Construction Time

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
Academy	1,440	1	1.2	720
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
Gods' Shrine	48	1	1.25	0
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 .