Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Projected balance
Simple and Eligibility modes
- FV
- balance at retirement
- PV
- current balance
- PMT
- yearly contribution
- r
- yearly return, as a decimal
- n
- years to retirement
Each contribution goes in at the start of its year, and the balance grows once a year. The contribution stays the same every year.
Source: Standard compound interest and annuity formula; no single publisher.
Reduced contribution limit
Eligibility mode, with a filing status and MAGI
- L
- the full 2026 limit: $7,500, or $8,600 at 50 or older
- MAGI
- your modified adjusted gross income
- Single
- $153,000 to $168,000; also heads of household, and married people filing separately who lived apart all year
- Joint
- $242,000 to $252,000
- Separate
- $0 to $10,000, for married people filing separately who lived together at any time in the year
The 2026 range for your filing status gives bottom and top. Inside it, the limit is rounded up to the next $10 and is never below $200; at or above the top it is $0.
Source: Based on 26 U.S.C. §408A(c)(3) [1] and IRS Publication 590-A, Worksheet 2-2 [2], with the 2026 ranges and limits from Notice 2025-67 [3] and news release IR-2025-111 [4].
Tax-free withdrawal amount
Simple and Eligibility modes
- FV
- projected balance at retirement
The calculator counts the whole balance as tax-free. That holds for a qualified distribution, made at least five years after the start of your first Roth IRA contribution year. It must also come at 59½ or later, or after disability or death, or for a first home, up to $10,000.
Source: Based on IRS Publication 590-B [5], which defines a qualified distribution. A Roth IRA has no required distributions in the owner's lifetime [5], and since 2024 neither does a Roth 401(k), under 26 U.S.C. §402A(d)(5) [6].
Sources
- United States Code. 26 U.S.C. §408A, Roth IRAs, subsection (c)(3), limits based on modified adjusted gross income. 2024 edition, GovInfo.
- Internal Revenue Service. Publication 590-A (2025), Contributions to Individual Retirement Arrangements (IRAs), chapter 2, Table 2-1 and Worksheet 2-2. 2025 edition.
- Internal Revenue Service. Notice 2025-67: 2026 Amounts Relating to Retirement Plans and IRAs, as Adjusted for Changes in Cost-of-Living, Internal Revenue Bulletin 2025-49, page 761. December 1, 2025.
- Internal Revenue Service. 401(k) limit increases to $24,500 for 2026, IRA limit increases to $7,500, news release IR-2025-111. November 13, 2025.
- Internal Revenue Service. Publication 590-B (2025), Distributions from Individual Retirement Arrangements (IRAs), chapter 2, the section on qualified distributions. 2025 edition.
- United States Code. 26 U.S.C. §402A, Optional treatment of elective deferrals as Roth contributions, subsection (d)(5) and its 2022 amendment note. 2024 edition, GovInfo.
What this calculator does not cover
- It models one Roth IRA at one return. It does not apply later years' limit changes or the rules of a Roth 401(k).
- It does not model withdrawals, the five-year rule or conversions.
- The reduced limit assumes your taxable pay is at least the limit and that you made no traditional IRA contributions that year.
- It gives the $1,100 catch-up (2026) by your age today. The IRS allows it for the whole year in which you turn 50.
Sources checked on .