The real math behind Coast FIRE

Coast FIRE says: save hard until the pot, left alone, is expected to reach a FIRE number by the date you actually stop working. Then contributions go to zero and compounding is asked to finish the job. That is a real identity if returns are a constant. It is a bet if returns are a sequence. This page is the bet, on one frozen worker.

Specimen B4_COAST: age 35, $200,000, 80/15/5, $3,000/mo net deployed until the coast date (or until 65). FIRE stake: $1,500,000 at 65, which is 25× a $60,000 spending year. Success at 65 is the share of paths whose real wealth is at least that stake. No withdrawals before 65. Seed 20260622, 1,000 paths. Coast ages on the card: 40, 45, 50, 55, plus continue-to-65.

The real math behind Coast FIRE

If every year were 7% real, you could solve for the pot that, with no new savings, hits $1.5 million at 65. That algebra is the blog-post version. This engine is not 7% real every year. Keep saving until 65 and only 56.0% of lives still hold $1.5 million at 65. The median is $1,658,359, which is above the stake, and the left tail (p5 $547,974) is not. Coast math that quotes the median as the plan is quoting a household that already won.

Stop contributions at 45: stake-hit 32.5%, median $988,497. At 40: 23.8%, $784,680. At 50: 39.1%, $1,175,664. At 55: 45.2%, $1,352,164. The dashed line on the chart is the continue-to-65 share. Nothing on the coast-age grid reaches it. The card said a coast-at-45 matching continue-to-65 (gap under 2 points) would falsify the "not a free lunch" reading. The gap is 23.5 points. Lunch is not free.

Ruin on this accumulation run is 0.0% even when contributions continue, because there are no withdrawals to force zero. The interesting failure is missing the stake, not hitting literal zero. That is why the primary metric is stake-hit, not the engine's ruin flag. Using ruin here would have been a tautology.

What the identity drops

It drops sequence during the coast years. A crash at 46, after you have stopped saving, is a smaller pot compounding for 19 years instead of a smaller pot plus new savings. The continue-to-65 policy buys new units through the crash. The coast policy does not. That is not a moral. It is a cashflow.

It drops the difference between a point forecast and a share of lives. Spreadsheet coast calculators print an age. This freeze prints a curve of ages against a probability of still holding $1.5 million. If you wanted an age, you wanted the median path's age, and you should say so. The median continue-to-65 ending is $1,658,359, which clears the stake. The share that clear it is 56.0%. Those can both be true.

It drops fees, tax, and job risk. Q4 was not a fee-drag study. Tax is off. The contribution is a net $3,000/mo in the engine, not a gross salary. A real coast date would move if the $3,000 were 401(k) money with a match, or if the person's earnings fell. This specimen is one person with a smooth net save.

Scope

Q1 run. Q2 not run: inside this calibration; a lower ERP would move every coast date later. Q3 not run: not a historical claim. Q4: 5 bps, tax off, no extra fee drag. We did not then run a 4% withdrawal from 65. Clearing $1.5 million at 65 is not the same as a 30-year retirement succeeding. The 4%-at-40 article is that other question.

Coast date is chosen at t=0. The policy does not look at returns to pick a clever year. A rule that coasts after a bull market would be a different, look-ahead-adjacent study.

Medians versus shares, age by age

Continue to 65: median $1,658,359, p5 $547,974, p95 $6,038,994, stake-hit 56.0%. Coast at 55: median $1,352,164, stake-hit 45.2%. Coast at 50: median $1,175,664, stake-hit 39.1%. Coast at 45: median $988,497, stake-hit 32.5%. Coast at 40: median $784,680, stake-hit 23.8%. The median can sit near a million while the share at $1.5 million is still a coin flip or worse. That is why a FIRE number printed as a point is the wrong object.

Year-by-year median for continue-to-65 crosses $1 million around the late fifties on this freeze (year 19 of the 30-year worker path is $1,090,924). Coast-at-45 at the same year is $686,450. The lines are not close. Spreadsheet coast dates that ignore the contribution you no longer make will print a prettier age than this fan.

The $1.5 million stake is 25× $60,000. It is not a tested 4% retirement after 65 on this freeze. A household that coasts into 65 with $988,497 median and then starts a 4% withdrawal is a different experiment. Do not bolt this page onto the 4%-at-40 page and call it a plan.

See a coast date as a share

The Coast FIRE calculator is the matching tool. Read a printed age as a median identity, then ask what share of lives still hold the stake if saving actually stops. On this freeze that share is 32.5% at 45 and 56.0% if you never coast. The median at 45 is $988,497, which sounds like a plan until you remember the stake is $1.5 million. A calculator that prints only the median age at which the mean path crosses $1.5 million is the 7% identity in a hoodie. Ask for the share. If the tool will not give a share, you are looking at algebra, not at 1,000 lives.

Keep the contribution-stop date and the compounding bet in the same sentence. Drop either half and Coast FIRE becomes a slogan again. This page is the sentence, with the freeze underneath it.

What this page refuses to say

It refuses to print a coast age as a destiny. 32.5% of lives still hold $1.5 million if saving stops at 45. That is not zero, and it is not 56.0%. It refuses to treat the median of $988,497 as the plan when the stake is 1.5 million. It refuses to say anyone should stop working at 45. It refuses to test a 4% withdrawal after 65 on this freeze and then claim Coast FIRE was proven. Clearing a stake is not a retirement.

It refuses a look-ahead coast: wait for a bull market, then stop. That policy reads future returns in spirit even if it only uses past returns at the decision date, and it was not on the card. It refuses to add coast-at-42 because 45 looked ugly. It refuses to count engine ruin as the primary when ruin is ~0 by construction. Stake-hit is the primary. Quote it.

It refuses Q2 theater. We did not shave mu here. A lower premium would move every coast date later. The takeaway says so. Silence would have been an overclaim. It refuses a historical coast series. One worker from 35 to 65 on a tape is one life, not 1,000.

Spreadsheet coast math that assumes 7% real every year is the deterministic article in another hat. This fan is the correction. If your calculator prints an age without a share, it printed the identity, not the bet.

Replication spec

Worker starts at 35 with $200,000. Net $3,000/mo is income 8,000 minus spend 5,000 until the coast year, then income equals spend so net save is zero. Mix 80/15/5, static rebalance, seed 20260622, 1,000 paths, 30 years to age 65. Stake $1,500,000 in the real fan's last month. Continue-to-65 is labeled coastAge 65 on the CSV.

Stake-hit shares: 40 23.8%, 45 32.5%, 50 39.1%, 55 45.2%, 65 56.0%. Medians: $784,680, $988,497, $1,175,664, $1,352,164, $1,658,359. p5: $202,620, $263,525, $331,591, $408,482, $547,974. p95: $3,499,729, $4,204,469, $4,810,857, $5,456,850, $6,038,994. Ruin flags are ~0 because there is no withdrawal. Do not quote ruin as success.

Yearly median continue-to-65 at year 10 is $657,341, at year 20 $1,136,619, at year 30 $1,658,359. Coast-45 at those years: $521,926, $712,533, $988,497. CSV: /data/studies/real-math-behind-coast-fire.csv. Q2 not run. Q3 not run. 5 bps, tax off. Coast date chosen at t=0, no return look-ahead.

The 25× stake is a definition on this card, not a tested withdrawal. A 4% rule from the ending pot is a different freeze. If coast-at-45 had matched continue-to-65 within 2 points, the free-lunch reading would have stood. It did not. Gap: 23.5 points.

Last recap: age 35, $200,000, $3,000 a month until a coast date or 65, stake $1.5 million at 65. Stake-hit 23.8% / 32.5% / 39.1% / 45.2% / 56.0% at coast ages 40, 45, 50, 55, and never. Medians $784,680 through $1,658,359. Coast is a contribution-stop date plus a compounding bet. The bet does not match continue-to-65. Gap at 45: 23.5 points. Not a 4% test after 65. Not advice to quit a job. Algebra that prints only an age is the identity. This fan is the share.

Seed 20260622. 1,000 paths. Static 80/15/5. Coast date frozen at t=0. If you pick the coast year after a bull market, you are on a different card. p5 at coast-45 is still $263,525, which is not ruin and is not the stake. Quoting only p5, only the median, or only the stake-hit share is how the bet gets sold as a point again. Print the row. Print the gap. Print that Q2 was not run. Then stop. Do not add a coast age. Read the freeze file.

Notes. B4_COAST: age 35, $200,000, $3,000/mo net until coast or 65, 80/15/5, stake $1,500,000 real at 65, seed 20260622, 1,000 paths, static rebalance. Coast ages 40, 45, 50, 55, 65. Q1 run. Q2/Q3 not run. Q4: 5 bps, tax off. CSV: /data/studies/real-math-behind-coast-fire.csv. Card dated 2026-08-28. This article is educational analysis, not investment advice, and does not recommend any security or strategy.