
Hence, with the elevation considered, the two locations are 152.8 m apart. Note that, in this example, including the 25 m elevation only resulted in a difference of about 2 m (2 blocks).