Key takeaways
- How long money lasts depends on three numbers: the balance, the annual withdrawal, and the real (after-inflation) return.
- The formula is n = ln(1 ÷ (1 − r × P ÷ W)) ÷ ln(1 + r) — portfolio P, withdrawal W, real return r.
- If your withdrawal is less than the real return times the balance (W ≤ r × P), the money never runs out on paper.
- $1,000,000 spending $50,000 a year lasts 20 years at a 0% real return, 26 years at 2%, and 41 years at 4%.
- Every year of longevity you buy gets more expensive: going from 25 to 30 years costs far less than going from 30 to 35.
The formula
Start with a portfolio P, withdraw W at the end of each year, and earn a real return r on what is left. The number of years n before the balance hits zero is:
Everything is in today's dollars, so r is a real return — about 4% for a stock-heavy portfolio, about 2% for a balanced one, and 0% is a reasonable worst case for a very conservative one. Using real returns and a real withdrawal is what lets you ignore inflation in the rest of the arithmetic.
Worked, step by step
P = $1,000,000, W = $50,000, r = 4%:
- r × P = 0.04 × $1,000,000 = $40,000 — what the portfolio earns in year one.
- r × P ÷ W = $40,000 ÷ $50,000 = 0.8 — the share of the withdrawal that growth covers.
- 1 − 0.8 = 0.2 — the share that has to come out of principal.
- ln(1 ÷ 0.2) = ln(5) = 1.609; ln(1.04) = 0.0392.
- n = 1.609 ÷ 0.0392 = 41.0 years.
Step 2 is the one worth staring at. Only 20% of that $50,000 comes out of principal — which is why the balance lasts four decades rather than the twenty years a naive "$1m ÷ $50k" would suggest.
The table
| Annual withdrawal | Rate on $1m | 0% real | 2% real | 4% real | 6% real |
|---|---|---|---|---|---|
| $40,000 | 4.0% | 25.0 | 35.0 | Never | Never |
| $50,000 | 5.0% | 20.0 | 25.8 | 41.0 | Never |
| $60,000 | 6.0% | 16.7 | 20.5 | 28.0 | Never |
| $70,000 | 7.0% | 14.3 | 17.0 | 21.6 | 33.4 |
| $80,000 | 8.0% | 12.5 | 14.5 | 17.7 | 23.8 |
| $100,000 | 10.0% | 10.0 | 11.3 | 13.0 | 15.7 |
Read across any row and you see how much the return assumption is worth. Read down any column and you see how much the spending assumption is worth. In every case the spending column moves the answer more — which is the single most useful fact in retirement planning, because spending is the input you control.
The line where the money never runs out
Set W = r × P and the formula divides by zero: growth exactly covers the withdrawal and the balance never falls. That is the entire idea behind a "safe" withdrawal rate. At a 4% real return, withdrawing 4% is the boundary; at a 2% real return it is 2%.
So why does the 4% rule stop at 4% when stocks have historically returned more? Because real portfolios do not deliver a smooth real return. The rule's margin exists to survive the sequence of returns, not the average of them.
Why the average return misleads
This formula assumes the same return every year. Markets do not work that way, and when you are withdrawing, the order of returns changes the outcome even when the average is identical. Two retirees with the same average return can end up decades apart, because selling shares into a downturn permanently removes shares that would have participated in the recovery. That is sequence-of-returns risk, and it means the table above is a centre estimate, not a promise.
What the formula leaves out
- Social Security and pensions. Once they start, W falls sharply — often the single biggest improvement to the answer. Model the pre- and post-benefit phases separately rather than averaging them.
- Taxes. If the money sits in a traditional IRA, a $50,000 withdrawal is not $50,000 of spending. Use after-tax spending as W, or gross up the withdrawal — see which accounts to spend first.
- Required minimum distributions. From your RMD age onwards the IRS sets a floor on withdrawals from pre-tax accounts, whatever your plan says.
- Real spending patterns. Spending often falls in the middle years and rises again for healthcare late in retirement, rather than tracking inflation in a straight line.
Run it on your own balance
The retirement drawdown calculator applies exactly this arithmetic to your numbers, year by year, and the inflation impact calculator shows what a fixed withdrawal is worth after 20 or 30 years of price rises. If you are still building the balance, the compound growth calculator works the same maths in the other direction.
Frequently asked questions
How long will $1 million last in retirement?
At $40,000 a year it lasts 25 years with no real growth and never runs out at a 4% real return. At $60,000 a year it lasts about 17 years with no growth, 20 years at a 2% real return, and 28 years at 4%. The withdrawal amount matters more than the return.
What is the formula for how long savings will last?
n = ln(1 divided by (1 minus r times P divided by W)) divided by ln(1 plus r), where P is the balance, W is the annual withdrawal and r is the real return. If W is less than or equal to r times P the portfolio never depletes, because growth covers the whole withdrawal.
Should I use a real or a nominal return?
A real return, if your withdrawal is expressed in today's dollars — which is how people naturally think about spending. Mixing a nominal return with a real withdrawal is the most common error in these calculations and it overstates how long the money lasts by many years.
Does this account for market crashes?
No. The formula assumes a constant return, so it produces a central estimate. A poor sequence of returns in the first decade of withdrawals shortens the real answer, which is why plans add a cash buffer, flexible spending, or a lower starting withdrawal rate.
How does Social Security change the answer?
Dramatically, because it cuts the withdrawal the portfolio has to cover. A household spending $60,000 with a $30,000 benefit only needs $30,000 from savings, and halving the withdrawal typically more than doubles how long the balance lasts.
Stop guessing at the horizon
Planomy replaces the single-line formula with a full year-by-year projection: Social Security, taxes, required distributions and changing spending, all in one plan you can adjust and compare. Free, private, and running in your browser.