X, Y and Z: How 3D Space Works

In 3D, everything has three directions: X goes left and right, Y goes front and back, and Z goes up and down. With three numbers, one for each direction, you can describe any spot in the whole room, or on a 3D printer's plate.

These three directions are called axes (one is an axis). Once you understand them, you can put any shape exactly where you want it. In this lesson you'll learn what X, Y and Z mean and try them in Kids 3D Lab.

Practice gameMove itSlide a ball left and right (X), back and front (Y), and up (Z).Play →

Start with flat: X and Y

Imagine a map, or a sheet of squared paper. To tell a friend where something is, you need two numbers:

How far across (left or right). That's X.
How far up the page (towards the top or the bottom). On a printer's plate, that's Y: how far to the back or the front.

This is just like the game Battleship, or finding a square on a map: "Go 3 across and 5 up."

Two numbers find any spot on flat paper: X across, then Y back.

Add height: Z

Now imagine the map is a table top, and you want to say how high above the table a balloon is floating. You need a third number: Z, the height.

X: left (−) or right (+)
Y: front (−) or back (+)
Z: down (−) or up (+)

X and Y find the spot on the floor. Z says how high the balloon is.

With X, Y and Z, you can describe any point in 3D space. That's why it's called 3D: three dimensions.

Width, depth and height

The three directions also give us the three sizes of a shape:

Direction	Size word	Example
X	Width	How wide a box is, left to right
Y	Depth	How deep it is, front to back
Z	Height	How tall it is, bottom to top

Width goes with X, depth with Y, and height with Z.

In Kids 3D Lab, every shape has a Width, a Depth and a Height, in millimetres.

The middle of the plate is zero

Every 3D design program needs a starting point: the spot where X, Y and Z are all 0. It's called the origin. In Kids 3D Lab, the origin is the middle of the plate.

A shape at X 0, Y 0 is right in the middle.
X 20 means 20 mm to the right of the middle. X −20 means 20 mm to the left.
Y 30 means 30 mm towards the back. Y −30 means 30 mm towards the front.
Z 0 means sitting on the plate. Z 10 means lifted 10 mm into the air.

The printer plate seen from the top. Zero is in the middle. A blue ball sits at X +40 on the right and a green ball at X –40 on the left. Y +40 is at the back and Y –40 at the front. — Seen from the top: zero is the middle of the plate. Plus goes right and back, minus goes left and front.

Colours help you remember

Kids 3D Lab uses a colour for each direction:

Red is X (left and right)
Green is Y (front and back)
Blue is Z (up and down)

When you pick a shape, you see a red arrow, a green arrow and a blue arrow. Drag one to move the shape in just that direction. The numbers in Position and the arrows use the same colours. Lots of 3D programs use these same three colours, so you'll recognise them everywhere.

Try it in Kids 3D Lab

Open Kids 3D Lab and click New build.
Click Ball. Look at Position in the panel. What are X, Y and Z?
Set X to 0, Y to 0 and Z to 0. The ball moves to the middle of the plate.
Now set X to 40. Which way did it move?
Set X back to 0 and set Y to 40. Which way now?
Set Y back to 0 and set Z to 30. The ball floats in the air!
Click Drop to plate (the arrow-down button at the top of the panel) to bring it back down.

Challenge: the X, Y, Z treasure hunt

Add four Boxes.
Put one at each corner of a square: (X 30, Y 30), (X −30, Y 30), (X −30, Y −30) and (X 30, Y −30).
Put a Ball in the exact middle, floating at Z 20.
Now look from the top: click TOP on the view cube. Do the boxes make a perfect square?

The treasure hunt seen from the top: four boxes at X 30 and –30, Y 30 and –30 make a square, with a blue ball floating in the middle at Z 20 — What your treasure hunt should look like from the TOP.

Challenge: stack with numbers

Add a Box that is 20 tall.
Add another Box, and set its Z to 20. It sits exactly on top!
Add a third with Z 40. A tower of three!

A tower of three boxes, each 20 mm tall: blue at Z 0, green at Z 20 and pink at Z 40, with a blue ruler beside them — Each box's Z is the height of the boxes under it: 0, then 20, then 40.

The Z of each box is the height of all the boxes underneath. That's how you stack things exactly.

Practice gameLine things upPick the shape that stays put, and line the others up with it.Play → Practice gameLook from every sideAre you looking from the top, the front or the side?Play →

Questions kids ask

Why is up Z and not Y?

Different programs choose differently! In maths class, Y often means up, because a graph on paper goes up the page. 3D printers and many design programs use Z for up, because they start from the flat plate (X and Y) and build upwards. Kids 3D Lab uses the printer's way.

What is 3D?

3D means three dimensions: width, depth and height. A drawing on paper is 2D: it only has width and height. Things you can hold are 3D.

Can a shape go below zero?

Yes. A negative Z puts part of the shape under the plate. In Kids 3D Lab, the part under the plate is hidden and won't be printed. It's a handy way to cut the bottom off a ball and give it a flat base!

Do professional designers use X, Y and Z?

Yes, all the time. Engineers, game makers and animators all use X, Y and Z to place things in 3D.

For grown-ups

Coordinates usually appear in school maths around ages 8 to 11, starting with the first quadrant and moving to negative numbers. 3D design makes them concrete: children type a coordinate and immediately see the result, and negative numbers become simple directions. The colour coding (red X, green Y, blue Z) is a common convention across 3D software. A nice extension is to plan a model on squared paper, writing coordinates first, then building it. See Millimetres Made Easy for the measuring side, and 3D Shapes for Kids for shape names.

Try X, Y and Z →