The tax revenue equation is simple multiplication: tax revenue equals the tax rate multiplied by the tax base. If a city has $2 billion in taxable property value and levies a 1% rate, it collects $20 million. If the federal government taxes corporate profits at 21% and corporations report $2 trillion in taxable income, the arithmetic yields $420 billion. Every projection built on this formula, from a county levy to the roughly $5 trillion the federal government collects each year, comes down to those two variables and how they move.
The Two Variables
The base is the slice of economic activity a government has decided to tax. The rate is the percentage applied to it. Multiply, and you have revenue.
The arithmetic never changes. What changes is how each variable is defined and how they push on each other. Proposals to “broaden the base” pull more economic activity into the taxable pool. Proposals to “cut rates” reduce the multiplier. And the piece that most quick explanations skip: changing one variable often changes the other, because people and businesses adjust their behavior in response.
What Counts as the Tax Base
The base is whatever the taxing government says it is. For the federal income tax, the starting point is gross income, which covers wages, business profits, investment gains, rent, royalties, dividends, and pensions.1Office of the Law Revision Counsel. 26 US Code 61 – Gross Income Defined That gross figure then gets reduced by deductions and exemptions before the rate applies, so the actual taxable base is smaller than total economic output.
Other taxes use different bases. Sales tax runs on the dollar value of retail purchases. Property tax runs on the assessed value of real estate. Payroll tax runs on wages up to a capped amount. Each definition creates different incentives. A sales tax base that exempts groceries is narrower than one that doesn’t, which means the rate has to be higher to bring in the same revenue. A property tax base pulled from assessments five years old captures less current wealth than one reassessed annually.
Legislators shape the base every time they write an exclusion, deduction, or exemption. Qualifying nonprofits sit outside the corporate income tax base entirely, and often outside state sales and property tax bases as well.2Internal Revenue Service. Federal Tax Obligations of Nonprofit Corporations Every carve-out reduces the revenue the formula produces at any given rate.
How Rates Work
Rates come in two basic shapes. A flat rate charges the same percentage regardless of the size of the base. The federal corporate income tax works this way at 21% on all taxable corporate profits. Sales taxes are flat within a jurisdiction: every buyer pays the same percentage.
Progressive rates rise as the base grows. The federal individual income tax is the familiar case. For tax year 2026, a single filer pays 10% on the first $12,400 of taxable income, 12% on the next portion up to $50,400, 22% on the slice from $50,400 to $105,700, and so on through seven brackets, with the top rate of 37% applying only to income above $640,600.3Internal Revenue Service. Revenue Procedure 2025-32 The layered structure means no one pays the top rate on their entire income.
Marginal Rate vs. Effective Rate
Your marginal rate is the percentage on the last dollar you earn. Your effective rate is total tax paid divided by total income. In a progressive system the effective rate is always lower than the marginal rate, because the earlier dollars were taxed in lower brackets. Two people sitting in the same top bracket can have very different effective rates depending on how much of their income actually lands there.
Property Tax and Mill Levies
Property tax uses a slightly different notation. Many jurisdictions express the rate as a millage rate, where one mill equals $1 of tax for every $1,000 of assessed value. A 20-mill rate on a home assessed at $300,000 produces $6,000 in annual property tax. Same multiplication, expressed per thousand instead of per hundred.
The Equation Applied
Three quick examples show the formula holding across tax types.
- Sales tax: a $1,000 purchase in a jurisdiction with a combined 7% rate generates $70. The base is the purchase price; the rate is the sales tax percentage. Multiply across millions of transactions to get the jurisdiction’s total sales tax.
- Property tax: a home assessed at $250,000 with a local 25-mill rate produces $6,250 per year. Reassessments that raise home values expand the base and lift revenue even when the rate stays put.
- Income tax: a single filer with $80,000 in taxable income for 2026 doesn’t pay 22% on the full amount. The first $12,400 is taxed at 10% ($1,240), the next $38,000 at 12% ($4,560), and the remaining $29,600 at 22% ($6,512), for a total of roughly $12,312. The effective rate is about 15.4%.3Internal Revenue Service. Revenue Procedure 2025-32
The formula is identical in each case. What changes is the definition of the base, the structure of the rate, and how the two interact.
Why Doubling the Rate Doesn’t Double Revenue
The equation tempts people into treating revenue as a straight line. In practice, the base does not sit still while the rate moves. People work less, shelter income, shift investments, relocate to lower-tax jurisdictions, or simply report less. Economists call this the elasticity of taxable income, and it is the single most important variable the basic formula leaves out.
The logic is straightforward. If a 5-percentage-point rate increase causes taxpayers to reduce their reported income enough to offset the higher rate, total revenue stays flat or drops. The mechanical effect (more dollars per unit of base) gets partly eaten by the behavioral effect (fewer units of base). When elasticity is high, rate increases disappoint. When it is low, the formula’s simple prediction holds up better.
This is what the Laffer Curve illustrates. At a 0% rate, the government collects nothing. At a 100% rate, no one has any incentive to earn taxable income, so the government again collects nothing. Somewhere between sits a revenue-maximizing rate. The curve does not tell you where that peak is, and economists argue about it, but the underlying point stands: past a certain point, higher rates shrink the base faster than they raise the per-unit take.
Static vs. Dynamic Scoring
This is why budget analysts distinguish between static and dynamic scoring. A static estimate holds the size of the economy constant and multiplies the new rate by the existing base. A dynamic estimate tries to account for how the rate change will alter economic output and, in turn, the base itself. Official estimates from the Joint Committee on Taxation already incorporate many microeconomic behavioral responses, such as the assumption that higher capital gains taxes will reduce the number of assets people sell, but they traditionally hold total economic output fixed. Full dynamic scoring goes further by modeling changes to overall GDP.4Congress.gov. Dynamic Scoring for Tax Legislation: A Review of Models
Revenue the Formula Predicts but the Government Never Sees
Two forces drive a wedge between the formula’s output and the money that actually arrives.
Tax Expenditures Narrow the Base by Design
Federal law tracks revenue losses from provisions that grant special exclusions, exemptions, deductions, credits, preferential rates, or deferrals. These are called tax expenditures.5U.S. Department of the Treasury. Tax Expenditures Fiscal Year 2027 For fiscal year 2026, federal tax expenditures are projected at roughly $2.3 trillion. The ten largest provisions alone account for more than $1.4 trillion. Each one is a deliberate choice to shrink the base: the mortgage interest deduction, the exclusion of employer-paid health insurance premiums, 401(k) deferrals, and so on.
The standard deduction alone lifts a significant layer of income out of taxation. For 2026, it is $16,100 for single filers and $32,200 for married couples filing jointly.6Internal Revenue Service. IRS Releases Tax Inflation Adjustments for Tax Year 2026 A married couple earning $60,000 is taxed on only $27,800 of it. When analysts talk about broadening the base, they usually mean capping or eliminating expenditures like these so more income flows through the formula.
The Tax Gap
Even after the base is defined and the rate applied, the formula’s output is only what the government is theoretically owed. Actual collections are less. The IRS defines the gross tax gap as the difference between total tax liability for a given year and the amount paid on time. For tax year 2022, the gross gap was $696 billion.7Internal Revenue Service. IRS: The Tax Gap
The gap has three sources: non-filers, underreporters, and people who file correctly but don’t pay. After enforcement clawed some back, the net gap for 2022 was $606 billion. The voluntary compliance rate holds steady around 85%, meaning about 15 cents of every dollar owed goes uncollected without enforcement. A government projecting $100 billion in income tax revenue at a given rate and base should realistically expect closer to $85 billion on time, with additional recovery depending on audit capacity.
What Moves Revenue Without Any Change to the Formula
Both variables drift on their own. Three forces do most of the work.
Economic Cycles
In a recession, the income tax base shrinks as unemployment rises and corporate profits fall. The sales tax base contracts as consumers spend less. Property tax bases lag because assessments update slowly, but declining home values eventually pull them down too. Revenue drops even though no legislator voted to change a rate. Expansions run the tape in reverse: rising wages, profits, and spending swell the base and push revenue up on their own.
Inflation and Bracket Creep
When wages rise to keep pace with prices, workers don’t gain real purchasing power, but they can be pushed into higher brackets. This is bracket creep, and it effectively raises the tax rate on people whose real economic position hasn’t changed. The IRS adjusts bracket thresholds annually using the Consumer Price Index to counter it. For 2026, thresholds were adjusted upward under a formula established by the Tax Cuts and Jobs Act.3Internal Revenue Service. Revenue Procedure 2025-32 Without those adjustments, inflation would work as a quiet tax increase, pulling more revenue from a base that hasn’t actually grown.
Legislation
Laws often change both sides of the equation at once. The Tax Cuts and Jobs Act of 2017 cut the corporate rate from 35% to 21%, reduced individual bracket rates, nearly doubled the standard deduction, capped the state and local tax deduction at $10,000, and eliminated several miscellaneous deductions.8Cornell Law Institute. Tax Cuts and Jobs Act of 2017 Some of those changes shrank the rate variable. Others broadened or narrowed the base. The net revenue effect was the product of all those shifts interacting at once, which is why a single tax bill can be genuinely hard to score.
The same logic runs at smaller scales. A state sales tax holiday on back-to-school supplies temporarily zeroes the rate on part of the base. A new enterprise zone exemption carves a piece out of the property tax base. Every policy lever feeds back into the same multiplication, and the simplicity of the formula is what lets you trace those effects to a dollar figure.