The FIRE Math: Your Number and Timeline

Every FIRE plan rests on two numbers: the size of the portfolio you need, and how long it takes to build it. This chapter shows how both are computed, which assumptions drive them, and how much each assumption moves the answer. The arithmetic is simple. The judgement is in the inputs, and especially in the withdrawal rate, because a retirement that starts at 40 has to last much longer than the 30 years the classic research tested.

The number: spending divided by a withdrawal rate

Your FIRE number is your yearly spending divided by the share of the portfolio you plan to take out each year. At a 4% withdrawal rate it is 25 times spending. At 3.5% it is about 28.6 times; at 3% it is about 33.3 times.

The 4% figure comes from Bengen (1994), who tested a simple rule against US market history from 1926: withdraw a fixed share of the starting portfolio in year one, then raise that amount with inflation every year regardless of markets. Around 4% was the highest starting rate that lasted through every 30-year period he examined, for portfolios holding roughly half to three quarters in stocks. The Trinity study (Cooley, Hubbard and Walz, 1998) reached similar conclusions. Both are records of what happened, not forecasts, and both were built for 30-year retirements.

Here is a worked example. The card is computed by the engine behind the FIRE calculator.

Spending $60,000 a year at a 4.0% withdrawal rate gives a target of $1,500,000. Starting from $150,000 and adding $3,000 a month, the balance reaches it in about 21.2 years.

The timeline: savings plus growth, in today's dollars

The years come from adding monthly savings to a balance that compounds. Two details matter.

Work in real terms. The FIRE number is in today's dollars, so the growth rate must be too. The engine converts the 7.0% return before inflation to 3.9% after 3.0% inflation. Mixing a nominal return with a target in today's dollars is the most common spreadsheet error in FIRE planning: it makes the timeline look years shorter than it is.

Returns matter less than you might expect, but they still matter. Here is the same household if markets deliver less.

At 5.0% before inflation, growth after inflation falls to 1.9% and the timeline stretches to about 26.7 years. That is real, but it is not the dominant input. Early on, most of the balance is money you put in, not growth. Spending and the amount saved each month usually move the timeline more, which is why Chapter 3 is about savings rate.

How much the withdrawal rate matters

Choosing a withdrawal rate is choosing how much margin you carry. The same spending needs very different portfolios at different rates.

For $60,000 of spending, 4.0% needs $1,500,000, 3.5% needs $1,714,286, and 3.0% needs $2,000,000. Moving from the highest to the lowest rate adds $500,000, which at the savings in the first example is several more years of work. That is the cost of a safety margin, and whether it is worth paying depends on how long your retirement must last and how flexible your spending is.

Why a long retirement needs a lower rate

The classic studies tested 30 years. Someone who stops at 40 may need 50 or more. Longer periods give bad markets more chances to arrive and leave less room for the portfolio to recover. The engine below uses one steady return each year, which is a simplification (real markets do not move in a straight line), but it shows the effect of length on its own.

With $1,250,000, a first-year withdrawal of $50,000 raised with inflation, and a steady 6.0% return, the money lasts all 30 years (lasts: yes). Stretch the same plan to 50 years and it does not (lasts: no). On these assumptions the highest steady rate that survives 50 years is 3.7%, against 4.9% for 30 years.

This is why many early retirees plan around 3.25% to 3.5% rather than 4%, or plan to spend flexibly: cutting back after poor years, or earning a little. Neither choice is required. Each trades a larger target or a less predictable budget for a lower chance of running short.

A steady return also hides the biggest risk in early retirement: the order in which returns arrive. A crash in the first few years, while you are withdrawing, does far more damage than the same crash twenty years in. Chapter 8 covers this sequence-of-returns risk. To test it now, the safe withdrawal rate calculator checks one steady path, and the Monte Carlo simulator tests thousands of different orderings of returns.

What the basic number leaves out

The FIRE number is the first line of a budget, not the whole budget.

• Taxes. Withdrawals from traditional accounts are taxed as income; gains in a taxable account are taxed when you sell. Chapter 5 covers both.
• Health insurance before 65. If you leave work at 45, you need two decades of coverage before Medicare. Chapter 6 covers the costs and the subsidy rules.
• Social Security. A benefit that starts in your sixties lowers what the portfolio must supply later, but how much depends on your earnings record and when you claim. Chapter 8 returns to it.
• Lumpy spending. Cars, roofs, family events and medical bills do not arrive evenly. A budget built from twelve months of statements misses anything that happens less than once a year.