Every formula in one place. L is a level, ⌊x⌋ rounds down and ⌈x⌉ rounds up. "Economy speed", "lore
speed" and "march speed" come from the world's charter.
Costs and times
| What |
Formula |
| Building cost at level L |
base cost × factor^(L − 1), rounded down |
| Lore cost at level L |
base cost × factor^(L − 1) (factor 2 unless noted; Cartography rounds to 100) |
| Mana needed at level L |
base mana × factor^(L − 1) |
| Raze fee |
cost of that level × (1 − 4% × Stormcalling) |
| Build time (h) |
(iron + runestone) ÷ (2,500 × max(4 − L ÷ 2, 1) × (1 + Builders' Guild) × 2^Golem Foundry × economy speed) × (1 − kindred reduction) |
| Study time (h) |
(iron + runestone) ÷ (1,000 × (1 + linked Mage Tower levels) × lore speed) × (1 − study reduction, at most 75%) |
| Muster time per piece (h) |
(iron + runestone) ÷ (2,500 × (1 + Muster Hall) × 2^Golem Foundry × economy speed) × (1 − kindred reduction) |
| Finish now |
max(10, ⌈minutes left × 6⌉) Fateshards |
| Halve |
max(10, ⌈minutes left ÷ 2 × 6⌉) Fateshards |
Times are never shorter than 1 second. Kindred reductions are capped at 50%.
Production
| What |
Per hour, before bonuses |
| Iron Mine |
30 × L × 1.1^L |
| Runestone Quarry |
20 × L × 1.1^L |
| Aether Condenser |
10 × L × 1.1^L × (1.44 − 0.004 × highest temperature) |
| Mana used by a mine or quarry |
10 × L × 1.1^L |
| Mana used by a condenser |
20 × L × 1.1^L |
| Mana used by a Delver Golem |
50 |
| Ley Tap mana |
20 × L × 1.1^L |
| Aether Furnace mana |
30 × L × (1.05 + 0.01 × Mana Theory)^L |
| Aether Furnace burn |
10 × L × 1.1^L aether |
| Sun Prism mana |
⌊(highest temperature + 140) ÷ 6⌋ |
| Tithe |
30 iron and 15 runestone |
Yield = tithe × economy speed + mine output × throttle × min(1, mana produced ÷ mana required) ×
(1 + yield bonuses + golem bonus) × economy speed
Mana produced = (Ley Tap + Aether Furnace + Sun Prisms) × throttle × (1 + mana bonuses)
Golem bonus = min(50%, 0.02% × min(golems, 8 × (Iron Mine + Runestone Quarry + Aether Condenser levels)))
Vault capacity = 5,000 × ⌊2.5 × e^(20 × L ÷ 33)⌋ × (1 + storage bonuses)
Plots, holds and slots
| What |
Formula |
| Stronghold plots |
site plots + world bonus plots + Earthshaper plots + grants |
| Earthshaper plots |
5 per odd level + 6 per even level |
| Skyhold plots |
min(⌊(span ÷ 1,000)²⌋, 1 + 3 × Sky Keep) + Sky Grants |
| Strongholds held |
1 + ⌈Cartography ÷ 2⌉ |
| Quest slots |
⌊√Cartography⌋ (+1 Marshal, +2 Wayfarer) |
| Longest quest |
max(1, Cartography) hours |
| Banners |
1 + Banner Command (+2 Marshal, +2 Warlord, +1 full council) |
| Spell Battery slots |
10 × level (Counterspell 1, Meteor Spell 2) |
Marching
| What |
Formula |
| Distance, same site |
5 |
| Distance, same province |
1,000 + 5 × |Δ site| |
| Distance, same continent |
2,700 + 95 × |Δ province| (wrapping in a round world) |
| Distance, other continent |
20,000 × |Δ continent| (wrapping in a round world) |
| Unit speed |
base speed × (1 + drive bonus × drive lore level + other bonuses) |
| Host speed |
the slowest unit's speed |
| One-way time (s) |
(10 + (35,000 ÷ pace) × √(10 × distance ÷ speed)) ÷ march speed |
| March aether |
⌈Σ units × base aether × distance ÷ 35,000 × (pace ÷ 100 + 1)² × consumption⌉ + 1 |
| Camp aether |
⌈Σ units × base aether ÷ 10 × hours × consumption⌉ |
| Unit load |
base load × (1 + 5% × Planar Lore + other bonuses) |
Drive bonuses: Pathfinding 10%, Beastmastery 20%, Leystriding 30% per level. Consumption: the world's aether
consumption × 0.75 for a Warlord × (1 − kindred march aether reduction).
Battle
| What |
Formula |
| Might |
might × (1 + 10% × Weaponsmithing + kindred) |
| Ward |
ward × (1 + 10% × Warding + kindred) |
| Fortitude |
(iron + runestone) ÷ 10 × (1 + 10% × Armoursmithing + kindred) |
| Glancing blow |
might < 1% of the target's full ward |
| Rout chance |
1 − fortitude left ÷ full fortitude, when hit below 70% |
| Flurry chance |
(v − 1) ÷ v per extra strike |
| Plunder share |
100% outlaw; 50% dormant (75% Wayfarer); 75% if renown ≥ half the attacker's; else 50% |
| Spoils |
spoils share × (iron + runestone) of each destroyed unit |
| Fortifications rebuilt |
70% chance each (≤ 100 lost), else 60–80%; Master Mason restores half of the rest |
| Skyhold chance |
min(20%, 1% per 100,000 spoils) |
| Skyhold span |
random from 2,000 + 300 × chance to 3,000 + 300 × chance paces |
| Healers' Lodge share |
min(45%, 30% + 1% × (L − 1)) × (1 + kindred) |
| Lodge restoration time |
max(10 min, 2 h ÷ L ÷ economy speed) |
| Ordered retreat |
attackers ≥ 5 × defenders (3 × with the Marshal), strength = Σ √(might × (fortitude + ward)) |
| Retreat fee |
2 × Σ units × base aether |
| Reavers' take |
up to 30% of the new spoils |
Scouting, spells and Skyholds
| What |
Formula |
| Effective ravens |
ravens ± (difference in Spycraft)², + when yours is higher |
| Interception chance |
min(100%, ravens × units stationed ÷ 4 × 2^(their Spycraft − yours) %) |
| Meteor range |
5 × Beastmastery − 1 provinces, same continent |
| Meteor flight |
30 s + 60 s per province |
| Meteor damage |
12,000 × (1 + 10% × Weaponsmithing) per spell |
| Scrying range |
(level² − 1) provinces (× 1.2 for a Wayfarer) |
| Scrying cost |
5,000 aether |
| Waygate cooldown |
3,600 s × max(0.5, 1 − 0.1 × (L − 1)) ÷ economy speed |
| Sunder fall chance |
(100 − √span) × √Colossi % |
| Sunder Colossi loss |
√span ÷ 2 % |
Quests and kindreds
| What |
Formula |
| Quest points |
min(cap, Σ units × (iron + runestone) × 5 ÷ 1,000) |
| Picked clean |
max(30%, 100% − 10% × (quests in that province in 24 h − 3)) |
| Treasure |
points × tier factor × picked clean × (1 + finds) (×2 Rangers, ×1.5 × economy speed Wayfarer) ÷ (1 iron, 2 runestone, 3 aether) |
| Population cap |
50 + 200 × L × 1.15^L (50 with no dwelling) |
| Food |
30 + 110 × L × 1.16^L per hour |
| People fed |
food ÷ 0.5 |
| Population growth |
2% of the cap per hour × economy speed × (1 + growth bonuses) |
| Artisan cap |
300 × L × 1.12^L |
| Master cap |
50 × L × 1.12^L |
| Standing |
the highest S (up to 10) with favour ≥ 1,000 × S² |
| Art bonus |
value × level × (1 + 2% × standing) |
Renown and honour
| What |
Formula |
| Renown |
resources invested ÷ 1,000 |
| Fledgling |
renown < 50,000, not dormant, not an oathbreaker |
| Protected from |
lords with more than 5 × the fledgling's renown |
| Honour won |
renown destroyed, if the foe has ≥ half your renown |
| Honour lost |
renown destroyed (at least 1), if an active foe has < a fifth of your renown |