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About 3.6 million taxpayers are set to receive cash back this fall after state government hauled in taxes last year that surpassed the legal limit by nearly $3 billion, the administration of Gov. Charlie Baker announced Friday.

The plan does conflict with what some Democrat lawmakers expected.

Still, Baker’s team, which oversees the Department of Revenue, said the $2.941 billion that needs to be returned to taxpayers under a voter-approved law will take the form of mailed checks or direct deposits, likely starting in November.

Taxpayers will “automatically” receive their refunds without needing to submit any application. To be eligible, they must have filed a 2021 state tax return by Oct. 17, 2022.

The amount of each refund will be scaled based on how much someone paid in state personal income taxes in 2021, with larger checks going to those who paid larger shares of the tax haul.

Baker’s budget office estimated the refunds will total about 13% of how much a taxpayer owed to Massachusetts in personal income tax last year, stressing that figure could change once it is finalized in late October.

“With families facing continued pressure from high prices and inflation, these returns will provide some needed relief,” Baker said in a statement. “Even with nearly $3 billion going back to taxpayers, significant state and federal resources remain, and we look forward to working with the Legislature to invest this funding into our economy, communities and families.”

Bay Staters can use an online calculator the Baker administration launched to get a projection of what to expect.

Massachusetts has a flat income tax rate of 5%, so an individual who earned $50,000 in taxable income last year and had a tax liability of $2,500 could be in line for a rebate of roughly $325; toward the top of the scale, a Bay Stater who earned $1 million in taxable income and owed $50,000 in Massachusetts income taxes could face a rebate of $6,500.

However, the final amount of each check will depend on variables such as whether a taxpayer claimed earned income credit, senior circuit breaker credit, or dependent credits on their tax return.

Rebates might also be reduced due to refund intercepts for unpaid taxes, unpaid child support or other debts, officials said.

The administration’s implementation plans were rolled out a day after Auditor Suzanne Bump certified that Massachusetts collected $2.941 billion more in taxes last year than the cap set by a voter-approved 1986 law linking tax and wage growth.

“This rebate could not come at a better time,” said Retailers Association of Massachusetts President Jon Hurst. “Inflation has hurt our consumers and small businesses, and putting these tax dollars back in the pockets of the taxpayers will help with high heating and grocery costs, and will put important consumer dollars back into our local economy for the holidays.”

Top Democrats in the Legislature were caught off guard by the emergence this summer of the tax cap, and the news prompted them to toss aside a $4 billion economic development bill that included $1 billion in combined one-time and permanent tax relief.

They have now come around to the reality that the tax relief under Chapter 62F is due.

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