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Suppose my mana regeneration rate was calculated in this way:

ManaRegenRate = 0.01 × (BaseManaRegen + ManaRegenMultiplier × Willpower) × TotalMana

Where willpower is my attribute ranging from 0 to 100 and BaseManaRegen and ManaRegenMultiplier are some constants.

With this formula I would get mana regenerated per second.

How could I rearrange this formula to get the total amount of seconds to regenerate mana from 0 to full?

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    \$\begingroup\$ Can't you just do something like timeToFullMana = FullMana / ManaRegenRate ? \$\endgroup\$
    – TomTsagk
    Oct 25, 2019 at 15:15

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Assuming your "ManaRegenRate" is the mana regenerated per second, you just have to divide the TotalMana through the mana regen rate.

$$ TotalMana \over 0.01 × (BaseManaRegen + ManaRegenMultiplier × Willpower) × TotalMana $$

But because TotalMana appears on both sides of the fraction, you can simplify the fraction by removing it and arrive at:

$$ 1 \over 0.01 × (BaseManaRegen + ManaRegenMultiplier × Willpower) $$

You might notice that the time it takes to fully regenerate mana in your game is completely independent from how much mana the character can actually have.

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