Why the tax code needs the concept at all. Adjusted gross income is a statutory subtotal, defined by section 62 as gross income minus an enumerated list of deductions. Because it is a subtotal, it can be reduced by things Congress does not want counted when it is testing whether a household needs help or should face a limit. Someone with a large tax-exempt bond portfolio or a foreign earned income exclusion can show a modest adjusted gross income while having considerable resources. Adding those items back is what "modified" means. Each provision adds back the items its own drafters cared about, which is why there is no single answer.
The add-backs come from a short recurring list. Once you have seen a few definitions the pattern is visible: amounts excluded under sections 911, 931 and 933, which are the foreign earned income and U.S. possession exclusions; interest that is exempt from tax; the portion of Social Security benefits not otherwise included in income; and a small group of education and adoption exclusions. What varies is which of those a given provision reaches for, and in what combination.
A typed index of the versions this site covers.
Some provisions modify adjusted gross income without using the label. Section 219(g)(3), which governs the deduction phase-out for a taxpayer covered by a workplace retirement plan, is headed simply "Adjusted gross income" and then directs that the figure be determined after sections 86 and 469 and without regard to several exclusions and to the IRA deduction itself. That is a modified adjusted gross income in substance, and IRS publications call it one, but a reader searching the statute for the phrase will not find it there. The reverse also happens: section 86 defines a modified adjusted gross income and then uses it as an input to a further computation that the statute never names at all. That one also explains a discrepancy readers hit constantly. Section 86(b)(2)(B) folds tax-exempt interest into its own modified adjusted gross income, while the IRS and Social Security Administration worksheets present the same arithmetic as adjusted gross income plus tax-exempt interest plus half of benefits. The two produce an identical answer; they simply start counting in different places.
Timing is part of the definition, not a detail around it. Almost every tax version is computed from the current year's return. Medicare's premium surcharge is not. The Social Security Act directs that the figure be determined for "the second calendar year preceding the year involved", so a one-off event such as a large Roth conversion or the sale of a business raises the current year's tax measures immediately and raises Medicare premiums two years later. Treating those as one clock is a common and expensive error, because the two effects land in different years and the second one arrives after most people have stopped thinking about the transaction.
A practical consequence worth knowing before you go looking. If a household has no foreign income, no tax-exempt interest, no untaxed Social Security and no education exclusions, several of these definitions collapse onto adjusted gross income exactly. That is why the distinction is invisible to most filers most of the time, and why it tends to surface at the worst moment: the year someone buys municipal bonds, claims a foreign exclusion, or starts drawing Social Security.