Math for MoneyWhat is a FIRE number?
FIRE stands for "financial independence, retire early". Your FIRE number is the amount of invested money at which a yearly withdrawal at your chosen rate equals what you spend in a year. It depends on only two things: how much you spend and the withdrawal rate you plan with. Your income matters only through how much of it you save.
How it's calculated
The target comes from one division:
FIRE number = Annual spending ÷ Withdrawal rate
With the example values, $40,000 ÷ 4% = $1,000,000.
To find the time, the calculator grows your portfolio one month at a time until it reaches that target:
Balance = Balance × (1 + monthly return) + Annual savings ÷ 12
The monthly return is (1 + annual return)1/12 − 1, so twelve months of growth equal the annual return exactly. Savings are added at the end of each month. The count stops in the first month the balance is at or above the FIRE number, or after 100 years if it never gets there.
The same answer can be written as one formula, where m is the monthly savings amount and i is the monthly return:
Months = ln[(FIRE number + m ÷ i) ÷ (Current savings + m ÷ i)] ÷ ln(1 + i)
Worked example with the starting values: m = $24,000 ÷ 12 = $2,000, and i = 1.051/12 − 1 ≈ 0.4074%. The formula gives 249.4 months, which rounds up to 250 whole months, or 20 years 10 months. At that point the balance is $1,003,828: $550,000 from your current savings and new contributions, and $453,828 from investment growth.
Choosing a withdrawal rate
The withdrawal rate is the share of your portfolio you plan to spend each year. 4% is a commonly used planning rule of thumb, and it is the same thing as saving 25 times your annual spending. It is a starting point for planning, not a guarantee that the money will last. That depends on future returns, inflation, how long you need the money for and how flexible your spending is, and none of those can be known in advance.
A lower rate asks for a larger portfolio and leaves more margin. A higher rate gets you there sooner with less margin. This table shows how the choice changes the result, with the multiple of annual spending in brackets, for the example values ($40,000 of annual spending, $50,000 saved, $24,000 added per year, 5% return):
| Withdrawal rate | FIRE number | Time to reach it |
|---|---|---|
| 3% (33.3×) | $1,333,333 | 24 yr 11 mo |
| 3.5% (28.6×) | $1,142,857 | 22 yr 8 mo |
| 4% (25×) | $1,000,000 | 20 yr 10 mo |
| 4.5% (22.2×) | $888,889 | 19 yr 3 mo |
| 5% (20×) | $800,000 | 17 yr 10 mo |
Keep everything in today's dollars
The calculator does not adjust for inflation on its own. The simplest way to get a meaningful answer is to enter your spending in today's dollars and a return after inflation, also called a real return. Then the FIRE number, the annual savings and every balance on this page are in today's purchasing power.
If you enter a return before inflation instead, the balances are counted in future dollars while your spending target is still in today's dollars, and the time to reach it will look shorter than it really is. To convert, use real return = (1 + return) ÷ (1 + inflation) − 1. As a purely hypothetical example, a 7% return with 2% inflation is a real return of about 4.9%.
What this calculator leaves out
- Changing returns. It applies the same return every year. Real portfolios rise and fall, and the order of good and bad years affects both how fast you get there and how long the money lasts.
- Taxes and fees. Neither is included. You can allow for fees by lowering the return you enter. The investment fee calculator shows how much a given fee costs over time.
- Other income. A pension, Social Security or part-time work reduces what the portfolio has to cover. Subtract your own estimate from annual spending.
- Changes in saving. Annual savings stay the same every year. If you expect to save more later, the real path will be faster than shown.
Related calculators
- Compound interest calculator: see how a balance and monthly contributions grow over a fixed number of years.
- Investment fee calculator: see how much an annual fee takes out of your ending balance.
Frequently asked questions
What is a FIRE number?
It is the amount of invested money at which a yearly withdrawal at your chosen rate equals your annual spending. The formula is annual spending divided by the withdrawal rate. For example, $40,000 a year at a 4% withdrawal rate gives a FIRE number of $1,000,000, which is 25 times annual spending.
Is a 4% withdrawal rate safe?
Nobody can promise that. 4% is a commonly used planning rule of thumb, not a guarantee. Whether a portfolio lasts depends on future returns, inflation, how many years you need it for and how much you can cut spending in bad years. If you want more margin, enter a lower rate: the FIRE number gets larger and the time to reach it gets longer. The calculator lets you change the rate so you can see that trade-off for your own numbers.
Should I enter my return before or after inflation?
After inflation, if you want the answer in today's dollars. Your spending target is entered in today's dollars, so the return should be a real (after-inflation) return to match it. If you enter a return before inflation, the balances are in future dollars and the time to reach your target will look shorter than it really is.
Why does the calculator say "Over 100 years"?
The calculator follows your portfolio for at most 100 years. If the balance has not reached your FIRE number by then, it says so instead of showing a very large number. This happens when savings and growth are too small compared with the target, for example with no new savings and a return of zero. Try a higher annual savings amount or lower annual spending to see what would change the result.
Does the result include taxes, fees, Social Security or a pension?
No. The calculation only uses the five numbers you enter. If you expect other income in retirement, such as a pension or Social Security, you can subtract your own estimate of it from the annual spending figure, because the portfolio only has to cover the rest. If withdrawals will be taxed, add your estimate of that tax to annual spending. To allow for fund fees, reduce the return you enter by the fee.
How do monthly contributions work if I enter an annual amount?
The annual savings figure is split into 12 equal amounts, one added at the end of each month. With the example value of $24,000 a year that is $2,000 a month. The return compounds annually, so the monthly growth rate is (1 + annual return) to the power of 1/12, minus 1.