Quick Answer
Quick Answer: A 401(k) balance is calculated using the future value formula: FV = PV(1+r)n + PMT × [((1+r)n - 1) / r]. Starting with a $50,000 balance, contributing $20,500 per year with a $3,000 annual employer match at a 7% return for 25 years, the projected balance is approximately $1,757,724. The 2026 employee contribution limit is $24,500 per IRS Notice 2025-67. This page documents the complete math behind every number our calculator produces.
Run Your Own 401(k) ProjectionThe 401(k) Growth Formula in Plain English
When you contribute to a 401(k), your account balance grows from three distinct sources:
- Your existing balance grows through compound investment returns year after year
- Your new contributions grow as each year's deposit compounds for the remaining years until retirement
- Your employer's matching contributions grow in exactly the same way as your own contributions
Our 401(k) Calculator combines these three sources using two well-established financial formulas: the future value of a lump sum (for your existing balance) and the future value of an ordinary annuity (for ongoing contributions). Together, they project your total balance at retirement.
These formulas are standard in financial planning and are used by retirement plan providers including Fidelity(opens in new tab), Vanguard(opens in new tab), and the Federal Thrift Savings Plan (TSP)(opens in new tab). The mathematics dates back to the time-value-of-money principles formalized in the early 20th century.
The Mathematical Formula
Here is the exact formula used by our 401(k) Calculator to project your retirement balance. The total future value is the sum of three components:
FV = PV(1 + r)n + PMT × [((1 + r)n - 1) / r]
Where PMT represents the combined annual contribution from you and your employer. Our calculator tracks employee contributions and employer match separately using the same annuity formula for each, then sums the results:
FVtotal = FVbalance + FVemployee + FVmatch
This approach lets our calculator break down exactly how much of your future balance comes from your own contributions, your employer's match, and investment growth.
Our calculator uses annual compounding with end-of-year contributions (ordinary annuity). In practice, 401(k) contributions are deducted from each paycheck throughout the year. Annual compounding slightly underestimates growth compared to per-paycheck modeling, making our projections modestly conservative.
Variable Definitions
Each variable in the formula has a specific financial meaning. The table below defines every term with a concrete example.
| Variable | Meaning | How to Determine | Example Value |
|---|---|---|---|
| FV | Future value (projected balance at retirement) | Output of the formula | $1,757,724 |
| PV | Present value (current 401(k) balance) | Check your most recent account statement | $50,000 |
| PMT | Annual contribution amount | Salary × contribution percentage (employee and employer tracked separately) | $20,500 (employee) + $3,000 (match) |
| r | Annual rate of return (decimal) | Expected average annual return on your investment portfolio | 0.07 (7%) |
| n | Number of years until retirement | Target retirement age minus current age | 25 years |
| (1+r)n | Compound growth factor | Raise (1 + annual return) to the power of n | 1.0725 = 5.42743 |
The 7% default is a commonly used long-term estimate based on historical stock market performance. The S&P 500 has returned approximately 10% annually before inflation, or about 7% after inflation, over the past several decades. Your actual return depends on your asset allocation, fund selection, and market conditions. Conservative investors may want to use 5-6%; aggressive investors might use 8-10%.
Worked Example: $50,000 Balance Growing for 25 Years
This section walks through every arithmetic step of the 401(k) growth calculation. The scenario uses a 40-year-old earning $100,000 per year who plans to retire at 65.
Scenario Setup
| Input | Value |
|---|---|
| Current 401(k) balance | $50,000 |
| Annual salary | $100,000 |
| Employee contribution | $20,500 per year (20.5% of salary) |
| Employer match formula | 50% match up to 6% of salary |
| Expected annual return | 7% |
| Years until retirement | 25 |
Step 1: Calculate the Employer Match
The employer matches 50 cents for every dollar the employee contributes, up to 6% of salary. Since the employee is contributing 20.5% of salary (well above 6%), the full match is earned.
- Salary = $100,000
- Match limit = 6% of salary = $100,000 × 0.06 = $6,000 (maximum matchable contribution)
- Match rate = 50% of the matchable amount
- Annual employer match = $6,000 × 0.50 = $3,000
Step 2: Calculate the Compound Growth Factor
This factor determines how much a single dollar invested today will be worth after 25 years of 7% annual growth.
- (1 + r)n = (1 + 0.07)25
- = 1.0725
- = 5.42743
Step 3: Future Value of the Existing Balance
The $50,000 already in the account compounds for 25 years with no additional deposits.
- FVbalance = PV × (1 + r)n
- = $50,000 × 5.42743
- = $271,372
Your existing $50,000 grows to $271,372 without a single additional dollar contributed. This illustrates the power of compound growth: the account gains $221,372 in investment returns on the original $50,000.
Step 4: Calculate the Annuity Factor
The annuity factor determines the cumulative growth of a series of equal annual contributions. It is used for both employee contributions and employer match.
- Annuity factor = ((1 + r)n - 1) / r
- = (5.42743 - 1) / 0.07
- = 4.42743 / 0.07
- = 63.2490
Step 5: Future Value of Employee Contributions
Each year's $20,500 contribution earns returns for the remaining years. The first contribution compounds for 25 years, the second for 24 years, and so on. The annuity formula captures this entire series in a single calculation.
- FVemployee = PMTemployee × annuity factor
- = $20,500 × 63.2490
- = $1,296,605
You contribute $20,500 × 25 = $512,500 out of pocket over 25 years, but compound growth turns those contributions into $1,296,605. The investment returns on your contributions total $784,105.
Step 6: Future Value of Employer Match
The employer match follows exactly the same growth formula as your contributions.
- FVmatch = PMTmatch × annuity factor
- = $3,000 × 63.2490
- = $189,747
Your employer contributes $3,000 × 25 = $75,000 in total match dollars. Compound growth turns that into $189,747 -- an additional $114,747 in investment returns on the employer match alone.
Step 7: Sum All Components
- FVtotal = FVbalance + FVemployee + FVmatch
- = $271,372 + $1,296,605 + $189,747
- = $1,757,724
Where the Money Comes From
| Source | Amount Contributed | Future Value | % of Total |
|---|---|---|---|
| Starting balance growth | $50,000 | $271,372 | 15.4% |
| Employee contributions | $512,500 | $1,296,605 | 73.8% |
| Employer match | $75,000 | $189,747 | 10.8% |
| Total | $637,500 | $1,757,724 | 100% |
Investment growth accounts for $1,120,224 of the total -- 63.7% of the final balance comes from compound returns, not from money you or your employer put in. Values calculated using the standard future value formulas and verified against our 401(k) Calculator.
Verify This Projection With Our 401(k) CalculatorIRS 2026 Contribution Limits
The IRS sets annual limits on how much you can contribute to a 401(k) plan. These limits are adjusted annually for inflation. The following table reflects the 2026 limits per IRS Notice 2025-67(opens in new tab).
| Limit Type | 2026 Amount | 2025 Amount | Change |
|---|---|---|---|
| Employee contribution (under 50) | $24,500 | $23,500 | +$1,000 |
| Catch-up contribution (ages 50+) | +$8,000 (total: $32,500) | +$7,500 (total: $31,000) | +$500 |
| Super catch-up (ages 60-63, SECURE 2.0) | +$11,250 (total: $35,750) | +$11,250 (total: $34,750) | +$1,000 (base increase) |
| Total annual addition limit (IRC 415(c)) | $70,000 | $70,000 | $0 |
Source: IRS Notice 2025-67(opens in new tab). The total annual addition limit (Section 415(c)) includes employee deferrals, employer contributions, and forfeitures allocated to the participant's account.
How the Calculator Enforces Limits
Our calculator automatically caps your employee contribution at the applicable IRS limit based on your age:
- Under 50: Maximum employee deferral is $24,500 per year
- Ages 50-59 and 64+: Maximum is $32,500 (base $24,500 + $8,000 catch-up)
- Ages 60-63: Maximum is $35,750 (base $24,500 + $11,250 super catch-up under SECURE 2.0 Act(opens in new tab))
If your salary percentage input would exceed these limits, the calculator displays a warning and caps the contribution accordingly. Employer match amounts are not counted against the employee deferral limit -- they fall under the separate Section 415(c) total limit of $70,000.
Starting in 2025, workers aged 60 to 63 can contribute an additional $11,250 instead of the standard $8,000 catch-up. This enhanced limit applies only during this four-year window -- at age 64, you revert to the standard catch-up amount. Our calculator automatically applies the correct catch-up level based on your entered age.
How Employer Matching Formulas Work
Employer match is often described as "free money" -- and the math confirms it. Match formulas vary by employer, but they all follow the same basic structure: the employer contributes a percentage of what you contribute, up to a cap.
Common Match Formulas
| Match Formula | How It Works | Annual Match ($100K Salary) | 25-Year FV at 7% |
|---|---|---|---|
| 100% up to 3% | Dollar-for-dollar on first 3% of salary | $3,000 | $189,747 |
| 50% up to 6% | 50 cents per dollar on first 6% of salary | $3,000 | $189,747 |
| 100% up to 6% | Dollar-for-dollar on first 6% of salary | $6,000 | $379,494 |
| Dollar-for-dollar up to 4.5% | Full match on first 4.5% of salary | $4,500 | $284,621 |
| No match | Employer does not contribute | $0 | $0 |
Future values calculated using the ordinary annuity formula at 7% for 25 years. See our Employer Match by Company guide for specific employer programs.
The Match Calculation Formula
Our calculator determines the annual match using this formula:
Annual Match = Salary × min(Contribution%, Match Limit%) × Match Rate%
The min() function ensures that only the portion of your contribution up to the match limit earns a match. Contributing above the limit does not increase your match -- it only increases your own tax-advantaged savings.
Maximizing Your Match: A $3,000 Example
On a $100,000 salary with a "50% up to 6%" match formula:
- Match limit: 6% of $100,000 = $6,000 (maximum matchable contribution)
- If you contribute 3%: Match = $100,000 × 3% × 50% = $1,500 (leaving $1,500 on the table)
- If you contribute 6%+: Match = $100,000 × 6% × 50% = $3,000 (full match earned)
- If you contribute 10%: Match still = $100,000 × 6% × 50% = $3,000 (match caps at 6%)
The takeaway: contribute at least enough to earn the full match before allocating money to other savings vehicles. See our How to Maximize Your 401(k) Match guide for detailed strategies.
Vesting Schedules
Employer match contributions may be subject to a vesting schedule, which determines how much of the match you get to keep if you leave the company before a certain period.
| Vesting Type | Schedule | IRS Maximum |
|---|---|---|
| Immediate | 100% vested from day one | Allowed |
| Cliff vesting | 0% until a specific year, then 100% | Maximum 3 years |
| Graded vesting | Increases incrementally each year (e.g., 20% per year) | Must reach 100% by year 6 |
Vesting rules per U.S. Department of Labor ERISA guidance(opens in new tab). Your own contributions are always 100% vested immediately.
Our calculator assumes full vesting of all employer match contributions. If you are subject to a graded or cliff vesting schedule and may leave your employer before fully vesting, your actual match benefit could be lower than projected.
Tax-Deferred Growth: The 401(k) Advantage
One of the most significant benefits of a 401(k) is tax-deferred compounding. In a traditional 401(k), you do not pay taxes on contributions, investment gains, dividends, or interest until you withdraw the money in retirement. This means your full balance compounds year after year without being reduced by annual tax bills.
How Pre-Tax Contributions Work
When you contribute to a traditional 401(k), your contribution is deducted from your gross pay before federal income tax is calculated. This provides an immediate tax benefit:
- Annual salary: $100,000
- 401(k) contribution: $20,500
- Taxable income: $100,000 - $20,500 = $79,500
- At a 22% marginal tax rate, the tax savings is: $20,500 × 22% = $4,510
You effectively invest $20,500 but your take-home pay only decreases by approximately $15,990 due to the tax savings. The IRS effectively subsidizes a portion of your contribution up front.
Tax-Deferred vs. Taxable Compounding
In a taxable brokerage account, you owe taxes on dividends, interest, and realized capital gains each year. This annual tax drag reduces the amount that compounds. The following comparison illustrates the difference over 25 years.
| Factor | 401(k) Tax-Deferred | Taxable Account |
|---|---|---|
| Nominal return | 7% | 7% |
| Annual tax drag (22% bracket) | None (deferred) | ~1.54% effective drag |
| Effective annual return | 7.00% | ~5.46% |
| $20,500/year for 25 years | $1,296,605 | ~$1,060,127 |
| Tax-deferral advantage | ~$236,478 more in the 401(k) | |
Simplified comparison assuming 22% marginal tax rate on all investment income annually. Actual tax drag varies based on turnover, dividend yield, and holding periods. The 401(k) balance will be subject to income tax upon withdrawal, but the compounding advantage generally outweighs this, especially if your tax rate in retirement is lower than during your working years.
A Roth 401(k) reverses the tax timing: contributions are made with after-tax dollars, but withdrawals in retirement are completely tax-free. The compound growth math is identical, but the tax benefit occurs on the back end rather than the front end. See our Roth 401(k) vs Traditional 401(k) comparison for help choosing.
Inflation Adjustment: Nominal vs. Real Returns
Our calculator uses nominal returns (before adjusting for inflation) by default. A projected balance of $1,757,724 in 25 years will not buy as much as $1,757,724 today because of inflation. To understand your future balance in today's purchasing power, you need to convert nominal returns to real returns.
The Fisher Equation
The standard method for converting between nominal and real returns is the Fisher equation, named after economist Irving Fisher:
Real Return = ((1 + Nominal Return) / (1 + Inflation Rate)) - 1
Example: Converting 7% Nominal to Real Return
Using an assumed long-term inflation rate of 3% (approximately the historical average per Bureau of Labor Statistics CPI data(opens in new tab)):
- Nominal return = 7% (0.07)
- Inflation rate = 3% (0.03)
- Real return = (1.07 / 1.03) - 1
- = 1.03883 - 1
- = 0.03883 or approximately 3.88%
Impact on Your Projected Balance
Running the same projection at 3.88% real return instead of 7% nominal shows what your balance can buy in today's dollars:
| Metric | Nominal (7%) | Real (3.88%) |
|---|---|---|
| FV of $50,000 balance | $271,372 | $129,635 |
| FV of $20,500/yr contributions | $1,296,605 | $577,133 |
| FV of $3,000/yr match | $189,747 | $84,410 |
| Total projected balance | $1,757,724 | $791,178 |
Real return calculated using the Fisher equation with 3% inflation. This means your $1,757,724 nominal balance has approximately $791,178 in today's purchasing power. Both projections assume constant annual returns, which is a simplification -- actual returns vary year to year.
The 3% inflation assumption reflects historical averages, but actual inflation varies significantly from year to year. The Bureau of Labor Statistics(opens in new tab) reports the Consumer Price Index (CPI) monthly. Higher-than-expected inflation erodes purchasing power faster; lower inflation preserves it. Consider running projections with 2-4% inflation to see a range of outcomes.
How Contribution Timing Affects Growth
Our calculator models contributions as end-of-year deposits (ordinary annuity). In reality, 401(k) contributions are deducted from each paycheck throughout the year, meaning money enters the account gradually. This difference affects the projection in a predictable way.
| Timing Model | Description | 25-Year FV of $20,500/yr at 7% |
|---|---|---|
| End-of-year (our calculator) | Full contribution invested at year end | $1,296,605 |
| Mid-year approximation | Contribution invested at mid-year | ~$1,341,346 |
| Beginning-of-year (annuity due) | Full contribution invested at year start | $1,387,367 |
The annuity due value is calculated as the ordinary annuity value multiplied by (1+r). Mid-year approximation uses (1+r)0.5 adjustment. Our end-of-year model is the most conservative, underestimating the final balance by approximately 3-7% compared to actual paycheck-by-paycheck investing.
This conservative bias is intentional: it is better for a retirement projection to slightly underestimate your balance than to overstate it.
How Each Variable Affects Your Balance
Small changes in rate of return, contribution amount, or time horizon can produce dramatically different outcomes. This sensitivity analysis shows how much each variable moves the needle, using our worked example as the baseline ($50,000 balance, $20,500 contribution, $3,000 match, 7% return, 25 years).
| What Changes | Baseline | Revised | Projected Balance | Difference |
|---|---|---|---|---|
| Baseline scenario | -- | -- | $1,757,724 | -- |
| Return drops to 5% | 7% | 5% | $1,291,753 | -$465,971 |
| Return rises to 9% | 7% | 9% | $2,413,200 | +$655,476 |
| 5 fewer years (20 years) | 25 years | 20 years | $1,161,629 | -$596,095 |
| 5 more years (30 years) | 25 years | 30 years | $2,541,113 | +$783,389 |
| Max out at $24,500/yr | $20,500 | $24,500 | $2,010,737 | +$253,013 |
All scenarios hold other variables constant at baseline values. Values calculated using the same future value formulas documented above.
Time is the most powerful variable: 5 additional years of compounding adds $783,389, while increasing annual contributions by $4,000 adds $253,013. Starting early and maintaining consistent contributions typically matters more than chasing higher returns.
Data Sources and Methodology Notes
Our 401(k) Calculator uses the standard future value formula documented above. Here are the specific data sources and assumptions that inform our calculations and educational content.
IRS Contribution Limits
All 2026 contribution limits are sourced from IRS Notice 2025-67(opens in new tab). The IRS adjusts these limits annually based on cost-of-living increases per IRC Section 402(g) for employee deferrals and Section 415(c) for total annual additions.
SECURE 2.0 Act Provisions
The super catch-up contribution for ages 60-63 is authorized by SECURE 2.0 Act of 2022(opens in new tab) (Section 109), effective for tax years beginning after December 31, 2024.
Rate of Return Data
The 7% default return rate reflects the long-term inflation-adjusted average return of the U.S. stock market. According to historical data compiled by NYU Stern School of Business(opens in new tab), the S&P 500 has returned approximately 10% nominally (7% real) over the long term. Individual portfolio returns depend on asset allocation and fund selection.
Inflation Data
Inflation estimates reference the Bureau of Labor Statistics Consumer Price Index (CPI)(opens in new tab). The approximately 3% long-term average inflation rate is a commonly used planning assumption, though actual inflation varies significantly by period.
Calculator Assumptions and Limitations
- All calculations assume a constant annual rate of return. Actual returns vary year to year and may include negative years. Our projections show a smoothed average growth path
- Contributions are modeled as end-of-year deposits (ordinary annuity). Actual paycheck-by-paycheck investing produces slightly higher balances
- The calculator assumes a constant salary and contribution rate over the projection period. It does not model salary increases, which would increase both contributions and employer match over time
- Employer match is assumed to be fully vested. Participants subject to vesting schedules may receive less if they leave before full vesting
- The calculator does not account for fund expenses or management fees, which reduce net returns. A typical expense ratio of 0.1% to 1.0% reduces the effective return accordingly
- Calculations use pre-tax (traditional 401(k)) assumptions. Withdrawals in retirement will be subject to ordinary income tax. The calculator does not model after-tax withdrawal values
Frequently Asked Questions
How is 401(k) growth calculated?
401(k) growth is calculated using the future value formula with two components: the growth of your existing balance (FV = PV × (1+r)n) and the growth of ongoing contributions (FV = PMT × [((1+r)n - 1) / r]). PV is your current balance, PMT is your annual contribution plus employer match, r is the annual rate of return, and n is the number of years until retirement. For example, a $50,000 balance with $20,500 in annual contributions and a $3,000 employer match growing at 7% for 25 years reaches approximately $1,757,724.
What is the 401(k) contribution limit for 2026?
The 2026 401(k) employee contribution limit is $24,500, up from $23,500 in 2025. Workers aged 50 and older can contribute an additional $8,000 catch-up contribution for a total of $32,500. Under SECURE 2.0, workers aged 60 to 63 qualify for a super catch-up of $11,250 additional, bringing their total to $35,750. The total annual addition limit under IRC Section 415(c), including employer contributions, is $70,000. These limits are set by IRS Notice 2025-67(opens in new tab).
How does employer match work in a 401(k)?
An employer match is free money your employer contributes to your 401(k) based on your own contributions. A common formula is "50% match up to 6% of salary," which means for every dollar you contribute up to 6% of your salary, the employer adds 50 cents. On a $100,000 salary, contributing at least 6% ($6,000) earns a $3,000 match. If you contribute less than the match threshold, you leave free money on the table. Match amounts are not counted against your $24,500 employee contribution limit -- they fall under the separate Section 415(c) total limit(opens in new tab) of $70,000.
How does tax-deferred growth benefit a 401(k)?
Tax-deferred growth means you do not pay taxes on investment gains, dividends, or interest each year while the money remains in the account. In a taxable account earning 7% with a 22% marginal tax rate, your effective after-tax return is approximately 5.46%. Over 25 years, $20,500 per year at 7% tax-deferred grows to approximately $1,296,605, while the same amount at 5.46% in a taxable account grows to approximately $1,060,127 -- a difference of over $236,000 due solely to the tax-deferral advantage.
How do I convert nominal returns to real (inflation-adjusted) returns?
Use the Fisher equation: Real Return = ((1 + Nominal Return) / (1 + Inflation Rate)) - 1. With a 7% nominal return and 3% inflation, the real return is ((1.07) / (1.03)) - 1 = 0.0388 or approximately 3.88%. This means a projected $1,757,724 balance in 25 years has roughly $791,178 in purchasing power in today's dollars. Our calculator uses nominal returns by default, so applying the Fisher equation helps you understand what your future balance can actually buy.
Sources
- IRS -- 401(k) Contribution Limit Increases for 2026 (Notice 2025-67) (opens in new tab)
- IRS -- Retirement Topics: 401(k) Contribution Limits (opens in new tab)
- SECURE 2.0 Act of 2022 (H.R. 2954) (opens in new tab)
- U.S. Department of Labor -- Retirement Plans and ERISA FAQs (opens in new tab)
- Bureau of Labor Statistics -- Consumer Price Index (CPI) (opens in new tab)
- NYU Stern School of Business -- Historical Returns on Stocks, Bonds, and Bills (opens in new tab)
- Fidelity -- 401(k) Contributions Calculator (opens in new tab)
- Vanguard -- Retirement Income Calculator (opens in new tab)