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## Generalized Formulas

Normal build time formula for a given level:
${ Time ~(seconds) = \left \lbrack ~ \frac{A}{B} \times \left ( ~ C^{~Level} ~ \right ) - D ~ \right \rbrack }$
Accumulated build time formula for a given level:
${ Accumulated ~time ~(seconds) = \left \{\ ~ \frac{ \left ( ~ A \times C ~ \right )}{\lbrack ~ B \times ~ \left ( ~ C - 1 ~ \right ) ~ \rbrack} \times \left ( ~ C ^ {~Level} -1 ~ \right ) - \left ( ~ D \times Level ~ \right ) ~ \right \}\ }$

## Coefficients

### Town Buildings

#### Standard Buildings

Building Coeff A Coeff B Coeff C Coeff D
Barracks 25,200 11 1.1 1,728
Black Market 4,321 1 1.1 4,627
Dump 32,000 13 1.17 2,160
Embassy 96,000 7 1.05 10,080
Governor's Residence 11,520 1 1.4 0
Hideout 96,000 7 1.05 12,960
Museum 18,000 1 1.1 14,040
Palace 11,520 1 1.4 0
Sea Chart Archive 1,472,465 509 1.12 504.5
Shipyard 64,800 7 1.05 7,128
Tavern 10,800 1 1.06 10,440
Temple 2,160 1 1.1 0
Town hall 1,800 1 1.17 -1,080
Town wall 57,600 11 1.1 3,240
Trading port 50,400 23 1.15 1,512
Trading post 108,000 11 1.1 9,360
Warehouse 2,880 1 1.14 2,160
Workshop 96,000 7 1.05 11,880
Building Coeff A Coeff B Coeff C Coeff D
##### Notes
1. The Academy, Barracks, Town wall and Trading port at level 1 does not follow the above formulas, as they have had their construction times reduced when they were added to the in-game tutorial.
2. The Warehouse at levels 1 and 2 do not follow the above formulas, as they have had their construction times reduced when they were added to the in-game tutorial.
3. The Town hall at level 1 does not have a building time, because it is never constructed.

#### Production Buildings

Building Coeff A Coeff B Coeff C Coeff D
Alchemist's Tower 72,000 11 1.1 6,120
Forester's House 72,000 11 1.1 6,120
Glassblower 72,000 11 1.1 6,120
Stonemason 72,000 11 1.1 6,120
Winegrower 72,000 11 1.1 6,120
Building Coeff A Coeff B Coeff C Coeff D
##### Note
The Production Buildings have the exact same formula!

#### Reduction Buildings

Building Coeff A Coeff B Coeff C Coeff D
Architect's Office 125,660 37 1.06 2,628
Carpenter 125,660 37 1.06 2,808
Firework Test Area 125,660 37 1.06 2,628
Optician 125,660 37 1.06 2,772
Wine Press 125,660 37 1.06 2,232
Building Coeff A Coeff B Coeff C Coeff D
##### Note
The Reduction Buildings have the exact same formula, except for Coeff D!

### Island buildings

Building Coeff A Coeff B Coeff C Coeff D
Crystal Mine 14,400 1 1.1 14,400
Quarry 14,400 1 1.1 14,400
Saw Mill 7,200 1 1.1 7,200
Sulphur Pit 14,400 1 1.1 14,400
Vineyard 14,400 1 1.1 14,400
Building Coeff A Coeff B Coeff C Coeff D
##### Note
The buildings have the exact same formula!

## Example

We would like to know the time in seconds for building the level 46 of the Town Hall :

Town Hall ( A , B , C , D ) = ( 1800 , 1 , 1.17 , -1080 )

${ ~Time ~(seconds) = \left \lfloor \frac {A} {B} \times C ^ {~level} - D \right \rfloor }$

${ ~Time ~(seconds) = \left \lfloor \frac {1,800} {1} \times 1.17 ^ {~46} + 1,080 \right \rfloor }$

${ ~Time ~(seconds) = \left \lfloor 1,800 \times 1.17 ^ {~46} + 1,080 \right \rfloor }$

${ ~Time ~(seconds) = \left \lfloor 1,800 \times 1,369.46 + 1,080 \right \rfloor }$

${ ~Time ~(seconds) = \left \lfloor 2,465,028 + 1,080 \right \rfloor }$

${ ~Time ~(seconds) = \left \lfloor 2,466,109.63 \right \rfloor }$

${ ~Time ~(seconds) = 2,466,110 }$

And 2,466,110 seconds equals 28 D 13 h 1 m 50 s (The displayed time is 28D 13h)

Using {{BTime|s={{#expr:( 1800 / 1 * ( 1.17 ^ 46 ) - -1080 ) round 0}}|ng=|nsbt=|na=}} produces 28 D 13 h 1 m 50 s

Respectively, the accumulative time required until Level 46 of the Town Hall is:

\begin{align}\text{Accumulative time (seconds)} & = \left \lbrack \frac{A \times C}{B \times \left (C-1 \right)} \times \left (C ^ \text{Level} - 1 \right ) - D \times \text{Level} \right \rbrack -3,186\\ & = \left \lbrack \frac{1,800 \times 1.17}{1 \times \left (1.17-1 \right)} \times \left (1.17 ^{46} - 1 \right ) + 1,080 \times 46 \right \rbrack -3,186 \\ & = \left \lbrack \frac{2,106}{0.17} \times 1,368.4609 + 49,680 \right \rbrack -3,186 \\ & = \left \lbrack 16,952,815.62 + 49,680 \right \rbrack -3,186\\ & = \left \lbrack 17,002,495.62 \right \rbrack -3,186 \\ & = 17,002,496 - 3,186 \\ & = 16,999,310 \end{align}

And 16,999,310 seconds equals 6 Months 16 days 18 hours 1 minute 50 seconds or 6 M 16 D 18 h 1 m 50 s
Using {{BTime|s={{#expr:(1800*1.17*(1.17^46-1)/0.17+1080*46-3186) round 0}}||ng=|nsbt=|na=}} produces 6 M 16 D 18 h 1 m 50 s . Template:DEFAULTSORT

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