Transport belts/Physics

The belt transport system in Factorio is among the most detailed simulations in the game. Items in chests and other containers are stored simply as summed totals, and items on uninterrupted stretches of belts are moved in aggregate as an optimization, but in the end items on belts are simulated individually, especially when they get picked up or put down by inserters. This leads to some intricate behaviors, in particular when it comes to inserter throughput.

Belt properties

• Density. How many items fit onto a certain length of belt, measured in items per tile per belt lane. This is 4 on a straight belt, regardless of the type of item and type of belt. The item density on belts can be different from what they take up when just dropped on the ground (using the Z key). Density of items can be increased with the use of stack inserters, but there are still at most 4 stacks per tile per lane.
• Speed. The speed of items on a belt is measured for practical reasons in tiles per second. Note that internally it is measured in positions (1/256 tile) per tick (1/60 sec). More on that below. The speed of a basic transport belt is 1.875 tiles per game-second. Fast transport belt is twice as fast, express transport belt is three times as fast, and turbo transport belt is four times as fast.
• Throughput. How many items per second that are moved from one tile to the next. That is density (items per tile) multiplied by speed (tiles per second), e.g. for a basic belt it is 4 * 1.875 = 7.5 items per second, for one belt lane. For both lanes it is doubled, i.e. 15 items per second.
• Compression. If there is no empty space between items on the belt it is called fully compressed, otherwise its compression is only partial and it does not have optimal throughput. Entities that put items onto belts – inserters, splitters, other belts coming from the side, mining drills, etc - make room for their item by enlarging a small gap until it is exactly big enough for the item. That means belts naturally become fully compressed before items start to back up.
• Lanes. Belts have two parallel lanes, and the density and speed of each lane is constant and independent of the other one, regardless of twists and turns. So items in the inner lane of a turn exit it before those in the outer lane, since their speeds are equal and the inner lane is shorter than the outer one.

Belt speeds

Given the values above we can calculate the speed and throughput of the three types of belts. Measurements confirm these values.

Belt type	Speed		Throughput
	Factor	Tiles/sec	Single lane, items/sec	Single lane, items/min	Both lanes, items/sec	Both lanes, items/min
Transport belt	1	1.875	7.5	450	15	900
Fast transport belt	2	3.75	15	900	30	1800
Express transport belt	3	5.625	22.5	1350	45	2700
Turbo transport belt	4	7.5	30	1800	60	3600

Items on belts

As mentioned earlier, items take space on belts in terms of density and compression. However, every item on a belt is logically on exactly one belt tile at any moment in time.

For example, even though in a screenshot it might look like an item is halfway out from one tile and halfway onto the next, it will be accounted to exactly one of the two tiles:

• If you stop the belt tile the item is on, it stops; else it continues moving - there are no in-between states.
• If you connect the two belt tiles to a circuit network and get them to report statistics about the items they carry, you will see the item being accounted to exactly one of them.
• An inserter can only pick up items that are logically on the tile in front of it, not items butting in from the neighboring tiles.

In this sense it is useful to think of items as points with a certain minimum distance between them, rather than things with an area lying next to each other. For belt calculations and circuit networks involving belts it doesn't really matter where those "center points" are within the graphic of the item, but they appear to be in the middle:

In the image above the belts have been started at 1 tick offsets, then all the top row tiles have been stopped at once, causing the front-most stopped items to poke out by varying amounts. The items on the leftmost belt are almost halfway into the next tile, which means their center points are the closest to the edge of the upper stopped tile.

Below is a schematic example showing some items moving over two straight fast transport belt tiles and what their read signals would be at each tick. Their center points are marked with *. (The space between belt tile 1 and 2 is only for visualisation - in the game there are no such gaps between tiles.)

Tick  Belt tile 1                      Belt tile 2                       Read belt tile 1  Read belt tile 2
      |------------------------------| |------------------------------|    Pulse   Hold      Pulse   Hold
  0         <---*-->  <---*--> <---*-- ><---*-->            <---*-->         0       3         0       2
  1           <---*-->  <---*--> <---* --><---*-->            <---*-->       0       3         0       2
  2             <---*-->  <---*--> <-- -*--><---*-->            <---*--      0       2         1       3
  3               <---*-->  <---*--> < ---*--><---*-->            <---*      0       2         0       3
  4   ->            <---*-->  <---*-->  <---*--><---*-->            <--      0       2         0       2
  5   *-->            <---*-->  <---*- -> <---*--><---*-->            <      1       3         0       2
  6   --*-->            <---*-->  <--- *--> <---*--><---*-->                 0       2         1       3
  7   <---*-->            <---*-->  <- --*--> <---*--><---*-->               0       2         0       3
  8     <---*-->            <---*-->   <---*--> <---*--><---*-->             0       2         0       3

Belt positions and lengths

Careful measurement shows that the outer lane of a turn is exactly 1.15234375 times longer than a straight belt, or 295/256 in fractional format. That means each straight belt tile has 256 positions an item can be in, even though measuring the position with that precision can only be done indirectly.

Here are the speeds and lengths of the various types of belt tiles in terms of these positions:

What		Number of positions
Basic transport belt speed, per tick		8
Fast transport belt speed, per tick		16
Express transport belt speed, per tick		24
Turbo transport belt speed, per tick		32
Length of an item on a belt (of any speed)		64
Length of one lane of a straight belt tile and underground belt		256
Length of one lane of the splitter input line		179 (128+51)1
Length of one lane of the splitter output line		128
Length of the inner lane of a turn		106
Length of the outer lane of a turn		295
Length travelled by an item sideloaded late on a straight belt or underground exit		68
Length travelled by an item sideloaded early on a straight belt or underground entrance		188

⁽¹⁾includes a buffer of 51 positions [1]

For example, given the figures above, we can deduce the speed of a basic belt:

8 (positions per tick) / 256 (positions per straight belt tile) * 60 (ticks per second) = 1.875 tiles per second

Its throughput per belt lane is:

8 (positions per tick) / 64 (positions per item) * 60 (ticks per second) = 7.5 items per second

See also

• Belt transport system
• Jan 04 FFF #276: Belt item spacing & Script rendering
• Feb 03 FFF #176: Belts optimization for 0.15
• Accurate belt segment measurements (discusses 0.17)
• About belt numbers, from boskid