Derivation
Where the 4% rule comes from, and what it does not say
It is a research finding about 30-year windows in US market history — not a law, and not a promise. The arithmetic it implies is exact. What it was measured over is narrower than almost anyone quoting it says.
The short version
A withdrawal rate turns spending into a target by dividing 100 by the rate. 4% is 25× annual spending; 3% is 33.33×. That one-point difference is 33.3% more capital. The rule was tested over 30 years of US history, on specific portfolios, before fees and tax — and it cannot express the risk that returns arrive in a bad order.
The arithmetic is the easy part
A withdrawal rate does one job: it converts a spending figure into a pot. If you intend to draw 4% of the pot in your first year, then the pot has to be 25 times that first year's spending, because 1 ÷ 0.04 = 25. That is the whole conversion.
multiple = 1 ÷ withdrawal rate
target = annual spending × multiple
On $40,000 of annual spending:
| Withdrawal rate | Multiple of spending | Target |
|---|---|---|
| 5% | 20.00× | $800,000.00 |
| 4.5% | 22.22× | $888,888.89 |
| 4% | 25.00× | $1,000,000.00 |
| 3.5% | 28.57× | $1,142,857.14 |
| 3% | 33.33× | $1,333,333.33 |
| 2.5% | 40.00× | $1,600,000.00 |
Notice the shape. The multiple is 1 ÷ rate, which is a hyperbola — so the cost of lowering the rate accelerates. Moving from 5% to 4% adds 5× your spending to the target. Moving from 4% to 3% adds 8.33×, which on $40,000 of spending is$333,333.33 more capital for the same one percentage point. Caution is not linearly priced.
Where the 4% figure came from
In 1994 William Bengen published Determining Withdrawal Rates Using Historical Data in the Journal of Financial Planning. He took historical US market data and asked a specific question: if a retiree withdraws a fixed percentage in year one and then increases that dollar amount by inflation every year after, what is the highest starting percentage that would have survived a 30-year retirement beginning in any historical year he tested? The answer landed near 4%.
The Trinity Study — Cooley, Hubbard and Walz, 1998 — approached it from another direction, reporting success rates across a range of stock and bond mixes, withdrawal rates and horizons. Between them these two papers are why a number picked from mid-century American market history became a global rule of thumb.
Both are serious pieces of work. Neither claims what the phrase "the 4% rule" implies.
What it does not say
It does not say 4% is safe for any retirement length. The window studied was thirty years. A retirement beginning at 45 might run fifty, which is a different question with more opportunities to meet a bad sequence. Quoting 4% for an early retirement extends a finding past the horizon it was measured over.
It does not say anything about your market. The data is US, and covers a period in which US equities did unusually well relative to most of the world. A rule calibrated on the best-performing large market of the twentieth century is not obviously portable.
It does not include fees or tax. Platform charges, fund fees and tax on withdrawals all come out of the same pot and none of them is in the model. A 0.5% annual fee against a 4% withdrawal is an eighth of the income.
It does not describe how anyone actually spends. The model draws a constant inflation-adjusted amount for thirty years regardless of what markets do. Real retirees cut back in bad years, which is both obvious and the reason the historical failure rates are pessimistic in one direction and the rigid-spending assumption is unrealistic in the other.
The risk a constant rate cannot express
This is the important one, and it is demonstrable rather than arguable. Take$1,000,000, withdraw$40,000 at the start of each year, and apply ten annual returns. Now apply exactly the same ten returns in the reverse order.
The arithmetic mean is 10% either way. The same numbers. Only the order differs:
| Order | After ten years |
|---|---|
| Bad years first (−15%, −10%, …) | $1,573,834.11 |
| Good years first (+25%, +15%, …) | $1,835,954.59 |
| Difference | $262,120.48 |
$262,120.48 of difference from ordering alone. The reason is that a withdrawal taken during a downturn sells more units to raise the same cash, and those units are not there to recover. Losses early in a drawdown do permanent damage; the same losses later do far less.
This is sequence-of-returns risk, and no constant-rate projection can show it — including ours. A smooth curve at 5% a year is a way to compare scenarios against each other. It is not a forecast, and its confidence is an artefact of the arithmetic rather than a property of markets.
How we use the rate
Our Coast FIRE calculator takes the withdrawal rate as your input, not our recommendation. It uses it for exactly the conversion at the top of this page — spending into a target — and then discounts that target back to today. It defaults to 4% because that is the convention a reader will recognise, and the field is editable because the convention is contested.
Every figure on this page can be reproduced with a calculator, and the verification page shows how we check the ones the tool produces.
Common questions
- What is the 4% rule?
- A research finding, not a law. Bengen (1994) tested historical US market data and found that withdrawing 4% of a portfolio in the first year of retirement, then adjusting that amount for inflation each year, survived a 30-year retirement even in the worst historical starting years he examined. The Trinity Study (1998) tested success rates across a range of portfolio mixes and withdrawal rates and reached broadly similar territory.
- How do I turn a withdrawal rate into a savings target?
- Divide 100 by the rate to get the multiple of annual spending. At 4% that is 25 times; at 3.5% it is 28.57 times; at 3% it is 33.33 times. For $40,000 of annual spending: $1,000,000, $1,142,857.14 and $1,333,333.33 respectively.
- Why does dropping from 4% to 3% raise the target so much?
- Because the multiple is 1 ÷ rate, which is a hyperbola, not a line. Going from 4% to 3% adds 8.33 times your annual spending to the target — a 33.3% increase in capital for a one-point change in the rate. The same one-point move from 5% to 4% adds only 5 times. Small changes at the low end are expensive.
- Does the 4% rule work for a retirement longer than 30 years?
- It was not tested for one. Bengen studied 30-year windows. A 45-year retirement is a different question with more chances to encounter a bad sequence, and the research does not answer it. Anyone quoting 4% for an early retirement is extending a finding past the horizon it was measured over.
- What is sequence-of-returns risk?
- The order returns arrive in changes the outcome, even when the average is identical. Two portfolios drawing $40,000 a year from $1,000,000, given exactly the same ten annual returns in opposite orders — a 10% arithmetic mean either way — end $262,120.48 apart. A constant-rate projection cannot show this, which is the single biggest thing it hides.
- Does QuickOper recommend a withdrawal rate?
- No. The Coast FIRE calculator takes the rate as your input, uses it to convert spending into a target, and shows the arithmetic. Which rate is appropriate depends on your horizon, your portfolio, your tax position and your tolerance for running out — none of which a calculator knows.
Sources
- Bengen, W. (1994) — Determining Withdrawal Rates Using Historical Data — retrieved 2026-08-08
- Trinity Study (Cooley, Hubbard & Walz, 1998) — Retirement Savings — retrieved 2026-08-08
- The papers are cited for what they studied. Every number on this page is computed here — the multiples from 1 ÷ rate, and the sequence comparison from ten annual returns applied in both orders to a $1,000,000 portfolio drawing $40,000 a year. No figure is transcribed from either study.
Written and maintained by Vikash Singh. Last verified 2026-08-08.