Roth vs Traditional Calculator
The whole decision reduces to one comparison: is your tax rate higher now, or will it be higher when you take the money out? Everything else is detail.
Roth comes out ahead by
$14,639.65after tax
- Traditional — pot
- $731,982.60
- Traditional — after tax
- $556,306.77
- Roth — pot
- $570,946.43
- Roth — after tax
- $570,946.43
- Difference
- $14,639.65
- Into a Roth each month
- $468.00
- At these rates the Roth account comes out $14,639.65 ahead after tax — $570,946.43 against $556,306.77.
- You expect a higher tax rate later than now, which is the case for a Roth: pay the tax at today's lower rate and take the pot out untaxed.
- The comparison only holds if you contribute the same gross amount to both. Putting the same net figure into a Roth means contributing more in real terms, and the Roth then wins for that reason rather than on its merits.
- Tax rates are yours to enter, and nobody knows the later one. It depends on both your own income in retirement and on tax law decades from now.
- This is the core arithmetic and not the whole picture. Required withdrawals, the treatment of an inherited account and the effect on other means-tested benefits all differ between the two.
About the Roth vs traditional comparison
A traditional account takes the contribution before tax and taxes the whole pot on the way out. A Roth taxes the contribution now and takes nothing later. Both grow untaxed in between, and that is the only thing they have in common.
The consequence is cleaner than most people expect. If your tax rate is the same at both ends, the two produce exactly the same after-tax result — not approximately, identically. Multiplication is commutative: taxing before growth and taxing after growth come to the same thing at the same rate. So the entire decision rests on which rate is higher.
Expect a higher rate later and the Roth wins: pay at today's lower rate and take the pot out untaxed. Expect a lower rate later — which is common, since retirement income is often below working income — and the traditional wins. On $600 a month over thirty years at 7%, with 22% tax now and 24% later, the Roth ends about $14,640 ahead after tax.
One trap makes most comparisons of these wrong. The figures only mean anything if you contribute the same gross amount to both. Putting $600 into a Roth is not the same as putting $600 into a traditional account, because the Roth $600 is after-tax money and worth more. Compare $600 gross either way, as this does.
And nobody knows the later rate. It depends on your own income in retirement and on tax law decades from now, which is a reason many people hold some of each rather than betting the whole thing on a forecast.
What it works out
- Both pots, before and after tax
- Your own tax rates now and in retirement
- The point at which the two are identical
- What the same gross contribution buys in each
The formula
Traditional = Pot × (1 − Tax later) Roth = (Contribution × (1 − Tax now)) grown
The traditional account puts the whole gross contribution in, grows it, and taxes the result. The Roth taxes the contribution first, then grows what is left, and takes nothing at the end.
Write both out and the structure becomes obvious. Traditional is contribution × growth × (1 − tax later). Roth is contribution × (1 − tax now) × growth. Those are the same three terms multiplied in a different order, so when the two tax rates are equal the answers are identical — exactly, not roughly.
With $600 a month for thirty years at 7%, the traditional pot reaches about $731,983 and is worth $556,307 after 24% tax. The Roth contributes $468 a month after 22% tax, reaches $570,946, and is worth all of it. The Roth is $14,640 ahead, and the entire gap comes from the two-point difference between the tax rates.
The comparison only holds because both start from $600 gross. If you put $600 of take-home pay into a Roth, you are contributing more in real terms than $600 into a traditional account, and the Roth wins for that reason instead of on its merits.
- Contribution
- The gross amount, before tax, for both accounts.
- Tax now
- Your marginal rate today — the rate the contribution would otherwise be taxed at.
- Tax later
- The rate you expect on withdrawals. A guess, and the one that decides the answer.
- Pot
- What the contributions grow to before any tax.
A worked example
$600 a month for thirty years at 7%, taxed at 22% today and an expected 24% in retirement.
That works out to $14,639.65 after tax.
- Traditional — pot
- $731,982.60
- Traditional — after tax
- $556,306.77
- Roth — pot
- $570,946.43
- Roth — after tax
- $570,946.43
- Difference
- $14,639.65
- Into a Roth each month
- $468.00
Questions
Should I choose Roth or traditional?
Roth if you expect a higher tax rate in retirement than today, traditional if you expect a lower one. At the same rate they produce identical results, so there is nothing else to decide on.
Why do they come out the same at the same tax rate?
Because taxing before growth and taxing after growth are the same multiplication in a different order. Contribution × growth × (1 − tax) is the same number whichever of the last two you apply first.
Will my tax rate be lower in retirement?
Often, since retirement income is usually below working income — which argues for the traditional account. But not always: a large pot, a pension and other income can push you higher, and future tax law is unknowable.
Should I split between both?
Many people do, and the argument is straightforward: you are betting on a tax rate decades away that nobody can know. Holding some of each means you are less wrong whichever way it goes, and gives you the choice of which to draw from.
Is the Roth better because the growth is untaxed?
This is the most common misunderstanding. Growth is untaxed inside both — that is what makes them retirement accounts. The difference is only when the contribution is taxed, not whether the growth is.
Does the calculator account for contribution limits?
No. Limits apply, differ between account types, and change every year, so publishing them would date the page. Where a limit binds, the Roth effectively lets you shelter more, because its limit is on after-tax money.
What about required withdrawals?
Traditional accounts generally force withdrawals from a set age whether you need the money or not; Roths generally do not for the original owner. That is a real advantage for the Roth and it is not in this arithmetic.
Does this apply outside the US?
The names are American but the structure is not. Most countries have both a pay-tax-now and a pay-tax-later retirement wrapper, and the comparison between them is identical — enter your own rates.