Investing & retirement · Calculation notebook

401(k) vs Roth IRA calculator: formulas, examples and mathematical principles

Learn the inputs, formula and worked example behind the 401(k) vs Roth IRA calculator, including geometric growth and a stream of contributions, result interpretation, assumptions and sources.

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Purpose and steps

Project each balance with annual compounding. The pre-tax 401(k) includes the entered employer match and is reduced by the retirement tax rate; the Roth contribution uses the same employee out-of-pocket amount after the current tax rate. The calculation runs locally and keeps cash-flow timing consistent with the stated assumptions.

  1. Confirm currency and monthly versus annual amounts. U.S. tax and loan models should be used within their stated scope.
  2. Prepare Annual salary, Employee contribution rate, Employer match / salary, Current pre-tax 401(k) balance, Current Roth IRA balance, Expected annual return, Years until retirement, Current marginal tax rate, Retirement tax rate. Defaults demonstrate the model rather than your personal circumstances.
  3. Check the headline result and its components. A key interpretation for this tool is: A positive difference favors the modeled after-tax 401(k) value; a negative result favors the modeled Roth value.
  4. Compare the baseline with a changed scenario: Employer match, eligibility, contribution limits, withdrawal rules, and taxes can change the real decision.

Input reference and units

These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.

On a small screen, swipe the table horizontally to see all columns.

Parameters used by this calculator
ParameterDemonstration valueHow to enter it
Annual salary75000 USDUse dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars.
Employee contribution rate10 %Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal.
Employer match / salary3 %Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal.
Current pre-tax 401(k) balance0 USDUse dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars.
Current Roth IRA balance0 USDUse dollars and the monthly or annual period stated in the field label; do not enter thousands of dollars.
Expected annual return7 %A scenario assumption, not a promised investment yield; also test a lower return.
Years until retirement30 yearsUse years here. The model converts to months when the payment schedule requires it.
Current marginal tax rate24 %Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal.
Retirement tax rate22 %Enter a percentage such as 6.5, not 0.065. The equation converts it to a decimal.

Model-specific method

How this calculator produces its result

Project each balance with annual compounding. The pre-tax 401(k) includes the entered employer match and is reduced by the retirement tax rate; the Roth contribution uses the same employee out-of-pocket amount after the current tax rate.

Geometric growth and a stream of contributions

Compound growth multiplies the previous balance, including earlier interest, by the next period’s growth factor. The contribution term is another geometric sum: the first deposit compounds for longer than the last. It applies only to equal deposits and a constant rate; growing contributions require a different sum or period-by-period simulation.

A nominal rate compounded m times per year has effective annual growth (1+j/m)^m−1. An already effective annual return converts to a monthly rate as (1+g)^(1/12)−1. These are different conventions, so use the one specified by the tool. A constant return model says nothing about volatility or sequence-of-returns risk.

FV = P(1+r)^n
FV of end-period deposits = C × ((1+r)^n − 1)/r
Beginning-period deposits multiply the deposit term by (1+r)
  • P: initial amount
  • C: equal contribution per period
  • r: growth rate for that period
  • n: periods, with contributions and growth on the same schedule

Worked example

At $75,000 salary and a 10% contribution, the employee directs $7,500 before tax. At a 24% current tax rate, the matched out-of-pocket Roth comparison contributes $5,700 per year.

Reproduce the default scenario

This is a separate example, calculated using the exact engine on the tool page and the defaults in the input reference above. Health examples use metric units. Displayed rounding may differ from intermediate precision.

Estimated after-tax value difference (401(k) − Roth)
179,947.8 USD
401(k) value before retirement tax
920,992.67 USD
401(k) estimated after-tax value
718,374.28 USD
Roth IRA estimated value
538,426.48 USD
Annual pre-tax 401(k) contribution
9,750 USD
Annual after-tax Roth contribution
5,700 USD
Estimated retirement tax on 401(k)
202,618.39 USD

Reading results without overstating them

  • A positive difference favors the modeled after-tax 401(k) value; a negative result favors the modeled Roth value.
  • Employer match, eligibility, contribution limits, withdrawal rules, and taxes can change the real decision.

Assumptions and exclusions

  • This is a simplified tax-rate comparison, not account-eligibility or tax advice. It does not enforce annual IRA/401(k) limits, income phase-outs, vesting, fees, early-withdrawal rules, or required distributions.
Test a changed assumption in the calculator

Sources and content notes

Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.

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