FIRE Calculator

Financial independence arrives when your investments can pay for your life: when taking a safe percentage of them each year covers everything you spend. This calculator works out the size of that pot, your FIRE number, and how many years of saving it takes to build it from your take-home pay, your spending and what you have already invested. The defaults describe someone of 30 who takes home 80,000, spends 40,000 and holds 50,000 in investments. At a 5 percent return after inflation and a 4 percent withdrawal rate they need 1,000,000, and they get there in 15.4 years, at 45.4.

How the target and the date are worked out

Two numbers decide the answer. The first is the target. If you can safely withdraw a share w of a portfolio each year, it pays for annual spending of E once it reaches

T = E ÷ w

which at 4 percent is 25 times a year's spending. The second is how quickly you close the gap. Whatever is left of take-home pay after spending, S, is invested at the end of each year, and everything already invested, P, grows at the real return r. After t years the balance is P(1 + r)^t + S((1 + r)^t − 1) ÷ r, and setting that equal to the target gives the years directly:

t = ln((T × r + S) ÷ (P × r + S)) ÷ ln(1 + r)

At a zero return the balance simply adds up, so the years are the gap divided by the yearly saving, (T − P) ÷ S. The formula reproduces the results of Networthify's early retirement calculator, which likewise treats income as after tax and the return as after taxes and inflation. Working after inflation puts every figure on the page in today's money: the 1,000,000 target buys what 1,000,000 buys now, and spending and saving are assumed to rise with prices. Saving once a year, at the end of it, is slightly cautious next to saving from every paycheck, so the answer errs late rather than early.

A worked example at the defaults

Taking home 80,000 and spending 40,000 leaves 40,000 to invest each year, a savings rate of 50 percent. The target is 40,000 ÷ 0.04 = 1,000,000. At 5 percent the 50,000 already invested earns 2,500 in its first year, so the bottom of the fraction is 2,500 + 40,000 = 42,500, while the top is 1,000,000 × 0.05 + 40,000 = 90,000. The ratio is 2.1176, its natural logarithm is 0.7503, and dividing by ln 1.05 = 0.04879 gives 15.4 years, which makes you 45.4.

Saving year by year confirms it. After 15 years the balance is 967,089, still short, and after 16 it is 1,055,443, past the target. Starting from nothing, the same saver would need 16.6 years, so the 50,000 head start is worth 1.2 years. Progress, the last line of the result, is the share of the target already invested: 5 percent here.

Why the savings rate matters more than the pay

Start from nothing and the pay drops out of the arithmetic. Someone who takes home 40,000 and spends 20,000 and someone who takes home 200,000 and spends 100,000 both save half of what they earn, both need 25 years of their own spending, and both get there in 16.6 years. What moves the answer is the share saved, because spending appears twice: spending less shrinks the target and raises the yearly saving at the same time. Cutting the default spending by 5,000, to 35,000, lowers the target to 875,000 and brings the date forward from 15.4 years to 12.8. Earning 5,000 more instead only takes it to 14.2.

That was the point of "The Shockingly Simple Math Behind Early Retirement", which Pete Adeney published on his Mr. Money Mustache blog on January 13, 2012. Assuming a 5 percent return after inflation, the 4 percent rule and a net worth of zero, it put a family that saves 10 percent of its take-home pay on track to work for 51 years, and said that raising the rate to 15 percent would let them retire 8 years earlier. This calculator gives 51.4 and 42.8 years for those two cases. The table under the result repeats the exercise for your own pay and investments, from saving a tenth of your pay to saving nine tenths, with your current rate in its place among them.

Where the idea came from

The arithmetic is older than the acronym. Joe Dominguez and Vicki Robin's Your Money or Your Life, published by Viking in 1992, grew out of the seminars the two had been giving. Its authors named the crossover point: the moment when income from invested savings, which they put into Treasury bonds, covers your reduced spending. That moment, they said, brings financial independence, and it is the event this calculator dates.

What the book did not supply was a withdrawal rate. That came from research into conventional retirement. William Bengen's 1994 paper in the Journal of Financial Planning found that taking 4 percent in the first year and raising the amount with inflation had not exhausted a portfolio in under 33 years from any historical starting year he tested, and the 1998 Trinity study by three Trinity University professors tested payout periods of 15 to 30 years. The retirement savings calculator covers both in more detail. Dividing by 4 percent is what turns a spending figure into a target.

Early retirement writers joined the two ideas. Jacob Lund Fisker's Early Retirement Extreme was a blog before it became a 2010 book, subtitled A philosophical and practical guide to financial independence. Adeney began full-time work in 1997, at 22, and by his own account had stopped in his early thirties after about nine years of saving; he started the Mr. Money Mustache blog in April 2011. His 2012 post took its chart from Networthify, whose results the method above reproduces.

Is 4 percent enough for a 50-year retirement?

Bengen and the Trinity professors asked whether money would last about 30 years, the length of a conventional retirement. Someone who stops at 45 may need it for 50. In December 2016 the economist who writes the Early Retirement Now blog began a long series on safe withdrawal rates by running the same kind of test on monthly US stock and Treasury returns going back to 1871. A 4 percent withdrawal from a portfolio split evenly between stocks and bonds survived 95 percent of 30-year periods but only 65 percent of 60-year ones, and his summary was that 3.5 percent is the new 4 percent.

The withdrawal rate field exists for that reason. At 3.5 percent the default target rises from 1,000,000 to 1,142,857, and the date moves from 15.4 years to 16.9. At 3 percent the target is 1,333,333 and the wait 18.9 years. A lower rate buys safety with time, and the trade is gentler than the bigger target suggests, because the extra years of saving and growth do much of the work.

Assumptions worth knowing

The return is held constant, and real markets are not. A crash in the first years after you stop work does far more damage than the same crash later, which is the sequence-of-returns risk the withdrawal studies measure and this projection does not. Spending is held flat too, so the target assumes retirement costs what working life does, the same assumption Networthify makes. Count taxes due on withdrawals, and anything an employer pays for you now, such as health insurance, as spending.

Take-home pay means pay after all taxes. Adeney's advice is to add back any 401(k) or other savings deductions to the paycheck you see, since that money is being saved. Pensions and Social Security are left out, so anyone entitled to them later needs less from the portfolio once they start. Spending more than you take home is allowed: the investments still reach the target if their growth outpaces the shortfall, and the page explains when they cannot. An answer of more than 100 years is refused rather than printed.

This is a planning projection, not financial advice; real returns, inflation, taxes and fees will move every figure here. See the site disclaimer.

Frequently asked questions

What is a FIRE number?

It is the amount you need invested before the portfolio can pay for your spending on its own: your annual spending divided by the withdrawal rate you plan to use. Under the 4 percent rule that is 25 times a year's spending, so spending 40,000 a year means a FIRE number of 1,000,000. Plan on a 3.5 percent withdrawal rate instead and the same spending needs 1,142,857.

How many years does it take to reach financial independence?

Mostly it depends on the share of your take-home pay you save. Starting from nothing, with a 5 percent return after inflation and a 4 percent withdrawal rate, saving 10 percent takes 51.4 years, 20 percent takes 36.7, 50 percent takes 16.6 and 70 percent takes 8.8. Money already invested shortens each of those: the default saver, with 50,000 invested and half of an 80,000 take-home pay saved, needs 15.4 years.

Is the 4 percent rule safe for early retirement?

It was tested on retirements of about 30 years, and an early retirement can last far longer. Working with US returns back to 1871, the Early Retirement Now blog found in 2016 that 4 percent withdrawals from a portfolio split evenly between stocks and bonds lasted through 95 percent of 30-year periods but only 65 percent of 60-year ones, and suggested 3.5 percent instead. At 3.5 percent the default plan needs 1,142,857 and 16.9 years rather than 1,000,000 and 15.4.

Should I enter my investment return before or after inflation?

After. Every figure on the page is in today's money, so the return has to be what your investments earn beyond inflation. To convert, divide 1 plus the expected return by 1 plus inflation and subtract 1: a 7 percent return with 2.5 percent inflation is about 4.39 percent after inflation. Entering 4.4 with the other defaults gives 16 years instead of 15.4.

What counts as take-home pay and savings?

Take-home pay is what you earn after all taxes. Retirement contributions taken out of your pay before it reaches you, such as 401(k) deferrals, are savings, so add them back to take-home pay, along with any employer match. Everything left after spending is treated as invested at the end of each year.

Does the calculator include Social Security, pensions or taxes in retirement?

No. It counts only the investments you build up. A pension or Social Security that starts later reduces how much the portfolio has to cover from then on, so the answer is cautious for anyone entitled to one. Taxes you will owe on withdrawals are not deducted either, so include them in your spending figure.

Sources

1. Determining Withdrawal Rates Using Historical Data, William P. Bengen, Journal of Financial Planning (FPA reprint), 1994
2. Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable, AAII Journal, 1998
3. The Shockingly Simple Math Behind Early Retirement, Mr. Money Mustache, 2012
4. The Ultimate Guide to Safe Withdrawal Rates – Part 1: Introduction, Early Retirement Now, 2016
5. Your Money or Your Life, Joe Dominguez and Vicki Robin, Viking, via Internet Archive, 1992