Buildings/Construction Time

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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:

$${ Accumulated ~time ~(seconds) = \left \{\ ~ \frac{ \left ( ~ A \times C ~ \right )}{\lbrack ~ B \times ~ \left ( ~ C - 1 ~ \right ) ~ \rbrack} \times \left ( ~ C ^ {~Level} -1 ~ \right ) - \left ( ~ D \times Level ~ \right ) ~ \right \}\ }$$ __NOWYSIWYG__

Coefficients
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Town Buildings
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Standard Buildings
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
Note


 * The Production Buildings have the exact same formula! __NOWYSIWYG__

Reduction Buildings
Note


 * The Reduction Buildings have the exact same formula, except for Coeff D! __NOWYSIWYG__

Island buildings
Note


 * The 🇱🇺 buildings have the exact same formula! __NOWYSIWYG__

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 produces

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 produces.