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If a dwarf falls from a great enough height, they'll take damage upon landing. The amount of damage is determined by three things: the height fallen, the surface being landed upon, and how much Fall Damage Resistance the player has at the moment of impact. You have to fall a minimum distance before any Fall Damage gets applied, but then it quickly ramps up to lethal levels.

Summary

• Fall Damage is only taken when the player is falling faster than 10 m/sec
• Fall Damage Resistance is Additive, not Multiplicative. Each instance gets subtracted from the baseline multiplier of 1.0, down to a minimum of 0.0 (you can't heal from Fall Damage if you have more than 100% Fall Damage Resistance)
• There are three surfaces in the game that increase the Fall Damage velocity threshold from 10 m/sec to 15 m/sec:
• Engineer's Platforms with T2.A "Plastcrete MKII" equipped
• Glacial Strata's Deep Snow
• Fungus Bogs' Sticky Goo (generated as part of the level; not the goo dropped by Goo Bombers)
• Because Fall Damage is just a scalar multiplier of the player's falling velocity, it scales with time squared (x2) instead of linearly.

Sources of Fall Damage Resistance

• The Abyss Bar beer "Tunnel Rat" should provide 30% Fall Damage Resistance for the entire next mission, but due to a bug where buff beers get applied twice it actually provides 60%.
• Gunner's Zipline Launcher T3.A "Disconnection Protection" provides 25% Fall Damage Resistance to all players after disconnecting from the Zipline1
• Scout's Grappling Hook T4.A "Safety First" provides 25% Fall Damage Resistance to the Scout after releasing the Grappling Hook1 (re-uses the Zipline effect)
• Scout's Armor Rig T3.A "Shock Absorbers" provides a permanent 33% Fall Damage Resistance to the Scout

1. Note: there appears to be a bug where this 25% Fall Damage Resistance lasts until the player dies and all Status Effects get cleared. There's no reference of its duration in the game files, and it doesn't end after the player takes fall damage.

Equations

Converting Height (h) to falling Velocity (v)

Using the in-game gravity acceleration of g = 9.8 m/sec2

$v = \sqrt{2*g*h}$

$v = \sqrt{19.6*h}$

When the Low Gravity anomaly is active, then g = 4 m/sec2

$v = \sqrt{8*h}$

Calculating Fall Damage

Let 'R' represent the player's current Fall Damage Resistance

$D = (v - 10) * 17.5 * (1 - R)$

If landing on Platform Mk 2, Deep Snow, or Fungus Bogs' Sticky Goo:

$D = (v - 15) * 17.5 * (1 - R)$

Quick Reference Tables

Falling onto Regular Terrain

Height Fallen (m) Velocity upon Impact (m/sec) Fall Damage Taken (before Resistance)
5.1 9.99 0
6 10.84 14.7
7 11.71 29.925
8 12.52 44.1
9 13.28 57.4
10 14 70
15 17.15 125.125
20 19.8 171.5

Falling onto Platform Mk2

Height Fallen (m) Velocity upon Impact (m/sec) Fall Damage Taken (before Resistance)
11.47 14.99 0
13 15.96 16.8
14 16.56 27.3
15 17.15 37.625
20 19.8 84
25 22.14 124.95
30 24.25 161.875

Falling onto Regular Terrain (Low Gravity)

Height Fallen (m) Velocity upon Impact (m/sec) Fall Damage Taken (before Resistance)
12.5 10 0
15 10.95 16.625
20 12.65 46.375
25 14.14 72.45
30 15.49 96.075
35 16.73 117.775
40 17.89 138.075
45 18.97 156.975

Falling onto Platform Mk2 (Low Gravity)

Height Fallen (m) Velocity upon Impact (m/sec) Fall Damage Taken (before Resistance)
28.12 14.99 0
30 15.49 8.575
40 17.89 50.575
50 20 87.5
60 21.91 120.925
70 23.66 151.55

Trivia

• The dwarves will let out a shout if they fall further than 15m.
• Because Fall Damage only starts when falling faster than 10 m/sec, players can fall from a height up to 5.1m without taking Fall Damage. If falling onto a Platform Mk2 (or similar surface) then that height gets raised to 11.48m.
• When using the Laser Pointer to point down to the ground you're about to fall to, the distance shown will be 1.5m too high. For example: if the ledge was 5.1m tall, the Laser Pointer would show 6.6m looking down. Similarly, when using the Laser Pointer to look up, it will show a distance that is 0.9m too short. Again, using a height of 5.1m, from the ground looking up the Laser Pointer would show that the ledge is 4.2m away.
• Scout's Grappling Hook has a similar offset: when looking down it displays 1.2m too high (5.1m => 6.3m) and when looking up it displays 1.7m too short (5.1m => 3.4m).
• If you don't want to remember all of the complicated stuff, just use the Laser Pointer and remember 6.6m pointing down to regular terrain, or 13.0m pointing down to Platform Mk2 (or similar surface).
• It's possible for Scouts to become semi-permanently immune to Fall Damage. With his Armor Rig's T3.A (33%), Tunnel Rat (60%), and either Grappling Hook T4.A or Zipline Launcher T3.A (25%), Scout's Fall Damage Resistance becomes 118% (multiplies all Fall Damage by zero). Due to a bug where the Grappling Hook/Zipline effect only ends when the player dies, the Scout won't take any Fall Damage until they get killed by enemies, teammates, or the environmental hazards. Using the Grappling Hook again after being revived restores the Fall Damage immunity.
• In a similar vein, Gunners can provide their whole team with a semi-permanent 25% Fall Damage Resistance buff with just one Zipline. If any teammate dies and subsequently loses the buff, they can just hop on and off a Zipline to restore the buff.
• Because the Zipline Launcher T3.A and Grappling Hook T4.A both use the same Status Effect, they do not stack with each other to provide a 50% Fall Damage Resistance. Only one instance can be active on the player, so the best that this can do is 25%.