Traditional versus Roth

Traditional versus Roth

Traditional versus Roth: How It Works

What it does

U.S. retirement accounts come in two tax designs. In a Traditional account the contribution is deducted from income, so it goes in untaxed; it grows untaxed, and the whole withdrawal is taxed as ordinary income. In a Roth account the contribution is not deducted, so tax is paid on it first; it grows untaxed, and a qualified withdrawal is tax free. The page takes one amount, a return, a number of years and two tax rates that you enter, and works out what each design leaves after tax, the difference, and the retirement tax rate at which the two are equal. Every step is printed as formula, numbers put in, answer. It is an illustration, not tax advice.

The rules used

The page applies general U.S. federal rules as described in two Internal Revenue Service publications for 2025 returns. It uses these statements and no others:

Publication 590-A, Contributions to Individual Retirement Arrangements (IRAs): contributions to a Roth IRA cannot be deducted, unlike those to a Traditional IRA, and qualified distributions from it are tax free (chapter 2, "What Is a Roth IRA?"). An amount converted from a Traditional IRA to a Roth IRA is included in gross income and taxed as ordinary income; the 10% additional tax on early distributions does not apply to the amount converted, but an amount withdrawn and kept instead of converted is generally taxable and may be subject to it (chapter 1, "Converting From Any Traditional IRA Into a Roth IRA").

Publication 590-B, Distributions from Individual Retirement Arrangements (IRAs): when only deductible contributions were made, distributions from a Traditional IRA are fully taxable, as ordinary income (chapter 1, "Are Distributions Taxable?"). Distributions before age 59½ are early distributions and are generally subject to a 10% additional tax on the part included in income, with a list of exceptions (chapter 1, "Early Distributions"). A qualified Roth distribution is one made after the five-year period that begins with the first year a Roth contribution was made and, in general, on or after age 59½ (chapter 2, "What Are Qualified Distributions?"). In a Roth distribution that is not qualified, regular contributions come out first and are not taxed, then conversion amounts, then earnings; the earnings are taxable and may carry the additional tax, and so does a converted amount withdrawn within five years of its conversion (chapter 2, "Additional Tax on Early Distributions" and "Ordering Rules for Distributions").

Tax rates, contribution limits and income limits are not taken from these publications. The two tax rates are your entries. The yearly limits on how much may be contributed, on who may contribute to a Roth IRA and on who may deduct a Traditional IRA contribution change every year and are not checked; Publication 590-A prints the current ones.

The method

Symbols. C₀ is the amount; N the whole years to withdrawal; r the yearly return; t_n the tax rate now; t_r the tax rate in retirement. Rates are used as decimals: 22 % is 0.22. F = (1 + r)^N is what 1 contributed today grows to.

Same amount before tax (Simple mode). C₀ is pay set aside before income tax.

Traditional = C₀ · F · (1 − t_r)     Roth = C₀ · (1 − t_n) · F

Both are a product of the same amount, the same growth and one "keep" factor for tax. Because a product does not depend on the order of its factors, taxing before the growth or after it makes no difference in itself. Dividing, Traditional / Roth = (1 − t_r) / (1 − t_n): the return and the years cancel, and the two are equal exactly when t_r = t_n. The break-even retirement tax rate is therefore t_n. Difference = Traditional − Roth, also shown as a percent of the Roth result.

Same dollars in each (Advanced). If the same C₀ dollars go into either account, the Traditional deduction lowers this year's tax by C₀ t_n, and the comparison is fair only if that saving is invested too. It goes into an ordinary taxable account where a share d_x of each year's return is lost to tax, so it grows at r_s = r (1 − d_x):

Traditional = C₀ F (1 − t_r) + C₀ t_n (1 + r_s)^N     Roth = C₀ F

Break-even: t_r = t_n (1 + r_s)^N / F, which is below t_n whenever there is a drag. In before-tax terms a Roth dollar is a larger contribution than a Traditional dollar, which is why the largest allowed contribution shelters more in a Roth account.

Employer match. A match M_m is treated as untaxed money that is taxed when withdrawn: it adds M_m F (1 − t_r) to both results and leaves their difference unchanged.

Contribution every year. Contributions are made at the start of each year, the first today, each (1 + g_c) times the one before. The contribution of year k grows for N − k years, and the sum over the N years replaces F:

F = (1 + r) [(1 + r)^N − (1 + g_c)^N] / (r − g_c),   or N (1 + r)^N when g_c = r.

The same formulas then hold with this F (and, for the taxable account, the same expression at r_s). The tax rate now is taken to be the same in every contribution year.

Early withdrawal. With an additional tax rate p_x entered, the withdrawal is treated as early. Traditional keeps (1 − t_r − p_x) of the withdrawal. The Roth contributions come out untaxed; the earnings E = C_roth F − contributions are taxed: Roth = C_roth F − E (t_r + p_x). Both results remain straight lines in t_r, and the break-even rate is where they cross.

Conversion. An existing Traditional balance B₀, all contributed before tax, is moved to a Roth account; income tax t_n B₀ is due now. Tax from outside money: the whole balance converts, Converted = B₀ (1 + r)^N; without the conversion the outside money stays in a taxable account, Kept = B₀ (1 + r)^N (1 − t_r) + t_n B₀ (1 + r_c)^N. Tax from the balance: only B₀ (1 − t_n) converts, and the comparison is the Simple-mode one again. With a penalty rate entered, the part kept back to pay the tax carries the additional tax (it must equal t_n B₀ / (1 − p_x)), the earnings after the conversion are taxed at an early withdrawal, and a withdrawal within five years adds p_x on the converted amount.

What it assumes

One constant return, the same in both accounts. One tax rate now and one in retirement, each applied to the whole amount: real income tax has brackets, so a large contribution, withdrawal or conversion can span several rates. Everything is withdrawn at once after N whole years. The Roth withdrawal is qualified unless a penalty rate is entered. All Traditional money was deductible (no after-tax basis). The taxable account loses a fixed share of each year's return to tax and owes nothing more at the end. The employer match is pre-tax. No contribution or income limit is checked, and state tax counts only if you include it in the rates.

When it misleads

The retirement tax rate is unknown. It depends on future income, future law and where you live. The whole comparison turns on it, which is why the page shows a table and a chart across rates instead of one answer.

Marginal and average rates differ. A contribution is deducted at today's marginal rate, the rate on the last dollars earned. Withdrawals in retirement may fill the lower brackets first, so their average rate can be below the marginal rate of that time. Entering a single retirement rate hides this.

Things the page leaves out. Required minimum distributions from Traditional accounts, the effect of withdrawals on the taxation of benefits or on income-tested charges, the freedom to withdraw Roth contributions, inheritance, and plan rules of an employer all differ between the two designs and are not modelled.

Same dollars needs discipline. The same-dollars comparison assumes the Traditional tax saving is really invested every year. If it is spent, the Traditional result is only its first term.

A conversion changes this year's income. The page taxes the converted amount at the one rate entered; a large conversion can push part of it into a higher rate.

Worked example

The default case: 10,000 before tax, 30 years, a 6 % return, a tax rate of 22 % now and 15 % in retirement (both rates are examples).

Growth: F = 1.06³⁰ = 5.7435.

Traditional: 10,000 × 5.7435 × (1 − 0.15) = 57,435 × 0.85 = 48,820.

Roth: the contribution after tax is 10,000 × (1 − 0.22) = 7,800, and 7,800 × 5.7435 = 44,799.

Ratio: 0.85 / 0.78 = 1.0897. Difference: 48,820 − 44,799 = 4,020, which is 8.97 % of the Roth result. The Traditional account leaves more here only because the retirement rate entered is lower than the rate now; at a retirement rate of 22 % both would leave 44,799, and above 22 % the Roth account leaves more. The break-even retirement tax rate is 22 %.

Advanced, conversion of 50,000 with the tax paid from outside money and a 15 % tax drag: tax now 0.22 × 50,000 = 11,000; r_c = 0.06 × 0.85 = 0.051. Kept = 50,000 × 5.7435 × 0.85 + 11,000 × 1.051³⁰ = 244,098 + 48,919 = 293,017. Converted = 50,000 × 5.7435 = 287,175. Not converting leaves 5,842 more at a 15 % retirement rate; the two are equal at 17.03 %.

The page's results carry full precision; the hand figures above are rounded, so a last digit can differ.

An illustration, not tax advice. A calculator for education and analysis, not investment advice.