Roth vs Traditional: The Bracket Math That Decides Which Wins

You are two clicks into your payroll portal, and the plan wants you to pick one: Roth or pre-tax. There is no “explain this” link. Whatever you choose sits there for years, quietly compounding one decision you made in ninety seconds between meetings.

Here is the answer. If your marginal tax rate today is higher than your marginal rate on the day you pull the money out, pre-tax (Traditional) wins. If today’s rate is lower, Roth wins. If the two rates match, the after-tax result is identical to the penny — not close, identical — no matter how long the money grows or how well it does. Everything below is about working out which of those three you are in, and by how much.

The whole thing is one fraction

Traditional and Roth are the same equation with the tax applied at opposite ends.

With Traditional you contribute C dollars of pre-tax income, it grows by some factor G, and you pay rate T₂ on the entire withdrawal. Final value is C × G × (1 − T₂). With Roth you pay rate T₁ on C first, the remainder grows by the same G, and qualified withdrawals come out untouched. Final value is C × (1 − T₁) × G.

Multiplication doesn’t care about order. Divide one by the other and the ratio of Traditional to Roth is:

(1 − T₂) ÷ (1 − T₁)

G is gone. The time horizon is gone. Your rate of return is gone. Two tax rates decide the whole thing.

That is why “Roth is better because it grows tax-free” is wrong as usually stated. Traditional grows tax-free too — nothing inside either account is taxed annually. Traditional just settles the bill on the way out instead of on the way in.

One important distinction before the numbers. T₁ is your marginal rate, the rate on your last dollar of income, not your average rate. T₂ is harder: it’s the marginal rate on the specific dollars you withdraw in retirement, which is not your average retirement rate and often not the bracket you’d guess from a spreadsheet.

Follow one person through it

Meet Simone. She’s 41, earns enough to sit in the 24% federal bracket, and directs $10,000 of pre-tax income into her 401(k) each year. She lives in a state with no income tax and expects to stay there. Her best guess is that she’ll retire around 70 and draw enough from the account to land in the 12% bracket.

Say her money grows threefold over the next 30 years, which is roughly 3.7% a year after inflation.

Traditional: the full $10,000 goes in untaxed and becomes $30,000. She withdraws it at 12%, paying $3,600, and keeps $26,400.

Roth: she pays 24% up front, so $2,400 goes to the IRS and $7,600 lands in the account. It triples to $22,800, and she owes nothing.

Traditional leaves her $3,600 ahead, which is 15.8% more spendable money. Now rerun the same thing with the money growing tenfold instead of threefold: $88,000 versus $76,000. Still exactly 15.8%. Growth genuinely does not move the needle — it scales both sides by the same amount.

Two things had to be true for that comparison to be fair. Simone’s two accounts must hold the same investments, and — this is the one people break — she has to actually invest the $2,400 she didn’t pay in tax. Contribute pre-tax and spend the refund on a holiday and Traditional loses outright, by roughly the size of the refund plus everything it would have earned. That single behavioural failure swamps every bracket effect on this page.

Every bracket pair, in one grid

Find your rate today down the left, your expected retirement rate across the top. The cell is how much more after-tax money Traditional leaves you compared with Roth. Negative means Roth wins by that much. The rates are the current federal ordinary income brackets, plus a 0% column for anyone whose retirement income will fall under the standard deduction.

Each cell is [(1 − T₂) ÷ (1 − T₁) − 1] × 100.

The diagonal is all zeros. Equal rates, identical outcome, no cleverness available to anybody.

Notice the asymmetry. Simone’s 24-to-12 drop earns Traditional 15.8%. A colleague going the other way, 12% now and 24% later, hands Roth only 13.6%. Falling rates pay a bit better than rising rates cost, because the denominator (1 − T₁) is smaller when today’s rate is small.

The 12% row is worth staring at for a second. Even if your retirement rate falls all the way to zero, Traditional beats Roth by at most 13.6% from a 12% bracket. There is no room underneath you. That is the structural case for Roth during low-earning years — a first job, a sabbatical, a year with a big business loss.

Moving states is a bigger lever than moving brackets

Simone’s numbers assume no state income tax at either end. Change that and the swings get large fast, because state tax stacks more or less additively on top of the federal rate.

Suppose Simone had spent her working years in a state taxing her at 9% and still retired somewhere with no income tax. Her combined rate now would be 33% and her retirement rate 12%, which makes Traditional worth 31.3% more than Roth. That is the largest single swing in this article, and it comes from geography rather than from income.

Run it backwards and the damage is symmetric. Work in a no-tax state at 24% federal, then retire to a state that takes 9% while your federal rate holds at 22%, and Traditional goes from a modest win to a 9.2% loss. People who plan to retire somewhere greener rarely price this in.

Stay put and pay 5% state tax at both ends and almost nothing changes: 29% now against 27% later gives Traditional +2.8%, barely different from the +2.6% without any state tax at all. State tax only matters when it changes between your working years and your withdrawal years.

Treat those figures as illustrations of the mechanism, not as a lookup for any particular state. Many states exempt some or all retirement income, and the rules differ enough that you have to check your own two states rather than a table.

How far does the rate have to fall to be worth it?

Turn the question around. You want Traditional to beat Roth by some specific margin M. What’s the highest retirement rate you can tolerate? Solve the fraction for T₂ and you get T₂ = 1 − (1 − T₁) × (1 + M).

Read Simone’s row. At 24% today, her retirement marginal rate has to land at 16.4% or lower for Traditional to win by a full 10%. Her guess of 12% clears that comfortably. If she thought her retirement rate would be 20% instead, she’d be fighting for about five percent of the final balance, and the softer factors — flexibility, the contribution cap, her own guess at future tax law — would reasonably decide it.

Why “I’ll be in a lower bracket later” sometimes isn’t true

Simone’s forecast of a 12% retirement rate is doing a lot of work. Three mechanisms can quietly push her actual marginal rate higher than the bracket table suggests.

Required minimum distributions force money out. Traditional balances have to start distributing at age 73 under current law, whether Simone needs the cash or not, per the IRS guidance on required minimum distributions. A $1.5 million Traditional balance at 73 pushes roughly $56,600 out in the first year using a life expectancy factor of 26.5, and that sum stacks on top of Social Security and anything else she has coming in. She doesn’t get to choose a small withdrawal to stay in a low bracket.

Social Security taxation multiplies the damage. Traditional withdrawals count toward provisional income, and inside the phase-in range each extra $1,000 withdrawn can drag $850 of otherwise-untaxed benefits into the taxable pile. The dollar you withdraw is then effectively taxed on $1,850 of income. A nominal 12% bracket becomes 22.2% at the margin; a nominal 22% becomes 40.7%. If Simone’s real retirement rate is 22.2% rather than 12%, her expected 15.8% Traditional edge shrinks to about 2.4%.

IRMAA thresholds are cliffs, not slopes. Medicare Part B and D surcharges step up at income thresholds. A single dollar over a line can add several hundred dollars of annual premiums, behaving like a marginal rate of several hundred percent on that specific dollar. Traditional withdrawals count toward the income that triggers it; qualified Roth withdrawals do not.

None of this makes Traditional wrong for Simone. It makes her 12% estimate a projection with real error bars, and the error runs in one direction.

Where the arithmetic stops being reliable

The fraction is exact. The inputs are what break.

You’re maxing the limit. This is Roth’s one genuine structural advantage, and it exists only at the cap. Seven thousand dollars of Roth room holds $7,000 of after-tax money. Seven thousand dollars of Traditional room holds only $7,000 × (1 − T₂). At 24% both ends, filling Roth to the cap is equivalent to putting $9,211 into a Traditional account — which the rules won’t let you do. If Simone is maxing out and wants to shelter as much real money as possible, that gap is worth something the bracket table doesn’t show.

Your marginal rate isn’t your bracket. Phase-outs stack on top of the posted rates. The student loan interest deduction, the child tax credit, ACA premium credits, and the qualified business income deduction all phase out over income ranges, and each one adds to your true marginal rate. Someone nominally in the 22% bracket while losing an ACA subsidy can face an effective rate north of 40%, which changes their answer completely.

Tax law is not a constant. Current rate schedules can be raised, lowered, or restructured by a future Congress. Roth is a bet that rates go up; Traditional is a bet that rates go down or that your own income does. Neither bet is free, and nobody gets to skip making one.

Your taxable account interacts with this. If you hold investments outside retirement accounts, Traditional withdrawals raise your modified AGI and can push taxable-account gains across the thresholds where long-term capital gains rates step up. The IRS topic page on capital gains and losses sets out those rates, and the net investment income tax topic covers the extra 3.8% above certain income levels.

Heirs change the sign. Inherited Traditional balances are taxed at the beneficiary’s rate. If Simone’s children will be earning in a 32% bracket when they inherit and she’s at 24% now, the family-level answer inverts her individual one.

What this doesn’t tell you

The tables above cover federal marginal rates with a simple state overlay, and nothing else. They say nothing about your income, filing status, deductions, or which state you actually live in. They assume you retire when you plan to — and your retirement date moves T₂ more than most tax variables do. They ignore vesting schedules, plan-specific rules, and the ordering problem of which account to draw from first in retirement, which is its own optimisation. They ignore estate tax, which runs on a separate schedule. And they ignore the behavioural fact that people treat Roth balances as more fully “theirs” and spend them differently.

The arithmetic is sound. Whether the two rates you plug into it describe your life is a question the arithmetic cannot answer.

FAQ

Is Roth or Traditional better if I’m in the 22% bracket?

It depends entirely on your retirement rate, and the 22% bracket is wide enough that people sit in it for a decade while everything else about them changes. Against 12% later, Traditional wins by 12.8%. Against 22% it’s a dead tie. Against 24% Roth wins by 2.6%, and against 32% Roth wins by 12.8%.

Does Roth beat Traditional if I hold it long enough?

No. The time horizon cancels out of the equation entirely. Run $10,000 at 22% both ends through growth factors of 2, 3, 5, or 10 and the after-tax result is identical every time. Anyone claiming Roth wins “given enough decades” is quietly assuming a rate change or assuming you spend the tax savings.

How much do I actually lose by choosing wrong?

Somewhere between nothing and about 30% of your final after-tax balance, depending on the size of the bracket gap. Most real-world errors are small: picking Roth at 24% when you’ll retire at 22% costs 2.6%, which on $10,000 of pre-tax income grown threefold is about $600. The expensive mistakes involve a state move or a swing like 32% down to 12%.

What if I have no idea what my retirement bracket will be?

Split the contribution. If Simone puts half in each and her retirement rate turns out to be 12%, she ends up about 6.8% short of the all-Traditional result; if it turns out to be 32%, she’s about 5.3% short of all-Roth. Going all-in on the wrong one would have cost her 13.6% or 10.5% instead. Splitting is optimal in no single scenario and is a reasonable answer to genuinely not knowing.

Do Roth conversions use the same math?

Same formula, but T₁ is harder to pin down. In a conversion, T₁ is the rate on the converted amount stacked on top of your other income for that year, which usually spans more than one bracket. If $10,000 of a $50,000 conversion falls in the 12% bracket and the remaining $40,000 in the 22% bracket, your blended T₁ is 20%, not 12%. Use the blended figure in the table.

Does my employer match affect the choice?

No. Matching contributions go into a pre-tax account regardless of what you pick for your own deferrals, so the match is the same constant on both sides of the comparison and cancels out. It does affect your projected retirement balance, though, and therefore your projected retirement bracket — which feeds straight back into T₂.

Where to look next

Three inputs decide whether any of the above applies to you. Your true marginal rate this year, including whatever phase-outs you’re sitting inside, which is frequently several points above the bracket you’d name. Your projected retirement income sources and the order you’ll draw them, since that mix is what sets T₂. And whether a state move is realistically on the table, because that is the single largest swing factor here.

Contribution limits and eligibility phase-outs change every year. Check the current figures at the source rather than trusting any article, this one included.

This article is general information, not financial advice. See our disclaimer.

Also worth reading: Qualified vs Ordinary Dividends: The Tax Rate Gap on the Same Payout

Also worth reading: HSA Triple Tax Advantage: What It’s Actually Worth in Dollars

Also worth reading: RMD Penalty Math: What a 25% Excise Tax Costs If You Miss the Deadline

Also worth reading: 401(k) Vesting: What You Forfeit by Leaving at Year 2

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