Roth vs Traditional: The Breakeven Tax Rate

The arithmetic

Almost every Roth versus Traditional calculator on the web compares one dollar against another dollar. Those two dollars do not cost you the same. A Roth dollar has already been taxed, so it consumes more salary than a dollar deferred pre-tax. This module holds pre-tax salary constant instead, which is the only comparison that treats both routes alike.

The Roth route taxes your salary first, then shelters whatever survives:

$$V_{\text{roth}} = C\,(1 - t_0)\,(1 + r)^n$$

where:

• $C$ is the pre-tax salary you commit for one year, in dollars.
• $t_0$ is your marginal tax rate today, written as a decimal.
• $r$ is the expected annual return, written as a decimal.
• $n$ is the number of years until you withdraw.

The Traditional route sends the whole of $C$ into the account and taxes the withdrawal instead:

$$V_{\text{trad}} = C\,(1 + r)^n\,(1 - t_1)$$

where:

• $t_1$ is the marginal rate you expect to face at withdrawal, written as a decimal.
• $C$, $r$ and $n$ carry the meanings given above.

More money goes into the account on this route. The whole balance then leaves as ordinary income, so the tax lands at the end rather than the start.

Equal rates give identical results

Divide the second expression by the first. The compounding factor appears in both, so it cancels:

$$\frac{V_{\text{trad}}}{V_{\text{roth}}} = \frac{1 - t_1}{1 - t_0}$$

where:

• the ratio is Traditional spendable dollars per Roth spendable dollar at retirement.

Look at what vanished. The return is gone. The horizon is gone. The amount you commit is gone. Multiplication does not care about order, so taxing at the front and taxing at the back are the same operation.

Now set $t_1 = t_0$. The ratio is exactly one. Not close to one, and not one for reasonable inputs: one, at every return and every horizon, to the cent.

The decision therefore reduces to a single comparison. Below $t_0$, the Traditional route ends with more spendable money. Above $t_0$, the Roth route does. Nothing else in this arithmetic moves the answer.

Which side of that line you land on depends on your future income and on future tax law. Neither is knowable, and the module does not pretend otherwise. It takes $t_1$ as your input and shows the result across the whole range.

What happens to the tax saving

The comparison above puts the full $C$ into the Traditional account. Plenty of savers do something else. They fix a contribution figure and pay it in, whichever account they picked. Choosing Traditional then leaves cash on the table today, because the deduction cuts this year's tax bill.

Model that case by giving both accounts the same nominal contribution of $C\,(1 - t_0)$. The Traditional route now leaves $C\,t_0$ of salary uncommitted. Take it as cash, pay $t_0$ on it, and invest the remainder in a taxable account:

$$S = C\,t_0\,(1 - t_0)\,\big[(1 + r - d)^n (1 - g) + g\big]$$

where:

• $S$ is the after-tax value of the side account at retirement, in dollars.
• $d$ is the annual drag from dividends and turnover taxed along the way, as a decimal.
• $g$ is the capital gains rate charged on the accumulated gain at the end, as a decimal.

The bracket does two separate jobs. It compounds the seed at $r - d$ rather than at $r$, and it takes $g$ from the gain rather than from the whole balance. The Traditional total for this case is the sheltered balance plus that side account:

$$V_{\text{trad}}^{\text{side}} = C\,(1 - t_0)\,(1 + r)^n\,(1 - t_1) + S$$

where:

• $V_{\text{trad}}^{\text{side}}$ is total spendable dollars when the tax saving is invested rather than spent.

The Roth expression does not change between the two cases. That route has no leftover salary to invest, because the tax was already paid up front.

The breakeven withdrawal rate

Solve for the $t_1$ that leaves both routes level. The answer depends on which of the two toggles you set, and there are three cases rather than two. Getting them confused is the single most common error in this comparison.

Case one: the full pre-tax commitment goes into the plan

Set The Traditional route contributes to the full pre-tax commitment. Now the traditional account receives $C$ while the Roth account receives only $C(1-t_0)$, because the Roth contribution is made from taxed salary. Nothing is left over on either side. Everything cancels and the answer is exact:

$$t_1^{*} = t_0$$

where:

• $t_1^{*}$ is the withdrawal rate at which the two routes hand you the same spendable amount.
• $t_0$ is your marginal rate today.

This is the case the textbook result describes, and it is the cleanest statement of the whole decision. The two treatments are identical whenever your rate at withdrawal equals your rate today.

Case two: matched contributions, and the freed cash is invested

Set The Traditional route contributes to match the Roth nominally. Both accounts now receive $C(1-t_0)$, and the traditional route frees cash equal to the tax the Roth route had to pay. Invest that in a taxable account and:

$$t_1^{*} = t_0 \cdot \frac{A - g\,\max(0,\; A - 1)}{W}$$

where:

• $W = (1 + r)^n$ is the growth factor inside the shelter, where nothing is taxed along the way.
• $A = (1 + r - d)^n$ is the growth factor in the taxable account, reduced by the annual drag $d$.
• $g$ is the capital gains rate charged on the side account's gain at the end.

Because $A \le W$ whenever the drag is positive, this breakeven sits at or below $t_0$. The $\max$ term matters: if the drag exceeds the return, the side account ends below its basis, there is no gain to tax, and the expression reduces to $t_0 A / W$. Set both the drag and the gains rate to zero and it lands exactly on $t_0$, which is case one in disguise.

Case three: matched contributions, and the freed cash is spent

Same matched contributions, but the freed cash never reaches an account. Both routes started with the same $C(1-t_0)$ and grew it identically, and only one of them is taxed on the way out:

$$t_1^{*} = 0$$

There is no rate above zero at which the traditional route catches up. That is not a quirk of the model. It is what spending the deduction actually costs, stated exactly, and it is why the toggle defaults to investing it.

Drag is never negative, so $A \le W$ and the fraction never exceeds one. The breakeven therefore sits at or below your rate today. Set both $d$ and $g$ to zero and the fraction becomes exactly one: a taxable account that pays no tax is a shelter, and the dead heat returns.

Numbers show the size of the effect. At a 7% return over 30 years, with 0.5% drag and a 15% gains rate, the fraction is about 0.76. A 24% rate today then breaks even near 18% rather than near 24%. The band in which Traditional comes out ahead has narrowed, because part of its money sits outside the shelter and is taxed on the way.

The signature chart plots both routes against $t_1$ across its full range. The crossing point is the breakeven, and it is the only feature of that chart that carries the decision.

The contribution limit is a nominal number

Statutory limits are written in plain dollars, with no adjustment for tax treatment. The 2026 elective deferral limit is $24,500 whether you defer pre-tax or contribute to a Roth 401(k).

Those are not the same economic commitment. Contributing $24,500 to a Roth costs that figure divided by $(1 - t_0)$ in pre-tax salary. At a 24% marginal rate that is roughly $32,200 of salary, against $24,500 for the pre-tax deferral.

A saver who fills the limit in a Roth has therefore moved more economic value inside the shelter. This changes nothing about the rate comparison, which still turns on $t_1$ against $t_0$. What it changes is the ceiling on how much wealth either route can shelter in a single year. The module reports it as a second readout once your contribution reaches the limit you entered.

What this model does not do

Being explicit about this matters more than the breakeven figure itself.

Required minimum distributions are absent. Traditional balances must begin distributing at the statutory age, whether or not you want the money. Roth IRAs carry no such requirement during the original owner's lifetime. Forced distributions can lift a retiree into a higher bracket than the $t_1$ they entered here, and they remove the choice of when to realise the income. That asymmetry is real, it runs against the Traditional side, and this arithmetic does not capture any of it.

A single rate stands in for a whole tax system. Withdrawals fill brackets from the bottom, so a retiree's effective rate usually sits well below their marginal rate. Entering one $t_1$ treats every withdrawn dollar as though it were the last one. No state layer is modelled, so fold state tax into the same figure if you want it counted.

Future tax law is not forecast. Rates, brackets, and the treatment of retirement accounts have all changed before and will change again. The module takes $t_1$ from you and shows the answer across every value you might plausibly have meant.

One year, one commitment. The model runs a single year of salary through a single horizon. There is no annual escalation, no employer match, no partial Roth conversion, and no career path.

Account rules sit outside the arithmetic. The Roth five-year rules, income phase-outs on Roth IRA contributions, deductibility limits on Traditional IRAs when you are covered by a workplace plan, early withdrawal penalties, and the Saver's Credit are all absent.

A constant return is not reality. This matters less here than in a balance projection. The return cancels completely when the tax saving is spent, and it enters the invested case only through the ratio of $A$ to $W$. The breakeven rate is a far more stable output than any dollar figure on the screen.

Frequently asked

Why is the gap here smaller than on other calculators?

Because most of them compare equal contributions without adjusting for what those contributions cost in salary. $10,000 into a Roth and $10,000 into a Traditional account are different commitments, and the Roth one is larger. Hold pre-tax salary constant and the two routes collapse onto each other at equal rates. That collapse is the correct result, and a calculator showing a large gap at equal rates has made an error.

Does the expected return matter?

Hardly at all, which surprises most people who run it. In the spent case the return cancels out of the ratio, so a 5% assumption and a 9% assumption give the same verdict. In the invested case it survives only inside the ratio of $A$ to $W$, where a higher return slightly widens the cost of the drag. Changing the return moves the dollar figures a great deal and moves the crossing point very little.

What if I have no idea what my rate at withdrawal will be?

Then read the chart rather than the headline number. It shows the spendable amount at every withdrawal rate, so you can see how far your own estimate sits from the crossing point. A crossing you are nowhere near is a robust arithmetic result. A crossing you are sitting on top of means the two routes are close enough that this arithmetic is not what separates them.

Why default to the tax saving being invested?

Because it is the case people reason about worst, and the case where the breakeven stops being obvious. The spent case is the more common behaviour, and it is one click away. The interface always labels which of the two is on screen, since the two produce different breakevens from identical inputs.

Should I choose Roth or Traditional?

That is not a question this tool answers, and nothing here is advice. It computes the breakeven rate, draws both routes across the full range, and names what it leaves out. Where you expect your own marginal rate to land, and what weight you place on the rules the model omits, are matters for you and for a licensed tax professional.

Sources and further reading

• Internal Revenue Service, Roth comparison chart. The official side-by-side of Roth 401(k), Roth IRA, and pre-tax deferral rules.
• Internal Revenue Service, 401(k) and profit-sharing plan contribution limits. The authoritative elective deferral figure, re-indexed every plan year.
• Internal Revenue Service, Retirement topics: required minimum distributions. The rule this model does not capture, including which account types it reaches.
• R. M. Dammon, C. S. Spatt and H. H. Zhang (2004), Optimal Asset Location and Allocation with Taxable and Tax-Deferred Investing, Journal of Finance 59(3). The reference treatment of tax drag in a taxable account held alongside a sheltered one.

Educational research only. Not investment advice, not tax advice, and not a projection of your individual outcome.

Methodological sources

• Internal Revenue Service (2026). Roth comparison chart — Roth 401(k), Roth IRA, and pre-tax 401(k).
• Internal Revenue Service (2026). Retirement topics — 401(k) and profit-sharing plan contribution limits.
• Internal Revenue Service (2026). Topic no. 409, Capital gains and losses.
• Internal Revenue Service (2026). Retirement plan and IRA required minimum distributions FAQs.
• Office of the Law Revision Counsel, U.S. House of Representatives (2023). 26 U.S.C. § 402A — Optional treatment of elective deferrals as Roth contributions.
• Robert M. Dammon, Chester S. Spatt, Harold H. Zhang (2004). Optimal Asset Location and Allocation with Taxable and Tax-Deferred Investing.

Educational purposes only. Not investment advice.