How to compute the throughput of an inserter?

Question

The Factorio wiki is notorious for giving a lot of information, including Inserter Throughput, but the table is incomplete and no formula is given to fill the holes.

How can one compute the throughput of an inserter?

Answer 1

What's in a tick?

In Factorio, all entities execute actions in a tick. That is, 60 times per second -- nominally -- the game ticks and every entity is visited and performs an action.

The inserters are no different, within a tick an inserter can:

• Rotate, possibly incompletely.
• Extend or contract: that is, switch from close lane to far lane of a belt, or vice-versa.
• Grab or drop items¹.

And sometimes perform a combination of these actions.

Chest to Chest

Belts are complicated, so let's start with Chest to Chest inserter throughput. A complete cycle involves:

1. The inserter grabbing N items, which takes 1 tick.
2. The inserter rotating 180°.
3. The inserter dropping N items, which takes 1 tick.
4. The inserter rotating 180° again, to go back to its initial position.

For example, a Fast Inserter (or Bulk Inserter) performs 0.04 turn/tick. This means 12.5 ticks for 180° turn, rounded up to 13 ticks.

Naively applied, this would that 1 + 13 + 1 + 13 = 28 ticks are necessary to transfer one single item for a Fast Inserter, however measurements show it only takes 26 ticks.

Thus, it seems that the inserter can grab/drop items on the tick it gets in position to do so, with no extra tick spent. This is confirmed by using 26 ticks as the number of ticks to transfer N items, and matches the fact that for a single item, the number of turns per second of an inserter also matches the chest-to-chest throughput.

The formula, thus, is simply hand-size * 60 / full-turn-number-ticks.

Where the full-turn-number-ticks is rounded up to even as necessary to account for the fact that half-turns take an entire number of ticks.

Note: if I have time, one day, I'll reverse engineer again the Chest-to-Belt, which is trickier as the belt needs to clear away the items before the inserter can drop more.