Methodology & Accuracy
Every calculator on RetireCalculator.net is powered by a small, tested calculation engine. This page documents the formulas, the conventions we chose, and — just as importantly — the simplifications each model makes, so you can judge how far to trust a number.
How this page relates to the guides
This page documents arithmetic: what each engine function computes, from which inputs, within which limits. The four guides on this site document the rules and research that sit around the arithmetic, and the two are meant to be read together. 401(k), Roth IRA, and Taxable Accounts: How They Fit Together covers the tax timing that the growth engine deliberately ignores; Retirement Age Milestones covers the statutory ages that a projection runs straight through without noticing; The 4% Rule covers the provenance of the withdrawal-rate convention the drawdown tools use as their default; and RMD Rules Explained covers the distribution regime whose one-line formula the RMD engine implements. Where a guide states a rule, this page states how the engine encodes it — and where the engine encodes nothing, this page says so. The full set is listed under Guides.
The core formula
Almost everything here reduces to the future value of a series. A starting balance grows by a monthly rate r (the annual return divided by 12) over n months, and each contribution grows for the months remaining after it is made:
FV = P·(1+r)ⁿ + PMT·[((1+r)ⁿ − 1) / r]
The first term compounds the starting balance; the second is the standard annuity formula for a
stream of level contributions. A 0% return degrades gracefully to simple addition. The Savings
Goal Calculator runs this same equation in reverse, solving for the contribution
PMT that reaches a target. The Compound Interest and CD Calculators use the general form
FV = P·(1 + rate/m)^(m·t) so they can compound at any frequency m — daily through
annual.
Simulated where a formula won't do
Two models can't be captured by a single closed-form expression and are simulated month by month instead. The 401(k) Calculator steps through each month so that salary growth and the employer-match cap are applied correctly as pay rises. The retirement drawdown steps through retirement applying investment growth and then the withdrawal each month, escalating the withdrawal annually for inflation; if growth covers the withdrawals, the balance is reported as never exhausted rather than forced to a finite number.
Conventions
- Monthly compounding. The accumulation tools compound monthly at the annual rate ÷ 12. The Compound Interest and CD Calculators let you choose the frequency; the Inflation Calculator and the savings-runway mode step annually.
- End-of-month contributions. Contributions are treated as arriving at the end of each month unless a begin-of-month option is offered and selected.
- Nominal dollars. Balances are shown in future (nominal) dollars. To see purchasing power in today's dollars, enter a real (after-inflation) return.
- Constant return. Each projection assumes a single, steady rate of return. Real markets vary year to year, which the models do not attempt to simulate.
What the models do not include
These are planning tools, not tax or investment engines. They do not model taxes, Social Security, pensions, investment fees, contribution or income limits, or the sequence-of-returns risk that comes from variable real-world returns. Each calculator's page states its own key omissions, and every finance page carries a "not financial advice" note. Treat the output as a way to understand the shape of a decision, not as a guarantee.
Calculator-by-calculator reference
Each calculator page calls one or two functions from the engine. The subsections below name that function, list its inputs and the ranges its validation accepts, describe what it does with them, and show an example computed at build time. The examples deliberately use different inputs from the ones pinned on the calculator pages, so the same engine is seen from a second angle; every rate in them is an assumption chosen for illustration, not a forecast of anything.
Money inputs across the engine share one validation rule: a value must be a finite number, not negative, and no larger than $1,000,000,000,000. Fields that cannot sensibly be zero — a principal to compound, a goal to reach, a spending amount to withdraw — additionally reject zero. Rates are accepted from 0% up to and including 100% unless a subsection says otherwise, and projection terms from more than zero up to 80 years. The monthly-stepped tools round the term to whole months; the Compound Interest and CD Calculators accept fractional years and raise the per-period factor to a fractional power instead. A value outside its range does not produce a wrong number: the function returns a plain-language error instead of a result, and the page shows that message beside the field. No function ever returns a non-numeric balance; a runway that never depletes is reported with an explicit never-exhausted flag (and an unbounded years figure) rather than a fabricated finite number; an overflow is reported as an error. Where the engine exports a limit it is read at build time; every range quoted below is pinned by an automated test, so a change to an engine limit either updates this page automatically or fails the test suite until the page is corrected.
Investment Calculator — futureValue
The Investment Calculator is the core formula with nothing added. Inputs: a starting principal, a level monthly contribution, an annual return, a term in years, and an optional contribution timing (end of month by default, or begin). The function converts the annual rate to r = rate ÷ 12, the term to n = years × 12 rounded to whole months, and forms the growth factor (1+r)ⁿ. The principal is multiplied by that factor; the contribution stream is multiplied by ((1+r)ⁿ − 1) ÷ r. At exactly 0% the annuity term would divide by zero, so the engine substitutes contribution × n. Choosing begin-of-month multiplies the contribution stream by one more (1+r), because every deposit then earns one extra month. The result reports the balance, the total contributed (the principal plus every deposit), and growth as the difference.
Example: $25,000 plus $300 a month at an assumed 5% for 20 years reaches $191,126.11 — $97,000 contributed and $94,126.11 of growth. The same inputs with begin-of-month deposits reach $191,639.90, a difference of $513.79 that is exactly one month's growth on the contribution stream. At 0% the same inputs give $97,000, the deposits alone. A common misreading: "growth" here is everything the example did not deposit, so it already nets out the starting balance — it is not interest on the principal only.
Roth IRA Calculator — futureValue
The Roth IRA Calculator calls the same function with the same ranges. The engine has no notion of account type: nothing in the arithmetic knows the balance is a Roth. The label lives on the page, in the framing of what the growth means at withdrawal time — the mechanics of that framing are in the retirement accounts guide. The engine also does not know or enforce contribution limits; the guide explains that those change annually and points to the published figures rather than quoting them.
Example: $3,000 plus $150 a month at an assumed 8% for 40 years reaches $596,471.33, of which $75,000 was deposited and $521,471.33 is growth. Over a horizon that long, growth dwarfs deposits — that is the (1+r)ⁿ term doing its work, and it would look the same in any account.
Compound Interest Calculator — compoundInterest
The Compound Interest Calculator isolates the lump-sum
term. Inputs: a principal greater than zero, an annual rate, a term of up to 80 years, and
a compounding frequency m that must be a whole number from 1 to 365. The function computes
P·(1 + rate/m)^(m·t) and reports the balance and the
interest (balance minus principal). Unlike the monthly-compounding tools, this function does not
round the term to whole months: t is applied exactly as entered, so a fractional number of
years becomes a fractional exponent. Contributions are not part of this function — they belong to
futureValue above.
Example: $20,000 at an assumed 4% for 8 years grows to $27,371.38 compounded annually, $27,527.90 monthly, and $27,542.07 daily. The step from annual to monthly is worth $156.52; the step from monthly to daily only $14.17. The frequency effect saturates quickly, which is why monthly compounding is a reasonable house convention for the other tools.
Savings Goal Calculator — requiredContribution
The Savings Goal Calculator runs the core formula backwards. Inputs: a target greater than zero, a starting balance (zero allowed), an annual return, and a term. The function first grows the starting balance alone to the end of the term and reports that figure as the projection from growth alone. If it already meets or exceeds the target, the required contribution is zero and the result is flagged as already on track. Otherwise the shortfall is divided by the annuity factor: contribution = remaining × r ÷ ((1+r)ⁿ − 1), or remaining ÷ n at 0%.
Example: a $120,000 goal from $15,000 at an assumed 5% over 12 years requires $471.13 a month; the starting balance alone would reach $27,297.73. By contrast, a $10,000 goal from $9,000 at an assumed 5% over 3 years needs no contribution at all, because growth alone projects to $10,453.25 — the on-track branch. Reading the output: the monthly figure is level for the whole term; the model does not step contributions up over time.
401(k) Calculator — four01k
The 401(k) Calculator is the first of the two simulated models. Inputs: an annual salary greater than zero, an employee contribution percentage that must be above 0%, an employer match percentage, the salary percentage up to which the match applies, an annual return, a term, an optional current balance, and an optional annual salary growth percentage. All percentages are accepted from 0% to 100%. Before the loop, the engine fixes the matched fraction as the smaller of the contribution percentage and the match limit. Each month it computes that year's salary as the starting salary × (1 + growth)^year, the employee deposit as salary × contribution ÷ 12, and the employer deposit as salary × matched fraction ÷ 12 × match percentage; the balance is grown by one month's return and then both deposits are added. Because the matched fraction is capped, contributing above the limit raises the employee's deposits but not the employer's.
Example: a $65,000 salary contributing 10% with a 100% match on the first 4% of pay, an assumed 6% return, 25 years, a $12,000 starting balance, and an assumed 2% annual salary growth ends at $687,500.19: $208,196.95 from the employee, $83,278.78 of match, and $384,024.46 of growth on top of the starting balance. The match total is 40% of the employee total — four matched points out of ten contributed — and both rise with salary each year. What the match formula means, and how it converts to plain dollars for the other tools, is walked through in the retirement accounts guide.
Retirement Calculator — retirement
The Retirement Calculator chains accumulation to drawdown. Inputs:
a current age from 0 to 120, a retirement age up to 120 that must be greater than the current age
(and, because accumulation reuses futureValue, no more than 80 years later),
current savings, a monthly contribution, a pre-retirement return, a monthly retirement spending amount
greater than zero, a post-retirement return, and an optional annual inflation rate. Accumulation runs
the core formula with end-of-month contributions to produce the nest egg. Drawdown is then simulated:
each month the balance is grown by one month of the post-retirement return and the withdrawal is subtracted;
at the end of every twelfth month the withdrawal is multiplied by (1 + inflation). The loop stops
when the balance reaches zero or after 80 years of retirement, whichever comes first. A balance still
positive at the 80-year mark is reported as never exhausted — that is the precise meaning of the phrase.
The result reports the nest egg, the total contributed, how many months and years the money lasts,
and a depletion age equal to the retirement age plus those years.
Example A: age 40 to 67, $90,000 plus $700 a month at an assumed 6%, then $4,500 a month at an assumed 4% with an assumed 2.5% inflation escalator. The nest egg is $1,017,528.91 after $316,800 of contributions, and the drawdown lasts about 22.6 years, to about age 89.6. The identical inputs with no inflation escalator last about 35.2 years — in this example the escalator alone shortens the runway from about 35.2 years to about 22.6, which is why the page asks for it explicitly rather than assuming a figure. Example B: age 30 to 62, $20,000 plus $1,200 a month at an assumed 7%, then $4,000 a month at an assumed 5% with an assumed 2% inflation, builds $1,900,741.18 and is never exhausted within the 80-year window. Reading the output: years are counted in whole months, so a figure like 22.6 years is 271 months, and the depletion age is that fraction added to the retirement age. The statutory ages the projection passes through on the way — 59½, 62, 65, 67, 70, 73 — are described in Retirement Age Milestones; the engine does nothing special at any of them.
Retirement Planner — multiAccountRetirement
The Retirement Planner runs the core formula three times. Inputs:
the same age pair as the Retirement Calculator (gap of at most 80 years), a balance and monthly contribution
for each of a traditional account, a Roth, and a taxable account (each zero or more, at least one
greater than zero), one annual return shared by all three, and an optional assumed retirement tax
rate from 0% to 100%. Each bucket is projected with
futureValue at the shared return with end-of-month contributions; the three ending balances
are summed into a combined pre-tax figure, and that figure × 0.04 is reported as the first-year withdrawal
under the 4% convention. Only when a tax rate is supplied does the result add an after-tax illustration:
the traditional balance × (1 − rate), re-added to the Roth and taxable balances unchanged.
Example: age 45 to 65 at an assumed 5%, with $120,000 plus $800 a month traditional, $30,000 plus $300 a month Roth, and $200 a month into an empty taxable account. The buckets end at $654,343.77, $204,689.31, and $82,206.73; combined $941,239.81, with a 4% first-year figure of $37,649.59. At an assumed 20% rate the traditional slice illustrates as $523,475.02 and the combined figure as $810,371.06. The illustration does not touch the taxable bucket's own gains, and the rate is the example's assumption, not a projection of any tax law. Why the three balances are different kinds of dollars is the subject of the retirement accounts guide; what the 4% figure is and is not is the subject of The 4% Rule.
Retirement Withdrawal Calculator — withdrawalIncome and savingsRunway
The Retirement Withdrawal Calculator has two modes
backed by two functions. withdrawalIncome takes a portfolio greater than zero and an
initial withdrawal rate that defaults to 4% and is accepted only
from 2% to 6%. It multiplies the two and divides
by twelve — the first-year figure the convention defines, and nothing beyond it. The
convention's later years adjust that dollar amount for inflation rather than re-applying the
percentage, a distinction The 4% Rule guide spends most of its
length on. Example: $750,000 at 3.5% gives $26,250.00 in year one, or
$2,187.50 a month.
savingsRunway is a closed-form depletion formula with a different clock. Inputs: a portfolio
and an annual spending amount, both greater than zero, and a real return accepted from -20% to 20% — negative values model a return below inflation. Growth is applied
yearly and the withdrawal taken at the end of each year, so with W spending, P portfolio
and r real return the years to depletion are ln(W ÷ (W − P·r)) ÷ ln(1+r). When W is no more than P·r, growth
replaces the withdrawal and the balance never depletes; at exactly 0% the formula collapses to P ÷ W. The result also reports the annual amount growth alone would replace (P·r, floored at zero) and the first-year spending as a percentage of the portfolio.
Examples: $600,000 spending $36,000 a year at an assumed 2% real return lasts about 20.5 years, with growth replacing $12,000 a year; the same portfolio spending
$10,000 a year never depletes, because $10,000 is below that $12,000 threshold; and $240,000 spending
$24,000 a year at 0% lasts exactly 10 years. A frequent misreading: this
model and the Retirement Calculator answer similar questions on different terms — annual steps in
real dollars here, monthly steps in nominal dollars with an explicit inflation escalator there — so
they will not agree to the month, and neither is "wrong".
RMD Calculator — rmd
The RMD Calculator performs one division. Inputs: a prior year-end balance greater than zero and an age that must be a whole number from 0 to 130. An age below 73 is rejected with a message stating that no distribution is required at that age; from 73 upward the engine looks up the Uniform Lifetime Table divisor for the age, using the age-120 divisor for anyone older, and reports balance ÷ divisor along with the divisor itself and the distribution as a percentage of the balance. Example: $850,000 at age 77 uses a divisor of 22.9 for a required distribution of $37,117.90, 4.37% of the balance; the same balance at age 73 uses 26.5 for $32,075.47. The engine models an account owner using the Uniform Lifetime Table and nothing else — inherited accounts, the separate table for a much-younger spousal beneficiary, and multiple-account aggregation are outside it, as RMD Rules Explained spells out.
Inflation Calculator — inflation
The Inflation Calculator is the one growth tool that compounds annually rather than monthly. Inputs: an amount greater than zero, a rate from 0% to 50%, and a term from more than zero up to 100 years. It forms the factor (1 + rate)^years and reports the amount × factor as the future cost, the amount ÷ factor as the purchasing power of today's dollars at the end of the term, and (factor − 1) × 100 as the total percentage increase. Example: $2,500 at an assumed 2.5% for 15 years has a future cost of $3,620.75, while $2,500 of future dollars would then buy what $1,726.16 buys today — a total increase of 44.83%. The rate is the example's assumption; the engine carries no inflation figure of its own.
CD Calculator — cd
The CD Calculator is the compound-interest formula with an APY attached. Inputs: a deposit greater than zero, a nominal rate from 0% to 100%, a term from more than zero up to 50 years, and a compounding frequency m that must be a whole number from 1 to 365. The period rate is rate ÷ m; the maturity value is deposit × (1 + period rate)^(m·t); interest earned is the difference; and the APY is ((1 + period rate)^m − 1) × 100 — the effective annual rate the compounding implies, which depends on the rate and frequency but not on the deposit or the term. Example: $25,000 at an assumed 3.8% for 5 years matures at $30,204.14 with quarterly compounding (APY 3.85%) and $30,222.17 with monthly compounding (APY 3.87%). The function models the compounding only — nothing about early-withdrawal terms, taxes on the interest, or what happens at renewal.
Net Worth Calculator — netWorth
The Net Worth Calculator is pure addition. Inputs: a list of asset values and a list of liability values, each entry zero or more and no larger than the engine's money ceiling, with up to 100 entries per list and at least one entry overall; either list may be empty. A negative entry is rejected with a message explaining that a debt belongs in the liabilities list as a positive balance. The result is the sum of assets minus the sum of liabilities, and a negative net worth is returned as an ordinary result rather than an error. Example: four assets totalling $399,500 against three liabilities totalling $230,200 give a net worth of $169,300. No growth, valuation, or projection is involved; the only judgment in the tool is the reader's, in the values entered.
Life Insurance Calculator — dime
The Life Insurance Calculator implements the DIME method: Debts + Income + Mortgage + Education. Inputs: non-mortgage debts including final expenses, an annual income and the number of years it should continue (0 to 50), a mortgage balance, an education cost per child and a whole number of children (0 to 20), and optional offsets for existing coverage and liquid assets — every money field zero or more, and at least one of the four components greater than zero. The income component is income × years; the education component is cost × children; the DIME total is the sum of the four; the coverage gap is the total minus the offsets, floored at zero, with a flag set when the offsets cover the total. The result also reports income × 10, the classic "ten times income" figure, so the two rules of thumb can be compared — it is a heuristic shown for comparison, not a recommendation.
Example: $18,000 of debts, $72,000 of income for 12 years, a $195,000 mortgage, and $60,000 of education for one child total $1,137,000; $150,000 of existing coverage plus $25,000 of liquid assets offset $175,000, leaving a gap of $962,000. The ten-times heuristic on the same income is $720,000 — $417,000 apart from the DIME total, which is the point of showing both: they encode different assumptions about what coverage is for. Neither says anything about premiums, product types, or whether any policy suits anyone.
Rule-year data and how it is kept current
The engine encodes exactly two statutory facts, and it holds both in one place. The Uniform Lifetime Table divisors and the RMD start age live together in a single data file inside the planning engine, so an IRS revision is one visible change rather than a hunt through page copy. An automated test asserts that the table's divisors strictly decrease from age 73 through 120 and that ages below the start age are rejected. Nothing else in the engine encodes a statute: no contribution limits, no tax brackets, no benefit-claiming schedule. Those figures change on their own timetables, so the guides describe the mechanics and point to the official sources rather than freezing a number here — the reasoning is laid out in Retirement Age Milestones.
Rounding and display
Every function returns unrounded floating-point values; rounding happens only when a figure is displayed. The worked examples on this page show whole dollars where a figure is an input or a sum of inputs, and cents where it is a computed result. When a hand calculation disagrees with a tool by a few dollars, the usual cause is rounding the monthly rate (the annual rate ÷ 12) to a few decimal places before raising it to the power n — the engine never rounds it. The calculator forms are lenient about typing: a dollar sign, thousands separators, and a percent sign are stripped before the value is parsed, and a blank optional field takes its documented default rather than being treated as an error.
Worked examples can't drift
The numbers in each page's explanation — every "grows to about $X" — are computed at build time by the very same engine that runs the interactive calculator, not typed in by hand. If the calculation logic ever changed, the copy would change with it (or the build would fail), so the documentation cannot silently disagree with the tool.
Tested against reference figures
The engine is covered by automated tests that check it against independently computed reference values — for example, $10,000 plus $500 a month at an assumed 7% return for 30 years growing to about $691,150, or a $5,000 balance reaching a $50,000 goal in five years at an assumed 4% requiring about $662 a month. If you believe a result is wrong, that is exactly the kind of report we want: see the contact page, and confirmed issues are fixed in the engine and locked in with a new test.
Not financial advice: a general educational estimate that assumes a constant rate of return and excludes taxes, Social Security, fees, and market volatility. Your real results will differ. See the guides.