The math
Roth or traditional is a bet on one number.
The choice is usually argued as a matter of temperament. It is arithmetic. At equal tax rates the two accounts leave you exactly the same money, so the real question is whether your rate on the way out will be higher or lower than your rate on the way in. Two details that most comparisons skip move the answer further than people expect.
Why the two are identical at equal rates
A traditional account takes your money before tax and taxes it on the way out. A Roth taxes it on the way in and never again. That sounds like a large difference. At the same tax rate it is no difference at all, because multiplication does not care about order. Taxing a number and then growing it gives exactly the same answer as growing it and then taxing it.
Take $10,000 of pre-tax pay and a 22% marginal rate. Put it in a traditional account and the whole $10,000 goes in. Put it in a Roth and $7,800 goes in, because the tax is paid first. Both cost you the same $7,800 of take-home pay today.
Same take-home cost, same tax rate
7% a year for 30 years, taxed at 22% in and out
- Traditional, after tax at the end
- $59,376
- Roth, untaxed at the end
- $59,376
- Difference
- $0
$10,000 grows to $76,123 and loses 22% to tax. $7,800 grows to the same $59,376 directly. It is the same multiplication done in a different order.
Nor does time pick a side. Compounding multiplies both accounts by the same number, so the horizon changes how much you end up with and never which account wins.
| Years | Traditional, after tax | Roth |
|---|---|---|
| 10 | $15,344 | $15,344 |
| 20 | $30,184 | $30,184 |
| 30 | $59,376 | $59,376 |
| 40 | $116,801 | $116,801 |
So it is a bet on one number
Once the identity is clear, the whole decision collapses to a single comparison: the rate you save today against the rate you pay later. Hold today's rate at 22% and vary the later one.
| Rate on the withdrawals | Traditional | Roth | Ahead |
|---|---|---|---|
| 12% | $66,988 | $59,376 | Traditional by 12.8% |
| 15% | $64,704 | $59,376 | Traditional by 9.0% |
| 18% | $62,420 | $59,376 | Traditional by 5.1% |
| 22% | $59,376 | $59,376 | Tie |
| 26% | $56,331 | $59,376 | Roth by 5.4% |
| 32% | $51,763 | $59,376 | Roth by 14.7% |
The break-even is exactly today's rate. Below it traditional wins, above it Roth wins, and the margins are roughly symmetric: a few points of tax rate in either direction is worth a few percent of the final balance. Nobody's retirement is made or broken by this choice alone. It is worth getting right, and it is not worth agonizing over.
The number is an average, not your top rate
This is the part many comparisons skip, and it tilts the answer toward traditional. The rate you save today is your marginal rate, the rate on the last dollar you earn. The rate you pay later is not. When traditional withdrawals are your main income in retirement, they fill the tax schedule from the bottom: the first slice is taxed lightly, the next a little more, and so on. The rate that matters is the average across all of it.
Marginal now, average later
Half the withdrawals at 12%, half at 22%, against 22% today
- Average rate on withdrawals
- 17%
- Traditional, after tax
- $63,182
- Roth
- $59,376
- Traditional ahead by
- 6.4%
The slices are an illustration, not brackets. The point is structural: a saver whose top rate does not change at all can still come out ahead with traditional, because the money comes out across several rates and went in at one.
The caveat cuts the other way. If other income fills the bottom of the schedule first, such as a pension, rental income or the taxable part of Social Security, then your traditional withdrawals start higher up and the average rate on those dollars rises. The less other income you expect, the stronger the case for traditional.
Detail one: when the contribution is capped, a Roth holds more
Everything above compared equal take-home cost. But contributions are capped in dollars, and a Roth dollar is an after-tax dollar. Contribute the same $10,000 to each and the Roth holds more money, because the traditional account's balance still owes tax.
To keep the race fair, the traditional saver has to invest the $2,200 tax saving somewhere. If the sheltered space is full, that somewhere is an ordinary brokerage account, which is taxed every year on what it distributes and again on the gain at sale. We assume a 2% dividend yield and a 15% rate on dividends and gains.
The same $10,000 into each, 22% in and out
Traditional saver invests the tax saving in a taxable account
- Roth
- $76,123
- Traditional, after tax
- $59,376
- Plus the tax saving, invested
- $13,917
- Roth ahead by
- 3.9%
Untaxed, the $2,200 would have grown to $16,747 and the two would tie. The tax on the side account, every year on its dividends and once more on the gain at sale, costs $2,830, and that is the whole Roth advantage. It moves the break-even: when the contribution is capped, traditional needs a later rate below about 18% to win, not 22%.
Detail two: if you pick the number first
Most people do not decide a take-home budget and then choose an account. They decide a number, ten percent of pay or a round figure, and keep it whichever account it goes into. Then a Roth contribution of the same number is simply a larger contribution. At a 22% rate, putting the same nominal amount into a Roth rather than a traditional account is equivalent to saving 28.2% more.
And if the traditional saver spends the tax refund rather than investing it, the comparison is not between two accounts at all. It is between someone who saved $10,000 and someone who saved $7,800, both measured after tax. The Roth wins that race, but the account is not the reason. The saving is. That is not an argument for the Roth. It is an argument for saving more, which a Roth happens to enforce.
What else separates them
Required distributions. Traditional accounts eventually force withdrawals, taxed as ordinary income whether you need the money or not. According to the IRS, the required minimum distribution rules do not apply to Roth IRAs or designated Roth 401(k) and 403(b) accounts while the owner is alive. See required minimum distributions.
Control. Having both lets you choose each year which kind of income to take. Fill the low part of the schedule from the traditional account, and take anything above it from the Roth, untaxed. That is the idea behind which pocket you spend from, and it only works if you own both kinds of account.
Other things your taxable income touches. Traditional withdrawals count as income and Roth withdrawals generally do not, which matters for anything that keys off income in retirement, including how much of your Social Security benefit is taxed.
Moving. The later rate includes state tax. Saving in a high-tax state and retiring in a low-tax one favors traditional, and the reverse favors Roth.
Heirs. Money left in a traditional account passes on with its tax bill attached: beneficiaries owe income tax on what they withdraw. Qualified withdrawals from an inherited Roth generally owe none.
How to use this
In a low-income year, lean Roth. Early in a career, a sabbatical, a year between jobs. Today's rate is unusually low, and that is the bet you can see clearly.
At peak earnings with modest expected retirement income, lean traditional. You save tax at your highest marginal rate and pay it back across the bottom of the schedule.
When you cannot tell, split it. A mix gives you the control described above and caps the regret in either direction. Uncertainty about future tax law is a reason to diversify, not a reason to guess.
And if you are hitting the cap and want to save more, the Roth is the larger account. That is detail one: at equal rates and the same capped contribution, a Roth simply holds more after-tax money.
What this leaves out
Contribution limits, which change from year to year, and the income limits on direct Roth IRA contributions; check the current figures at the IRS. Employer matching, which is free money in either account and comes first; see the order of operations. Roth conversions, which are this same decision made later, deliberately, in a low-income year; see Roth conversion. And the fact that nobody knows what tax rates will be in thirty years. The arithmetic does not remove that uncertainty. It tells you exactly what you are betting on.
Sources and further reading
- IRS, Roth IRAs, for the rules that Roth contributions are not deductible and that qualified distributions are tax-free.
- IRS, Retirement plan and IRA required minimum distributions FAQs, for the rule that lifetime required distributions do not apply to Roth IRAs or designated Roth accounts.