How the numbers work
Every calculator here shows a number, and a number with no workings behind it is just an assertion. This page is the workings: the formula each tool uses, where its constants come from, and — the part most calculators skip — what each one cannot know.
Last reviewed 20 August 2026.
Lifespan
What it computes. A projected age at death, the years remaining, and a grid of your life in weeks.
The method. It starts from life expectancy at birth for your country and sex, drawn from a built-in table of roughly 50 countries (approximate recent WHO and national-statistics figures). It then applies a survivorship nudge: if you are over 40, it adds min((age − 40) × 0.15, 9) years, because someone who has already reached 50 has outlived the early-life risks baked into a figure quoted from birth. Twenty question modifiers are then summed and added. The result is clamped to between your current age + 0.5 and 105, and mapped to one of five verdict tiers by rounded age: under 60, 60–70, 71–80, 81–90, and above 90.
The honest caveat. Of the twenty questions, eight are real health factors — smoking, exercise, body composition, alcohol, diet, sleep, stress and social connection, all of which have genuine associations with mortality. The other twelve are satirical: doomscrolling, desk posture, energy drinks, unread-email count and so on. They still move your number, because the tool is built to be entertaining. That means the output is not an actuarial estimate and should not be read as one.
Further limits. Life expectancy at birth is a period measure — a snapshot of current mortality rates, not a forecast of your cohort's. It takes no account of your genetics, income, medical history or healthcare access, all of which matter more than any question we ask. Use the tool.
Savings goal, and the millionaire calculator
What they compute. The number of months until a balance reaches a target. The millionaire tool is the same engine with the target fixed at $1,000,000.
The method. Monthly compounding at a monthly rate i = annual rate ÷ 12. With a starting balance PV, a monthly contribution PMT and a goal FV, the closed-form answer is n = ln((FV + PMT/i) ÷ (PV + PMT/i)) ÷ ln(1 + i). Two edge cases are handled separately rather than by dividing by zero: at a 0% rate it is simply (FV − PV) ÷ PMT, and with no monthly contribution it reduces to ln(FV ÷ PV) ÷ ln(1 + i). If the goal is mathematically unreachable — no contributions and no growth — the tool says so instead of returning a number.
Inflation. Ticking the inflation option switches the projection to a real monthly rate, ((1 + r) ÷ (1 + π))1/12 − 1, so the answer is expressed in today's purchasing power rather than future dollars.
Limits. A single fixed rate, compounded monthly, with contributions that never change. Real markets do not deliver a constant return, and this model has no concept of sequence-of-returns risk, fees or tax. Use the tool.
Loan payoff
What it computes. Months until the balance reaches zero at a fixed payment, and the effect of paying extra.
The method. The standard amortization inverse, n = −ln(1 − (i × B) ÷ PMT) ÷ ln(1 + i), where B is the balance. Before that runs, the tool checks the payment against the first month's interest, i × B. A payment at or below that figure never touches principal, so instead of producing a nonsense answer it reports that the loan will not amortize and shows the minimum payment required. The month-by-month schedule is generated separately, with the final payment reduced to whatever is actually left owing, and is capped at 720 months.
Limits. Fixed rate, fixed payment, no fees and no variable-rate resets. Use the tool.
Student loan forgiveness
What it computes. Months until federal loans are forgiven under RAP, IBR or PSLF, counting forward from qualifying payments you have already made.
The constants. RAP forgives at 360 qualifying payments (30 years); PSLF at 120 (10 years); IBR at 240 for loans first borrowed on or after 1 July 2014, or 300 before that. The RAP monthly payment is calculated as 1%–10% of AGI annually, reduced by $50 per eligible dependent, with a $10 monthly floor.
Why this shows a range and not one number. A specific AGI-to-rate band table was proposed for this tool in August 2026 and tested against the code. It was rejected, and the reasoning is worth stating because the alternative looks more useful: the proposed table was non-monotonic at its own boundary — it made an income of $10,001 produce a lower annual payment than $10,000 — it contradicted the 1%–10% rule below an AGI of $1,200, it created cliffs where one extra dollar of income could cost around $1,000 a year, and it keyed off raw AGI with no household-size adjustment, unlike every other federal income-driven formula (including the FAFSA tool on this very site). No primary Department of Education source could be reached to confirm it. A table with those properties is a reconstruction, not the published rule, so the tool continues to show the statutory 1%–10% span. A calculator that guesses confidently is worse than one that admits the gap.
What we still deliberately do not assert. Whether IBR remains open to borrowers whose first loan is dated on or after 1 July 2026 is a point on which published sources conflict, so it is presented as a user choice rather than a silent assumption. Note also that forgiveness outside PSLF is taxable from 2026 onward — the ARPA exclusion expired on 31 December 2025. PSLF forgiveness remains untaxed.
Limits. Constants last checked 7 August 2026. This is not affiliated with or endorsed by the U.S. Department of Education. Confirm your qualifying payment count and plan eligibility with your loan servicer. Use the tool.
FAFSA and Pell
What it computes. A countdown to the 2027–28 FAFSA opening and federal deadline, plus whether household AGI falls inside the statutory automatic-maximum or automatic-minimum Pell bands.
The method. The 2027–28 award year uses prior-prior-year income — 2025 — and therefore the 2025 HHS poverty guidelines for the 48 contiguous states and DC (household sizes 1–8, plus $5,500 for each additional person), published by ASPE. Automatic maximum Pell applies at or below 225% of the guideline for a single parent and 175% otherwise. Automatic minimum Pell applies at 325% (dependent, single parent), 275% (dependent, not single) and 400% (independent single parent).
What we deliberately do not assert. The 2027–28 maximum Pell award has not been announced, so no figure is shown for it. For reference, 2026–27 was set at a $7,395 maximum and $740 minimum by Dear Colleague Letter GEN-26-01 (30 January 2026) under Pub. L. 119-37, which the Department itself notes could change pending further action by Congress. Alaska and Hawaii use separate poverty tables that we could not source in full by household size, so the tool refuses to compute for those states and links you to ASPE rather than quietly applying the wrong table. Where the published sources differ on whether a threshold test is "≤" or "<", we apply "≤" and show a borderline warning within 2% of either line, so no boundary case is presented as settled.
Limits. Constants last checked 7 August 2026. Not affiliated with, endorsed by, or approved by the Department of Education or Federal Student Aid. The FAFSA form is always free at studentaid.gov. Use the tool.
Retirement
What it computes. The year and age at which a portfolio can sustain your target spending.
The method. Your target is (annual spending − 12 × monthly Social Security) ÷ safe withdrawal rate. The projection then runs year by year — balance = balance × (1 + r) + 12 × monthly contribution — until the target is met or you reach 100, at which point the tool reports the gap rather than a retirement age.
Why the defaults are what they are. The 4% default withdrawal rate descends from the Trinity study and its successors, which found that a 4% first-year withdrawal adjusted for inflation historically survived 30-year retirements in most market conditions. It is a widely used starting point, not a guarantee. The default return is 5%, meant as a real (inflation-adjusted) figure rather than a nominal 8–10%, because your spending target and contributions are entered in today's dollars — feeding in a real return keeps the entire projection in today's purchasing power.
Limits. A constant annual return, applied once per year, with no sequence-of-returns modelling, no tax treatment and no variation in contributions. Use the tool.
Passport timeline
What it computes. An estimated arrival window by service tier.
The constants. Processing time and mailing time are separate facts and are stored separately. State Department processing runs 4–6 weeks routine and 2–3 weeks expedited, and it starts when the agency receives your application. Each mailing leg is 1–2 weeks; the delivery upgrade cuts the return leg to 1–2 days. The window the tool shows is the complete envelope — processing plus both mail legs — so routine spans 6–10 weeks (5–8 with the delivery upgrade) and expedited spans 4–7 weeks (3–5 upgraded). Agency and courier service is 3–5 business days from receipt and requires proof of travel within 14 days.
What changed, and why. The numbers are unchanged; what changed is that they are now derived rather than hard-coded. The page used to describe the model as “up to two weeks mailing each way”, which states no lower bound and therefore implies a 4-week routine floor the table never actually used. The real model — and the one the eight published figures fit exactly — puts a 1-week floor on each mail leg. Both ends now come from one versioned PASSPORT_SOURCE block, which is also what the tool renders in its “Source and review” panel, so the arithmetic is inspectable instead of implied.
Limits. These are published guidance ranges, not commitments, and they move with demand — peak season is materially slower. Plan against the later date. Reviewed quarterly against the State Department processing-times page. Use the tool.
Tax refund
What it computes. An estimated deposit window from your filing date and method.
The constants. E-file with direct deposit is treated as 21 days, matching IRS guidance that most such refunds arrive within that window; a paper check adds about 7 days of transit. A paper return runs 42–56 days (6–8 weeks). Returns claiming the EITC or ACTC are held under the PATH Act.
Two different facts, kept apart. The PATH Act is a permanent statute and says the IRS cannot issue these refunds before mid-February. Separately, the IRS publishes a season-specific expectation for when most such direct deposits actually land — for the 2026 season, 2 March. The tool previously collapsed both into a single hard-coded 27 February floor labelled as the statute, which was neither the law nor the season estimate. They are now stored separately and the season figure is stamped with the season it belongs to: file in a later year and the tool falls back to the statutory rule and says the new season’s date is not published yet, rather than asserting a stale one.
Limits. Every date here is a planning estimate, not a release promise; check the IRS status tool for a personalised date. Any return flagged for identity verification or review falls outside these windows entirely. Reviewed before each filing season against the IRS EITC/ACTC refund-timing page. Use the tool.
Countdown and days alive
What it computes. Time remaining to any date, and the number of days you have been alive with day-count milestones at 10,000, 15,000, 20,000 and 25,000 days.
The method. Whole calendar days are counted by mapping each local year/month/day onto UTC and differencing there. This matters more than it sounds: subtracting two local timestamps and dividing by 86,400,000 is wrong across a daylight-saving boundary, because one interval in the year is an hour short and another an hour long, so a naive floor drops a day each spring and a naive ceiling gains one each autumn. Mapping onto UTC — where every day is exactly 86,400,000 ms — removes the offset entirely.
Limits. Day counts are calendar days in your device's local time zone. Use the tool.
How often this gets reviewed
The tools divide into two kinds. The money calculators implement mathematics that does not change — those are stable, and only their defaults are revisited. The rest encode published policy, which does change, and each carries its own review cadence.
Editorial standards
These tools span health, money, student debt, taxes and travel policy. That is a category where being confidently wrong does real damage, so the rules we hold ourselves to are written down here rather than implied.
Every time-sensitive rule carries provenance. The passport, tax-refund, student-loan and FAFSA tools each render a Source and review panel naming the publishing body, the period the rule covers, the date we last checked it, when we will check it again, and who is responsible. If a tool shows you a government figure and no such panel, treat that as a bug and tell us.
We separate the rule from the estimate. A statute and a this-year expectation are different things and are stored as different values. Where a figure is a projection rather than a published rule, it says so on the page.
We say when we could not verify something. Where a primary government source could not be reached or read, the tool either shows a range instead of a point, asks you to choose, or declines to compute — and the limitation is named in this page. The RAP band table and the Alaska/Hawaii poverty tables are the live examples; both are described above.
Neutral language on health. The lifespan tool asks about smoking, body composition, alcohol, sleep, stress and social connection. Those answers are described in plain clinical terms, not as punchlines. The tool's humour lives in the twelve explicitly satirical modern-life questions and in the verdict tiers, not in how it describes someone's body or mental health.
Monetization never reads your inputs. Ads on this site are contextual to the page, not to anything you typed — your entries are not sent anywhere, and are not put in the page address unless you press a share button. We do not currently run affiliate links; if that changes, each one will carry a visible disclosure immediately next to it, will sit outside the answer itself, and will not appear on the FAFSA, student-loan, tax or lifespan result states at all.
Corrections
If a constant or formula here is wrong, we want to know and we will fix it. Send the page, the figure you think is wrong, and a link to the primary source to kevynsgrin@gmail.com. Corrections to a published rule are made in the tool's source configuration, which updates the figure and its Verified date together — so the fix and its provenance ship at the same time. Substantive changes are noted on this page.
This page and the tools it describes are maintained by the site owner. There is no separate editorial board; where a subject needs professional judgement — medical, legal, tax, financial aid — the tools point you to the official source rather than substituting for it.
What none of these are
None of these tools is financial, legal, medical or tax advice, and none of them knows anything about your circumstances beyond what you typed. Where a number depends on a rule we could not verify against a primary source, the tool shows a range, asks you to choose, or declines to compute — you will find each of those cases named explicitly above. That is deliberate: a calculator that guesses confidently is worse than one that admits the gap.
If you believe a constant or formula here is wrong, tell us and cite the source — corrections go to kevynsgrin@gmail.com.
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