PlanetsCentral

Maximum Population: The maximum population for a planet is a fixed number which depends on the planet's climate. With ClimateLimitsPopulation enabled, the maximum population on an ideally-tempered world is 100000 clans (10 million colonists). If configured, supplies help you support more colonists on a planet.

Eff_max_colonist_clans =
   Trunc(Eff_max_colonists / 100)

Eff_max_colonists =
   Max_colonists + Supply_bonus
      ...if ClimateLimitsPopulation is enabled
      ...at least 1
   25000000
      ...otherwise

Max_colonists =
   Trunc(10000000 * Sin(Temperature * PI / 200))
                    ...if colonists are Crystalline
                       and CrystalsPreferDeserts is enabled
                       and CrystalSinTempBehavior is enabled
                       and Temperature ≥ 15
   300 + MaxColTempSlope * Temperature
                    ...if colonists are Crystalline
                       and CrystalsPreferDeserts is enabled
                       and CrystalSinTempBehavior is enabled
                       and Temperature < 15
   100000 * Temperature
                    ...if colonists are Crystalline
                       and CrystalsPreferDeserts is enabled
                       and CrystalSinTempBehavior is disabled
   9000000
                    ...if colonists are Rebel and Temperature < 20
   300 + MaxColTempSlope * Temperature
                    ...if Temperature < 15
   100 + (100-Temperature) * MaxColTempSlope
                    ...if Temperature > 84
                    ...at least 6000 if colonists are Klingon, Robot, Rebel or Colony
   Trunc(10000000 * Sin(Temperature * PI / 100))
                    ...in all remaining cases

Supply_bonus =
   Trunc(100 * Supplies / 40)
                    ...if AllowEatingSupplies is enabled
   0                ...otherwise

► Note: Note that these formulas use colonists, not clans. A future PHost version may simplify that to clans, which would get slightly different rounding behaviour.

Native populations have simpler formulas. The absolute maximum is 15.6 million natives (156000 clans) for most races, 10 million for Siliconoids when they like it hot. Supplies do not help you to increase the limit.

Max_native_clans =
   156000
                    ...if ClimateLimitsPopulation is disabled
   1000 * Temperature
                    ...if natives are Siliconoid
                       and CrystalsPreferDeserts is enabled
                       and PHost is version 3.3c or newer
   Trunc(Sin(Temperature * PI / 100) * 156000)
                    ...in all remaining cases

It might be considered a bug that Siliconoids cannot reach the 15.6 million mark with CrystalsPreferDeserts enabled, but changing the formula would again complicate matters even more.

Growth: Growth depends on taxation and climate. Populations will never grow over the limit. The maximum growth rate is 5% per turn.

Colonist_growth_in_clans =
   Trunc(Round(Colonist_growth_rate * Colonist_clans / 100) *
           RaceGrowthRate / 100)
   ...at most Eff_max_colonist_clans - Colonist_clans

Colonist_growth_rate =
   0                ...if Colonist_clans ≥ Eff_max_colonist_clans
   0                ...if Colonist_happiness < 70
   0                ...if colonists are Crystalline
                       and CrystalsPreferDeserts is enabled
                       and CrystalSinTempBehavior is enabled
                       and Temperature < 15
   5 * Sin(Temperature * PI / 200) / (1 + Colonist_tax / 5)
                    ...if colonists are Crystalline
                       and CrystalsPreferDeserts is enabled
                       and CrystalSinTempBehavior is enabled
                       and Temperature ≥ 15
   5 * (Temperature / 100) / (1 + Colonist_tax / 5)
                    ...if colonists are Crystalline
                       and CrystalsPreferDeserts is enabled
                       and CrystalSinTempBehavior is disabled
   0                ...if Temperature < 15
   0                ...if Temperature > 84
   5 * Sin(Temperature * PI / 100) / (1 + Colonist_tax / 5)
                    ...in all other cases

Native growth is similar, but here the maximum growth rate is 4%. Natives do not grow on unowned planets(!).

Native_growth_in_clans =
   Trunc(Round(Native_growth_rate * Native_clans) / 100)
   ...at most Max_native_clans - Native_clans

Native_growth_rate =
   0                ...if Native_clans ≥ Max_native_clans
   0                ...if Native_happiness < 70
   4 * (Temperature / 100) / (1 + Native_tax / 5)
                    ...if natives are Siliconoids
                       and CrystalsPreferDeserts is enabled
                       and PHost is version 3.3c or newer
   4 * Sin(Temperature * PI / 100) / (1 + Native_tax / 5)
                    ...in all other cases