Roth vs. traditional: what the comparison really depends on

In a 401(k), 403(b) or IRA, Roth versus traditional comes down to two tax rates: the rate a traditional contribution saves you now, and the rate you will pay when that money comes out. Compared at the same take-home cost, the two accounts leave exactly the same after-tax amount when those rates are equal. The return and the number of years change how big both balances get, not which one wins.

Which is better, Roth or traditional?

Neither in general. Under the equal-cost comparison this guide uses, the rule is:

Two things complicate that rule. If you put the same dollar amount into either account, usually because you contribute the maximum, a Roth shelters more money from tax and can come out ahead even when the two rates are equal. And because nobody knows their future tax rate, splitting contributions trades the top result for a narrower range of outcomes.

Why do equal tax rates give equal results?

A traditional contribution is taxed once, at the end. A Roth contribution is taxed once, at the start. The growth in between multiplies both by the same factor, and the order of multiplication doesn’t change the product:

$$\begin{aligned} A_{\text{trad}} &= C \times G \times (1 - t_{\text{later}}) \\ A_{\text{Roth}} &= C \times (1 - t_{\text{now}}) \times G \end{aligned}$$

• $C$ is the pre-tax pay you set aside each year.
• $G$ is the growth factor, what $1 contributed at the end of each year grows to: $G = \dfrac{(1+r)^n - 1}{r}$ for an annual return $r$ over $n$ years.
• $t_{\text{now}}$ is the tax rate a traditional contribution saves today.
• $t_{\text{later}}$ is the tax rate on the traditional withdrawals.

Dividing one result by the other cancels $C$ and $G$:

$$\frac{A_{\text{Roth}}}{A_{\text{trad}}} = \frac{1 - t_{\text{now}}}{1 - t_{\text{later}}}$$

So the winner depends only on the two rates, provided both accounts hold the same investments and cost the same take-home pay.

What does “same take-home cost” mean?

It means the Roth contribution is smaller by the tax a traditional contribution would have saved. A $9,000 traditional 401(k) contribution at a 24% rate (an example rate) cuts your income tax by $2,160, so your take-home pay falls by only $6,840. A $6,840 Roth contribution costs the same $6,840. Payroll taxes don’t enter the comparison, because 401(k) deferrals are subject to Social Security and Medicare tax either way.

As a share of pay: 9% into the traditional account matches 9% × (1 − 0.24) = 6.84% into the Roth. Switching to Roth at the same 9% means saving more and taking home less, which is the same-amount case covered under investing the tax savings.

Worked example: $9,000 a year for 28 years

Example assumptions, not forecasts:

• $9,000 of pre-tax pay a year goes to retirement, and a traditional contribution saves tax at 24%.
• Traditional contribution $9,000; equal-cost Roth contribution $6,840.
• Both accounts earn 6% a year, contributions go in at the end of each year, for 28 years.
• The whole traditional balance is taxed at one rate when it comes out.

1. Growth factor: $G = (1.06^{28} - 1) / 0.06 = 68.52811162$.
2. Traditional balance before tax: $9,000 × 68.52811162 = $616,753.00, from $252,000 of contributions.
3. Roth balance, tax-free: $6,840 × 68.52811162 = $468,732.28, from $191,520 of contributions (the same take-home cost).
4. Tax the traditional balance at a range of retirement rates:

The gap is the traditional balance times the difference between the two rates: every 6 points is $616,753.00 × 0.06 = $37,005.18. In ratio terms, at 12% later the Roth ends at 0.76 ÷ 0.88 = 86.36% of the traditional result.

Which tax rate should you compare, marginal or effective?

Use your marginal rate today, not your overall effective rate (all your tax divided by all your income), and for retirement the rate your withdrawals add. Today’s marginal rate is the rate on the top slice of your income, plus any state income tax the contribution saves. A traditional contribution removes income from the top, and with bracketed rates only the income inside the highest bracket is taxed at the highest rate. If a large contribution reaches down into a lower bracket, the saving is a blend of the two rates.

In retirement, the rate that matters is usually not your top bracket. It is the extra tax your traditional withdrawals cause, divided by the withdrawals. Withdrawals stack on top of your other income, and the standard deduction and the lower brackets absorb part of them.

To show the effect, take invented brackets (not the real ones): the first $20,000 of income is untaxed, the next $30,000 is taxed at 10%, the next $50,000 at 20%, and anything above $100,000 at 30%. A retiree withdraws $40,000 from traditional accounts:

The middle retiree is in the 20% bracket, yet the withdrawals cost 13.75%. The last row is the warning: if pensions or other pre-tax savings will already fill the low brackets, every withdrawn dollar is taxed at the retiree’s top bracket rate, 20% here. The real rate can also exceed the bracket rate, because withdrawals count as other income in the test that decides whether, and how much of, your Social Security benefits are taxable.

Does investing the tax savings change the answer?

Only when both accounts receive the same dollar amount. In the equal-cost comparison, the traditional saver already invests the whole tax saving inside the account by contributing $9,000 instead of $6,840.

The same-amount case comes up when you contribute the maximum. Contribution limits are fixed dollar amounts, and in a 401(k) one limit covers Roth and pre-tax deferrals together. A dollar in a Roth is after-tax money; a dollar in a traditional account is pre-tax money, and part of it will go to tax. If the traditional account can’t take more, the equal-cost alternative to a $9,000 Roth contribution is a $9,000 traditional contribution plus the $2,160 tax saving invested in an ordinary taxable account, where dividends and realized gains are taxed along the way.

Same assumptions as the worked example, with 24% both now and later and a tax drag of 1 percentage point on the taxable account, so it grows at 5% instead of 6%. The $9,000 stands in for whatever your limit is:

The Roth leads by $21,871.14 even though the tax rates are equal. Without the drag, the side account would reach $148,020.72 and the two would tie again, so the Roth’s lead is exactly what the side account loses to tax along the way. For the traditional route to win, the retirement rate would now have to fall below about 20.45% ($126,149.58 ÷ $616,753.00) instead of 24%. The drag is a simplification: selling the side account’s investments would also trigger tax on gains not yet taxed, which widens the Roth’s lead.

Leaving the side account out entirely errs the other way. Comparing $616,753.00 with $468,732.28 shows a Roth lead of $148,020.72 instead of $21,871.14, because it ignores the extra $2,160 of take-home pay the Roth cost every year.

What if you don’t know your future tax rate?

Splitting contributions between the two accounts narrows the range of outcomes. Nobody knows the future rate exactly: tax law, retirement income and where you live can all change over decades. In this model the Roth result doesn’t depend on the future rate at all, while the traditional result carries all of that uncertainty. A 50/50 split of the equal-cost budget, $4,500 traditional plus $3,420 Roth (still $6,840 of take-home pay), lands exactly halfway every time:

Across rates from 12% to 30%, the all-traditional result swings by $111,015.54 and the split by $55,507.77. The split never wins outright and never comes last. Holding both kinds of account also lets you choose, year by year, how much taxable income to create in retirement, which a single-rate calculation can’t capture. Unless your plan lets you elect Roth treatment for it, an employer match goes into a pre-tax account even when your own contributions are Roth, so a Roth saver with a match ends up holding some of each anyway.

What the comparison leaves out

These are educational estimates, not tax advice. The calculation deliberately leaves out rules that change by year or by person, so check them separately:

• Contribution and income limits. Annual limits, catch-up amounts and Roth IRA income limits change with cost-of-living adjustments, and the IRS publishes the current figures. None are built in.
• Brackets. Every withdrawal is taxed at one rate. Real withdrawals are spread over many years and fill brackets from the bottom, as the invented-bracket table shows.
• State tax. Include it in each rate where it applies: the state tax a traditional contribution saves now and the state tax on the withdrawals later. Moving to a state with a different income tax in retirement changes the later rate.
• Required minimum distributions. Traditional IRAs and pre-tax plan accounts require minimum withdrawals from an age set by law (a workplace plan may let you wait until you retire), which can force taxable income in years you would rather skip. Roth IRAs and designated Roth accounts in 401(k) and 403(b) plans don’t while the owner is alive.
• Qualified distributions. Roth earnings come out tax-free only in a qualified distribution: generally the account has been held at least five years, and the withdrawal is made at or after age 59½, on disability, after death or, from a Roth IRA, for a first-time home purchase.
• The employer match. It depends on your contribution rate, not on the account type. Some plans let fully vested employees elect Roth treatment for matching contributions, which makes the match taxable income when it goes in. Cutting your contribution rate to keep take-home pay equal can shrink the match: with example tiers of a dollar-for-dollar match on the first 3% of pay and 50 cents per dollar on the next 5%, a $100,000 salary earns a $5,500 match at 9% but $4,920 at 6.84%.
• Fees and investments. Both accounts are assumed to hold the same investments at the same cost.

Try it

Enter the worked example in the Roth vs. traditional calculator:

1. Choose the comparison basis same take-home cost, then enter a traditional contribution of 9,000, a tax rate now of 24%, a tax rate on retirement withdrawals of 12%, 28 years and an annual return of 6%. Contributions go in at the end of each year, as in the example. Expect $542,742.64 for the traditional account after tax, $468,732.28 for the Roth, and a break-even tax rate on withdrawals of 24%. Change the tax rate on withdrawals to 18%, 24% and 30% to reproduce the table.
2. For the maximum-contribution case, switch the basis to same amount in each account. That puts the full $9,000 in the Roth and invests the traditional tax saving, $2,160 a year, in a taxable account. Enter a tax drag of 1% and set the tax rate on withdrawals to 24%. Expect $616,753.00 for the Roth against $468,732.28 + $126,149.58 = $594,881.86, and a break-even tax rate on withdrawals of about 20.45%.

To check the balances before tax, use the retirement savings calculator with no current savings, ages 37 and 65 (28 years), a yearly contribution of 9,000 with no yearly increase, a 6% expected annual return and contributions at the end of each period: it shows $616,753.00 in future dollars, and a contribution of 6,840 shows $468,732.28. To reproduce the match figures, open the employer match calculator and enter a salary of 100,000, a first tier with a match rate of 100 on the first 3 percent of pay, a second tier with a match rate of 50 on the next 5 percent, and contribution rates of 9% and then 6.84%.