The FMAP Section 1905(b) formula sets each state’s federal Medicaid match by comparing state per capita income to national per capita income, squaring that ratio, multiplying it by 45 percent to get the state’s share, and subtracting from 100 to get the federal share. The result is bounded: no state’s federal match falls below 50 percent or rises above 83 percent.1Office of the Law Revision Counsel. 42 USC 1396d – Definitions Codified at 42 U.S.C. § 1396d(b), the formula governs how hundreds of billions of dollars in annual Medicaid spending are split between Washington and the states.2Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2027)
The Equation
Written out, the calculation is:
FMAP = 100% − [(state per capita income ÷ national per capita income)² × 45%]
The bracketed portion is the state’s share. Whatever the state pays, the federal government pays the rest. So a state whose bracketed result comes to 35 percent has a 65 percent FMAP; the federal government reimburses 65 cents of every qualifying Medicaid dollar the state spends.1Office of the Law Revision Counsel. 42 USC 1396d – Definitions
Why the Ratio Is Squared
The squaring step is what gives the formula its bite. A straight ratio would move state shares in a strict line with income. Squaring makes the formula more responsive: a state earning slightly less than the national average gets a noticeably larger federal share, while a state earning slightly more sees its federal share drop faster than a straight-line calculation would produce. Poorer states are pulled up harder, wealthier states drop down harder, and the 0.45 multiplier scales the whole curve so the results land in a workable range before the statutory bounds are applied.
A Worked Example
Assume a national per capita income of $40,000. A state with per capita income of $38,000 runs the math like this:
- $38,000 ÷ $40,000 = 0.95
- 0.95² = 0.9025
- 0.9025 × 45% = 40.61% (state share)
- 100% − 40.61% = 59.39% (FMAP)
The federal government would cover roughly 59 cents of every Medicaid dollar in that state.
A wealthier state with per capita income of $42,000 runs the same steps: the ratio is 1.05, squared to 1.1025, times 45 percent yields a 49.61 percent state share, for a raw FMAP of 50.39 percent. In practice that state receives a 50 percent match, because of the floor discussed next.
The 50 Percent Floor and 83 Percent Ceiling
The raw formula can produce results below 50 percent for wealthy states and above 83 percent for very low-income states, but the statute caps both ends. No state’s FMAP may drop below 50 percent or rise above 83 percent.1Office of the Law Revision Counsel. 42 USC 1396d – Definitions
The floor is not a theoretical guardrail. For FY 2027, ten states are at 50 percent: California, Colorado, Connecticut, Maryland, Massachusetts, New Hampshire, New Jersey, New York, Washington, and Wyoming.2Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2027) Their formula results would come in below 50 percent; the floor guarantees an equal federal-state split at minimum. The 83 percent ceiling, by contrast, is not currently reached by any of the 50 states under the formula, though several U.S. territories are set at 83 percent by separate statutory provisions rather than by the 1905(b) calculation.
The Income Data Behind the Formula
The per capita income figures come from the Bureau of Economic Analysis within the Department of Commerce. The statute does not use a single year; it requires a three-year average. FY 2026 rates, for example, were calculated using per capita incomes from calendar years 2021 through 2023.3Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2026)
Averaging smooths the swings. A single unusual year cannot pull a state’s federal support up or down dramatically. The tradeoff is a built-in lag: FMAP rates trail current economic conditions by a few years.
The statute defines the national baseline as per capita income of “the continental United States (including Alaska) and Hawaii,” which in practice covers all 50 states.1Office of the Law Revision Counsel. 42 USC 1396d – Definitions
When New Rates Are Calculated and Take Effect
The Secretary of Health and Human Services runs the calculation each year using the updated BEA data and publishes the results in the Federal Register.3Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2026) The notice lists the rate for every state and territory along with the national per capita income figure used in that year’s calculation.
Publication typically lands in late November, about ten months before the rates take effect on October 1 of the following year. FY 2027 rates were published on November 28, 2025, and take effect October 1, 2026.2Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2027) Once effective, the rate remains fixed for the full 12-month fiscal year.
What the FY 2027 Formula Produced
The FY 2027 rates show the spread the formula creates in practice. Ten states sit at the 50 percent floor. Several land just above it: Virginia at 50.02 percent, Minnesota at 51.36 percent, and Alaska at 51.37 percent. Most states fall between roughly 55 and 72 percent. Mississippi has the highest formula-driven FMAP at 77.32 percent, followed by West Virginia at 74.25 percent and Alabama at 72.55 percent. The District of Columbia receives a 70 percent FMAP set separately by statute rather than by the 1905(b) formula.2Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2027)
What Section 1905(b) Does Not Set
The 1905(b) formula produces the standard Medicaid match. Several other categories of federal Medicaid spending use different rates that do not run through the per capita income calculation, and it is easy to assume the 1905(b) number governs everything when it does not.
The ACA Medicaid expansion population is covered under 42 U.S.C. § 1396d(y) at 90 percent from 2020 onward, regardless of the state’s regular FMAP.1Office of the Law Revision Counsel. 42 USC 1396d – Definitions CHIP uses an enhanced rate that starts from the regular FMAP and adds 30 percent of the gap between that FMAP and 100 percent, capped at 85 percent.4Office of the Law Revision Counsel. 42 USC 1397ee – Payments to States Family planning services and supplies are matched at 90 percent, and general administrative costs at a flat 50 percent, both set independently of the state’s FMAP.5Office of the Law Revision Counsel. 42 USC 1396b – Payment to States Services provided to eligible American Indian and Alaska Native patients at Indian Health Service or tribal facilities are matched at 100 percent.6Centers for Medicare and Medicaid Services. 100% FMAP for LTSS – Educate Your State U.S. territories are outside the formula entirely: their rates are fixed by statute (83 percent for American Samoa, Guam, the Northern Mariana Islands, and the Virgin Islands; 76 percent for Puerto Rico through September 30, 2027) and their total federal payments are capped by annual allotments under 42 U.S.C. § 1308.2Federal Register. Federal Financial Participation in State Assistance Expenditures – Federal Matching Shares for Medicaid, CHIP, and Aid to Needy Aged, Blind, or Disabled Persons (FY 2027)
A state’s total federal Medicaid reimbursement is therefore a blend: the 1905(b) FMAP applied to traditional Medicaid medical services, plus each of these other rates applied to their own categories of spending.