FIRE calculator

What is a FIRE number and how is it calculated?

FIRE stands for financial independence, retire early. Your FIRE number, or FI number, is the size of portfolio that could pay your yearly spending at the withdrawal rate you pick. The formula is one line: FI number = (yearly spending - other retirement income) / withdrawal rate.

With the default inputs, $40,000 of spending at a 4% withdrawal rate gives $40,000 / 0.04 = $1,000,000. Dividing by 4% is the same as multiplying by 25, which is why the 4% version is often called the 25x rule. At 3.5% the multiple is 28.57, and at 3% it is 33.33.

If part of your spending will come from elsewhere, such as a pension or rent, enter it under Other income and timing. Only the gap has to come from the portfolio, so $40,000 of spending with $10,000 of other income needs a portfolio that pays $30,000, or $750,000 at 4%.

How many years until I reach financial independence?

The calculator starts from the savings you already have invested, grows them at the real return you assume, and adds your yearly investment. It credits growth once a year and adds the yearly amount at the end of each year unless you choose the start. The answer is the first whole year in which the balance reaches the FI number.

On the defaults, $50,000 invested today plus $20,000 a year at an assumed 5% real return first passes $1,000,000 in year 24, when the balance is $1,051,295. Over those 24 years you put in $480,000 and growth adds $521,295, so growth makes up just under half of the final balance. Investing at the start of each year instead gives every payment one more year of growth and brings the finish forward to year 23.

If the balance never gets there within 100 years, the page says so and shows how far it got. That happens when nothing is invested each year and the return is zero, or when the number is very large compared with the yearly amount.

Which withdrawal rate: 3%, 4% or 5%?

The withdrawal rate is the single assumption that moves the FI number most. A 4% rate is a widely used rule of thumb in FIRE planning, and many people test 3% or 3.5% as well. No rate is right for everyone: the calculator treats it as an input you choose and shows the arithmetic of each choice, nothing more.

Here is the default plan, $40,000 a year of spending with $50,000 saved and $20,000 invested a year at an assumed 5% real return, with only the rate changed:

Going from 4% to 3% adds a third to the number but only four years to the wait, because the extra money is reached when the balance is already large and growing fastest. How a portfolio behaves once you start drawing from it is a separate question, covered by the safe withdrawal rate calculator listed below.

Why does the calculator use a real return?

A real return is the growth left after inflation. Using it keeps every figure in today's money: the $40,000 of spending means $40,000 of today's buying power in year 24, and the FI number is in the same terms. If you entered a nominal return instead, the balance would look larger in future dollars while the spending stayed at today's price, and the finish line would arrive too early.

To turn a nominal assumption into a real one, divide rather than subtract: (1 + nominal) / (1 + inflation) - 1. An assumed 7% nominal return with 2% inflation is 1.07 / 1.02 - 1 = 4.90% real. Subtracting gives 5%, close at low rates but further off as rates rise. Either way the return is an assumption you enter; returns on real portfolios vary from year to year and can be negative.

How each input changes your FIRE date

Holding the other defaults fixed, here is what one input at a time does to the years needed to reach $1,000,000:

• Assumed real return. At 0% it takes 48 years, because only contributions build the pot. At 3% it takes 29 years, at 5% it takes 24, and at 7% it takes 20.
• Yearly investment. $10,000 a year takes 33 years, $20,000 takes 24 and $30,000 takes 19. The first extra $10,000 saves more years than the second.
• Spending. Spending is counted twice: it sets the number, and in real life it limits what you can invest. At $30,000 the number falls to $750,000 and is reached in year 20; at $60,000 it rises to $1,500,000 and takes 30 years.
• Savings today. A larger starting sum shortens the path, but with no yearly investment at all, $50,000 growing at 5% would need more than 61 years to become $1,000,000.

The years figure is always a whole number, since the calculator checks the balance once a year.

FIRE examples in pounds and dirhams

The arithmetic is the same in every currency, and the calculator never converts between them.

United Kingdom. A 35-year-old who wants £30,000 a year and plans around a 3.5% withdrawal rate has a FI number of £857,143. With £80,000 already invested and £15,000 a year added at an assumed 4% real return, the balance first passes that number in year 26, at age 61. Using 3% instead makes the number £1,000,000 and the wait 29 years; using 4% makes it £750,000 and 24 years.

United Arab Emirates. A 40-year-old planning to spend AED 240,000 a year, with AED 60,000 a year expected from other income, needs the portfolio to cover AED 180,000. At a 4% rate the FI number is AED 4,500,000. From AED 600,000 invested plus AED 120,000 a year at an assumed 5% real return, it is reached in year 18, at age 58.

Tax treatment of retirement savings differs between these countries and is not modeled here; the figures are before any tax on growth or withdrawals.

How to calculate a FIRE number in Excel

The FI number needs no function: in any cell, divide yearly spending by the withdrawal rate, for example =40000/0.04.

For the time to get there, Excel's NPER function returns the number of periods for a rate, a payment, a present value and a future value: =NPER(0.05, -20000, -50000, 1000000) gives 23.26 years for the default plan. Money you put in is entered as negative. Add 1 as a fifth argument for payments at the start of each year, which gives 22.66.

NPER answers with a fraction of a year because it assumes the balance can be checked at any moment. This calculator counts whole years, so 23.26 becomes year 24, the first year-end at which the balance is actually above the number.

Lean FIRE, fat FIRE and coast FIRE

These are labels for the same arithmetic with different inputs. Lean FIRE means planning around low spending, which shrinks the number and the wait. Fat FIRE means planning around generous spending, often with a lower withdrawal rate as well, which raises both.

Coast FIRE asks a different question: how much do you need invested today so that, with no further contributions, growth alone reaches the FI number by a chosen age? The answer is the FI number divided by (1 + real return) to the power of the years left. At an assumed 5% real return, reaching $1,000,000 in 30 years needs $231,377 invested today; in 25 years it needs $295,303. To try it here, set the yearly investment to zero and adjust the savings until the finish lands on the age you want.

What this calculator leaves out, and common mistakes

It is arithmetic on a fixed real return, a fixed yearly investment and level spending. Real returns arrive unevenly, and a run of poor years just before or after you stop working can matter more than the average. It ignores tax on growth and withdrawals, account and fund charges, the age at which pensions or social security start, and any change in spending over a retirement that could last 40 years or more. Treat the result as a scenario to test, not a date anyone can promise.

• Mixing nominal and real. A nominal return against spending in today's money makes the plan look shorter than it is.
• Using take-home pay as spending. The FI number rests on what you spend, not what you earn.
• Forgetting costs that change. Health cover, housing and family costs can rise or fall once work stops.
• Leaving out other income. A pension that starts later still reduces what the portfolio must cover from that point.
• Reading the withdrawal rate as a promise. It is a planning assumption, and the same rate can last very different lengths of time in different markets.

Glossary

FI number: the portfolio that pays your yearly spending at your chosen withdrawal rate. Withdrawal rate: the first year's withdrawal as a share of the portfolio. Real return: growth after inflation, which keeps amounts in today's money. 25x rule: spending multiplied by 25, the same as dividing by 4%. Coast FIRE: having enough invested that growth alone could reach the FI number by a set age. Lean and fat FIRE: plans built on lower or higher spending.

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