Force limit

A force limit is a soft limit on how many ships or regiments a country can possess. It can be exceeded at a monetary price.

If a country goes past its force limit the maintenance cost per unit will increase by as many percent as they are above the force limit, eventually making further expansion of the army or navy prohibitively expensive.

There are two independent force limits, one for naval units and one for land units, but both operate largely the same.

Computing force limit

Province modifiers

Provinces contribute to the force limit through their development level and through the following modifiers and buildings. Note that only coastal provinces may contribute to a country's naval force limit.

Condition	Tech Level	Land Force Limit	Naval Force Limit
Per development		+0.1	+0.1
Regimental Camp	Mil 8	+1	0
Conscription Center	Mil 22	+2	0
Shipyard	Dip 6	0	+2
Grand Shipyard	Dip 19	0	+4
Important center of trade		0	+2
Being in trade company		0	+0.5
Local autonomy (per 1%)		-1%	-1%

Country modifiers

Condition	Force Limit multiplier
	Land	Naval
Independent nation	+6	+12
Subject nation	+2	+4
March nation	+2 / +30%	+4 / +30%
Trade good bonus: Grain	+10%	0
Trade good bonus: Naval supplies	0	+10%
Being the revolution target	+40%	+40%
Being an invading nation	+100	+100

Updating force limits

Force limits are normally recalculated by the game on the first day of each month. To force an update in the middle of a month, you can activate a privateer mission and wait one day for the force limits to refresh. This may be necessary if one changes local autonomy levels in the middle of the month for example.

More sources of force limit

Ideas and policies

Ideas and policies that increase force limits:

Land force limit

	Traditions	Ideas	Bonuses	Policies
+50%	—	Russian idea 4: Life-Long Conscription	Full Quantity	—
+33%	Scottish traditions	Sonoran idea 6: Uniting the Outlaws	Muscovite ambition Ottoman ambition	—
+25%	Chickasaw traditions Daimyo traditions Nepali traditions Satake traditions Sindhi traditions	Goslar idea 5: Hunting Down the Robber Barons Hessian idea 6: Hessian Mercenaries Moldavian idea 3: Upper Boyars Permian idea 7: Permian Army Reform Ryazan idea 1: The Arsenal of Ryazan Tripuran idea 4: Extended Military Control	Rûmi ambition Sukhothai ambition Welsh ambition	—
+20%	Arawak traditions Imagawa traditions Incan traditions Mazovian traditions Shoni traditions Toki traditions Tverian traditions Westphalian traditions	Offensive idea 6: Grand Army Albanian idea 1: All Lands Under Skanderbeg Ando idea 3: Clan Unification Ava idea 2: Rajadhiraja Cornish idea 5: Cornish Royalist Army Deccani idea 4: Empower the Paigah Hosokawa idea 4: The Eastern Army Mori idea 2: Leader of Kokujin Ikki Thomondian idea 2: Subdue the Clans	Baluch ambition Lan Xang ambition Laotian ambition Somali ambition	—
+15%	—	Roman idea 4: The Roman Legions Rothenburg idea 4: The Knights of the Hinterland Tyrone idea 4: Arming the People	—	—
+10%	—	Corsican idea 4: The Corsican League	—	Diplomatic-Quantity: The Pen Relies on The Sword Act Economic-Quantity: Agricultural Cultivation Quantity-Expansion: Colonial Garrisons

Naval force limit

	Traditions	Ideas	Bonuses	Policies
+50%	Dutch traditions	Maritime idea 4: Grand Navy Danish idea 6: Found the Copenhagen Dockyard Knights Hospitaller idea 6: Scourge of the Corsairs	—	—
+33%	—	Gutnish idea 6: Gutnish Merchant Navy	Cypriot ambition	Maritime-Expansion: Naval Infrastructure
+25%	Moroccan traditions Sulawesi traditions	Exploration idea 7: Global Empire Alaskan idea 6: Alaskan Navy Berber idea 1: Barbary Pirates Candarid idea 6: Sinop Shipyard Couronian idea 5: Couronian Colonization Dalmatian idea 6: The Independent Arsenal Estonian idea 2: Baltic Ties Genoese idea 6: Setup the Office of Grand Admiral Hadramhi idea 5: Sailors of the Indian Ocean Hormuz idea 7: Hormuzi Naval Expansion Ionian idea 5: Naval Expansion Kono idea 1: Shugo of Iyo Leonese idea 5: Expand the Leonese Navy Orissan idea 7: Heritage of the Sadhabas Pomeranian idea 7: German Navy So idea 6: Port Maintenance Spanish idea 3: Treasure Fleet Sumatran idea 7: Rule of The Sea Venetian idea 1: Venetian Arsenal West Indies idea 7: Colonial Legacy	Breton ambition Cham ambition Hamburger ambition Malagasy ambition Tunisian ambition	—
+20%	Corsican traditions Navarran traditions Sardinian traditions	Mogadishan idea 6: Horn of Africa Naxian idea 1: Maritime State Ragusan idea 4: Ragusan Arsenal Sligonian idea 6: Sligo's Naval Ambition	Al-Haasa ambition	—
+15%	Croatian traditions	—	—	Maritime-Defensive: The Fleet is our Wooden Wall
+10%	—	Aragonese idea 2: Protection of the Coastlines Provençal idea 6: Toulon Dockyard	—	—

Government

Land force limit

Type	Modifier
Steppe nomads	+10%/+20%/+30%
Tribal Federation	+10%
Dutch Republic	+25% if the Orangists are in power
Revolutionary republic	+20% if the Girondists are in power

Additionally, the Holy Roman Emperor gets +0.5 land force limit per member state.

Naval force limit

Type	Modifier
Dutch Republic	+10% if the Statists are in power

Subjects

• Vassals and client states give +1 land force limit to their master.
• Marches give +2 land force limit to their master.
• Large (more then 10 provinces) colonial nations give +5 land force limit and +10 naval force limit to their master.
• Junior partners in a personal union and protectorates don't increase the land force limit of their masters.

• Following ideas and policies that increase force limits increased by subjects

	Traditions	Ideas	Bonuses	Policies
+100%	—	Influence idea 7: Marcher Lords Andalusian idea 2: Taifa Administration Ashikaga idea 7: Reform the Shogun - Shugo System Bosnian idea 5: Land of Princes Herzegovinian idea 5: Land of Princes	—	Influence-Aristocratic: Autonomous Estates Influence-Economic: Vassal Obligations Act Plutocratic-Influence: Unified Army Command

Effect on maintenance

If a country has more land or naval units than the corresponding force limit, maintenance for those units will be multiplied by the ratio of units to the force limit. For example, being at twice the force limit will double the maintenance for each unit.

Light Ships suffer increased cost as well, which squares the effect on their maintenance.

Strategy

For purposes of this section, assume the average base maintenance per unit—that is, the maintenance cost of a unit before force limit modifiers—is constant. Define the force limit ratio as

${\text{force limit ratio}}={\frac {\text{number of units}}{\text{force limit}}}$

Total maintenance cost

The total maintenance cost of an army or navy is

${\text{total maintenance cost}}={\text{average base maintenance}}\cdot {\text{number of units}}\cdot {\text{max(force limit ratio, 1)}}$

In this case, when above the force limit:

• A multiplier to force limit has the same effect as a reciprocal multiplier to maintenance.
• The number of units that can be fielded for a fixed maintenance cost grows as the square root of the force limit.

For a navy of pure light ships, the total maintenance cost is instead

${\text{total maintenance cost}}={\text{average base maintenance}}\cdot {\text{number of units}}\cdot \left({\text{max(force limit ratio, 1)}}\right)^{2}$

In this case, when above the force limit:

• A multiplier to force limit has the same effect as a reciprocal squared multiplier to maintenance.
• The number of units that can be fielded for a fixed maintenance cost grows as the cube root of the force limit.

Footnotes

Warfare