How Much Do You Need to Retire? The Math, Step by Step

A retirement number is not one mystery figure. It is a chain of four small calculations: what you will spend, how much of that other income covers, how fast savings can be drawn down, and how long it takes to build the pile. Below, each link gets worked numbers you can change, a calculator joins them, and the 2026 limits¹ and rules sit where they matter. It is arithmetic, not advice: every figure is a worked example, and the inputs that decide the answer, spending and returns, are yours. The money section holds the formulas used here.

The retirement number in one line

The target is the yearly gap between spending and guaranteed income, divided by a withdrawal rate. Dividing by 4% is the same as multiplying by 25, so a $36,000 gap becomes $900,000 (our arithmetic, using the 4% rate of the Trinity study⁶). The 4% rate has a history: Cooley, Hubbard and Walz, known as the Trinity study, tested withdrawal rates from savings against rolling periods of U.S. market data⁶. Together with an earlier study, it was meant to dispel the notion that withdrawal rates like 6 percent or 7 percent are safe⁶.

1. Estimate yearly spending in today's dollars. Spending, not salary, sets the need; the next section shows why³.
2. Subtract income that does not come from savings. For most workers that is mainly Social Security, whose formula is worked out below³.
3. Divide the gap by a withdrawal rate. A classic finding uses 4% a year, adjusted for inflation, over 30 years⁶.
4. Compare the result with what your savings will grow to. The savings annuity formula does that, and the calculator below runs it⁷.

Step 1: spending, not salary

Replacement-rate rules such as “70% of your salary” hide a trap, because the share of pay that Social Security replaces falls as earnings rise: the replacement rate is 83% for very low earners and 37% for high earners³. A hypothetical medium earner in the Congressional Research Service example has average indexed monthly earnings of $4,618 and a primary insurance amount of $2,071.60³. Worked example (our arithmetic). Inputs³: 2,071.60 ÷ 4,618 = 0.449, so Social Security replaces about 45% of that worker’s average indexed earnings³.

Because the share differs by person, the lowest-error starting point is the yearly spending you expect, written in today’s dollars. The rest of this page uses $60,000 a year as an illustration, with $2,000 a month ($24,000 a year) coming from Social Security. Those two inputs are assumptions chosen for the example, and the calculator lets you replace them³.

Step 2: how Social Security is calculated

Social Security turns your work history into a monthly benefit in two steps. First comes average indexed monthly earnings, AIME: for retired workers it is the average of the highest 35 years of indexed earnings, divided by 12³. If the person worked fewer than 35 years in covered employment, the missing years count as zeros³. A worker is first eligible for retirement benefits at 62 and must generally have worked for 10 years³.

Second comes the primary insurance amount, PIA, the benefit at full retirement age. The AIME is cut into three brackets at two dollar amounts called bend points, which are $1,286 and $7,749 for workers who become eligible in 2026⁴. Three factors fixed in law, 90%, 32% and 15%, apply to the three brackets³. The PIA is rounded down to the nearest dime³.

Worked example (our arithmetic). Inputs: an AIME of $5,000 (an illustration, not an average). Bend points⁴ and factors³ as above.

The formula is progressive, which is why the share returned shrinks as earnings rise (shares computed by us, our arithmetic).

The claiming age changes the check

For workers born in 1960 or later the full retirement age is 67³. A claim before it carries a permanent reduction of five-ninths of 1% a month for the first three years and five-twelfths of 1% a month beyond that³. Claiming after it earns a delayed retirement credit of 8% for each year, up to age 70³. In the Congressional Research Service table the PIA share is 70.0% at 62, 86.6% at 65, 100.0% at 67 and 124.0% at 70³.

Worked example (our arithmetic). Inputs: the $2,345.80 PIA above and the shares³. Benefits round down to the dollar and exclude later cost-of-living adjustments³.

Cost-of-living adjustments come on top: the most recent was 2.8%, paid in January 2026³⁴.

What earnings produce a $3,000 monthly check?

Run the formula backwards. To reach a PIA of $3,000 at full retirement age, the AIME must fall in the middle bracket, so $3,000 = 1,157.40 + 0.32 × (AIME − 1,286). That gives an AIME of about $7,045 a month (our arithmetic)³⁴.

Worked example (our arithmetic). Inputs: the 2026 bend points⁴, the factors and claiming shares³; benefit before cost-of-living adjustments.

The yearly column is the indexed 35-year average, set against the 2026 taxable maximum of $184,500, above which earnings are not counted³⁴. Waiting from 62 to 70 cuts the needed history by almost two thirds (our arithmetic).

Step 3: the withdrawal rate

A withdrawal rate is the share of the starting balance taken out in the first year, then raised with inflation. A classic finding from the Trinity study is the case of an inflation-adjusted 4 percent withdrawal rate over a 30-year retirement horizon with a fixed 50/50 strategic asset allocation of stocks and bonds⁶. In rolling periods of the historical data, that strategy had a 96 percent success rate⁶. The count behind the 96 is 55 starting years from 1926 to 1980, of which the 4 percent rate failed twice, in 1965 and 1966, so the success rate is 53/55 = 96.4 percent⁶.

Success is not a guarantee. At a 5 percent rate, 17 of the 55 retirement dates fell short, which leaves a 69 percent success rate⁶. The data are one country’s: for 30-year retirements, the 4 percent rule failed in 62.5 percent of the historical cases in Italy and in 42.5 percent of the historical cases in France⁶. The paper warns that retirees who think of 4 percent as a worst-case rate will be ill-prepared for the spending cuts that flexibility may entail⁶. Its author argues that conservative retirees should adjust forecasts for future returns downward, which implies lower sustainable withdrawal rates⁶. The paper dates from May 26, 2011, so newer research may differ⁶.

Worked example (our arithmetic). The target for a yearly gap at three withdrawal rates, from the formula target = gap ÷ rate. The 4% and 5% rates are the two rates tested in the study⁶; 3% is a more cautious illustration.

Payout annuity math is a different question

A payout annuity starts with money in the account and takes money out on a regular basis, with the remaining money earning interest, until after a fixed amount of time the account is empty⁸. Payout annuities are typically used after retirement⁸. With P as the starting balance, w the regular withdrawal and r the annual rate, the textbook formula is P = w × (1 − (1 + r/k)^(−kt)) ÷ (r/k)⁸. In a textbook example, $1000 a month for 20 years at 6% interest needs $139,600 in the account⁸.

Worked example (our arithmetic). Inputs: $36,000 a year for 30 years, yearly withdrawals, a constant rate. Payout formula⁸.

These totals sit below $900,000 because the formula fixes the return and the payment. The Trinity method instead replays real market sequences with inflation-adjusted withdrawals, the harder question⁶. The two answers measure different risks, so the gap between them is the price of not knowing returns in advance.

Step 4: building the pile

Most retirement plans like 401k plans or IRA plans are examples of savings annuities⁷. In the annuity formula, A is the balance after t years, d is the regular deposit, r is the annual interest rate in decimal form and k is the number of compounding periods in one year⁷: A = d × ((1 + r/k)^(tk) − 1) ÷ (r/k). The textbook case is $100 a month into an IRA earning 6% for 20 years, which grows to $46,200 from $24,000 of deposits⁷.

Worked example (our arithmetic). Solve the formula for the deposit d. Inputs: a $900,000 target (the 4% example above), monthly deposits, the rates in the first row. Savings annuity formula⁷.

Ten extra years cut the monthly amount by about half at 6% (our arithmetic). That is the compounding in the Rule of 72: at 6% money doubles roughly every 12 years, so more doublings carry the load⁷.

The textbook’s own goal example, $200,000 in 30 years at 8%, needs a deposit of $134.09 a month⁷. Using the unrounded monthly rate gives $134.20; the textbook rounds the rate to 1.00667 along the way (our arithmetic).

What you may put in during 2026

The IRS announced the 2026 limits on November 13, 2025¹. The annual limit for 401(k), 403(b), governmental 457 and Thrift Savings Plan participants rose to $24,500 from $23,500¹. The limit on annual IRA contributions rose to $7,500 from $7,000¹. These limits are reset by the IRS each year, so a later year will differ.

Worked example (our arithmetic). Inputs: deposits at the 2026 limits for a worker under 50, held fixed for 30 years at a 6% return with monthly deposits. 2026 limits¹, savings annuity formula⁷.

Limits cap the pace of saving, not the amount that is needed. Most retirement plan distributions are subject to income tax², so a balance and the spendable income it supports differ by the tax owed.

Try your own numbers

Worked example (our arithmetic). The defaults above, which are assumptions and not forecasts. Inflation of 2% is the Federal Reserve’s longer-run goal¹⁰; 4% is the withdrawal rate of the Trinity example⁶; the savings formula is the annuity formula⁷.

Inflation changes the answer

The Federal Reserve judges that inflation of 2 percent over the longer run, measured by the annual change in the price index for personal consumption expenditures, is most consistent with its mandate for maximum employment and price stability¹⁰. At 2% a year, $60,000 of today’s spending costs 60,000 × 1.02^30 = $108,682 in 30 years, and a dollar then buys about 55 cents of today’s goods (our arithmetic)¹⁰. That is why this page works in today’s dollars and cuts the return by inflation.

Fees work the same way as a lower return. Even small differences in fees can translate into large differences in returns over time, and a fund with high costs must perform better than a low-cost fund to generate the same returns¹¹. The Rule of 72 shows the size of a 1% fee: at 6% money doubles every 12 years instead of every 10.3 years at 7%¹¹.

Can I retire at 62 with $400,000?

Run the same chain with a smaller pile. The only free input is spending, so the table shows the withdrawal rate each spending level would need. Worked example (our arithmetic). Inputs: a $400,000 balance; an illustrative AIME of $5,000, a 70% benefit at 62³, and the PIA computed earlier, giving $1,642 a month, or $19,704 a year.

Compare each rate with the historical record: the 4 percent rate had a 96 percent success rate over 30 years, and 5 percent a 69 percent success rate⁶. A retirement that starts at 62 and lasts to 92 is that 30-year window. Two dates matter besides the arithmetic. A claim at 62 locks in the reduced check for life³, and Medicare Part A and Part B are available from age 65, so health insurance for the first three years sits outside the table⁹.

Can I retire at 40 with $2 million?

Four percent of $2,000,000 is $80,000 a year (our arithmetic). The catch is the length. The Trinity time horizons were 15, 20, 25 and 30 years⁶. Retiring at 40 asks for 50 years or more, which that evidence does not cover.

For a horizon that long, the payout annuity formula shows how sensitive the answer is to the real return, the return after inflation⁸. Worked example (our arithmetic). Inputs: a $2,000,000 start and $80,000 withdrawn each year, with the number of years from the payoff formula on the loan payoff page, n = −ln(1 − P×i/PMT) ÷ ln(1 + i).

Three rules sit in the gaps of that timeline. Withdrawals from an IRA or retirement plan before age 59½ are early distributions, and an additional 10% tax applies unless an exception does². One exception is a series of substantially equal payments². Medicare is 25 years away at 65 (our arithmetic)⁹. And Social Security is first available at 62, 22 years out (our arithmetic)³.

Work history matters too. Worked example (our arithmetic). Inputs: a wage-indexed $80,000 a year, the 2026 bend points⁴ and the rule that missing years count as zero³.

Because fewer than 35 years count as zeros³, 18 years of work earns a PIA that is 64% of the 35-year figure (our arithmetic).

What typical savings look like

The Federal Reserve’s 2022 Survey of Consumer Finances counts retirement accounts such as individual retirement accounts and employer-sponsored accounts like 401(k), 403(b) and thrift savings accounts⁵. Such accounts were held by 54.3 percent of families in 2022⁵. Among those holding them, the conditional median value was $86,900 and the conditional mean $334,000⁵.

The mean sits far above the median because a few large balances pull it up. A $1,000,000 balance is above the mean of every group in the table, including the top decile (our arithmetic)⁵. The survey reports figures for 2022, and balances move with markets.

Mistakes that spoil the number

• Mixing nominal and real dollars. A target in today’s dollars needs a return after inflation¹⁰.
• Treating 4% as a promise. It is a historical success rate, and in other countries it failed far more often⁶.
• Counting Social Security from the wrong age. A claim at 62 pays 70% of the full amount³.
• Forgetting the zero years. Fewer than 35 years of work average in zeros³.
• Forgetting tax. Most retirement plan distributions are subject to income tax².
• Using the 2026 limits for later years. The IRS resets them annually¹.

Next steps

Write down three numbers: yearly spending in today’s dollars, the Social Security estimate from your own statement, and a withdrawal rate you would test, then run them through the calculator above with two different returns. The growth side of the math is in the Rule of 72 and the compound interest formula; the payoff arithmetic is on the loan payoff page. For primary sources, see the IRS’s 2026 limits announcement, the Congressional Research Service’s benefit calculation overview and the Federal Reserve’s Survey of Consumer Finances report.