Is it permissible for a Muslim to pay Zakat with an increase, intending it as Sadaqah, if they are unsure about its precise calculation?

If a Muslim doubts the calculation of his Zakat, he must investigate. If what he doubted becomes clear to him, he should act upon it. Otherwise, he should build upon certainty, which is the lesser amount, because the fundamental principle is the acquittal of the obligation. It is preferable for him to be scrupulous and cautious in his religion by paying the amount he doubted, for if it is not from the obligatory Zakat, then it is a voluntary charity.