Freedom Calcs

The Coast FIRE formula, explained

Inspect the Coast FIRE formula, purchasing-power conventions, monthly contribution timing, and limits behind the Freedom Calcs calculator.

Maintained by Freedom Calcs team · Model 1.0.0 · Content prepared October 8, 2026

Work backward from retirementToday’s purchasing power throughout
  1. 01 / SpendingAnnual portfolio spendingE
  2. Divide by withdrawal rate w02 / Retirement targetAssets needed at retirementF = E / w
  3. Discount by real growth over N years03 / Coast target todayAssets needed nowC = F / (1 + r)N
A formula map, not a growth prediction. The real return r adjusts nominal return for inflation; the model assumes it stays constant.

A constant-return model, in today’s dollars

Let E be annual retirement spending funded by the portfolio, w the initial withdrawal rate, g the effective nominal annual return, i annual inflation, N years until retirement, and P current invested assets. Rates are decimals in the formulas: 4% means 0.04.

Retirement asset target
F = E / w
Effective real annual return
r = (1 + g) / (1 + i) − 1
Coast threshold today
C = F / (1 + r)^N
Assets at retirement if you stop contributing
P_stop = P × (1 + r)^N
Current gap
gap = max(C − P, 0)

F = E / w is an algebraic spending target. Discounting F to C follows from constant compound growth. Neither formula tests whether the portfolio will support retirement withdrawals.

The real-rate conversion is the exact ratio described by the Federal Reserve Bank of St. Louis. Subtracting inflation from return is an approximation. We keep full precision until display. We do not inflate spending a second time; doing so would mix purchasing-power conventions.

Monthly contributions and the first Coast month

For M = 12 × N months and monthly real return q:

q = (1 + r)^(1/12) − 1
P(0) = P
P(m + 1) = P(m) × (1 + q) + s
C(m) = F / (1 + q)^(M − m)

s is the month-end contribution, fixed in today’s purchasing power. Its nominal dollar amount increases with the assumed inflation rate. This is different from contributing a fixed nominal amount for the whole period.

The engine searches months 0 through M for the first P(m) ≥ C(m). If no month qualifies, it reports that the milestone is not reached by retirement. Zero contributions keep P(m) / C(m) constant, so someone below the threshold does not catch up just by getting older.

The comparison paths continue contributing to retirement even after reaching Coast FIRE. They do not simulate switching contributions off at that milestone.

An independent closed-form check is:

P(m) = P × (1 + q)^m + s × ((1 + q)^m − 1) / q
When q = 0: P(m) = P + s × m

Effective monthly return uses a twelfth root rather than annual return divided by 12. The implementation uses logarithmic conversion for precision near zero and monthly recurrence for balances. The chart samples yearly points and includes the first milestone month.

A reproducible hypothetical example

Current age 30, retirement age 65, invested assets $100,000, annual spending $40,000, monthly contribution $1,000, nominal return 7%, inflation 3%, and withdrawal rate 4%.

  1. F = $40,000 / 0.04 = $1,000,000.
  2. r = 1.07 / 1.03 − 1 = 3.8834951456% per year.
  3. C = $1,000,000 / (1.07 / 1.03)^35 = $263,554.6273.
  4. Current gap = $263,554.6273 − $100,000 = $163,554.6273.
  5. Stopping now projects $379,427.9805 at retirement.
  6. Keeping $1,000 monthly contributions projects $1,258,123.2594 and first meets the Coast threshold at month 232: age 49 + 4 months.
  7. At $500 a month, retirement assets are $818,775.6200; Coast is not reached before retirement.

Every amount is in today’s USD. These are deterministic estimates, not actual user results.

What the withdrawal rate means here

The rate is first-year portfolio-funded spending divided by the initial retirement portfolio. The familiar inflation-adjusted strategy then changes the dollar withdrawal with inflation; it does not mean withdrawing 4% of each year’s changing balance.

Bengen’s 1994 historical work and Cooley, Hubbard, and Walz’s 1998 study provide context for withdrawal planning. The latter tested US stock and corporate-bond portfolios using 1926–1995 returns over 15–30-year payout periods, omitting taxes and transaction costs. Different portfolios, horizons, and spending rules have different implications.

Historical survival through a specified period is not a guarantee of future success, permanent income, or principal preservation. We do not reproduce a historical success percentage or generate a retirement-success probability. A 4% default is an editable example, not a personalized recommendation.

What this estimate leaves out

Inflation is constant in this model. As the Bureau of Labor Statistics explains, CPI represents group purchasing patterns; your own cost changes can differ. None of the default rates comes from an official forecast for your portfolio or household.

Input limits are product safeguards: ages 18–100 in whole years, assets up to $1 billion, yearly spending $0.01–$10 million, monthly contributions up to $1 million, nominal return −50% to 50%, inflation −20% to 50%, and withdrawal rate 0.1%–20%. Dollar inputs allow two decimals. High withdrawal rates trigger a caution but are not assessed for sustainability.

Sources and their scope

The Coast threshold and monthly contribution formulas are basic algebraic derivations documented above. Citing research does not mean its authors endorse this calculator.

Verification and editorial responsibility

The model has been checked against independently recorded examples, an independent closed-form calculation, zero and negative real returns, equal retirement ages, input boundaries, and the no-contribution invariant. Browser checks have covered calculation updates, errors, keyboard form navigation, responsive layouts, and financial-input data handling in Chromium, Firefox, and WebKit on Windows.

These software and arithmetic checks do not establish future investment performance or replace professional financial review. They are not a real-device or external user study. No independent licensed financial review has been completed.

Freedom Calcs team maintains the implementation, checks sources against their scope, and updates explanations alongside model changes. Contact and correction instructions explain how to describe a reproducible issue without sharing sensitive financial details.

Model and content updates

— Initial candidate, model 1.0.0: exact effective real/monthly return, month-end contributions in fixed purchasing power, three contribution paths, and return sensitivity. This date records actual preparation; rebuilding does not change it.

Return to the calculator.

October 8, 2026 — Display correction: positive estimates below one cent use scientific notation instead of rounding to $0. Sub-dollar amounts retain cents. The underlying model and milestone calculation are unchanged.