Roth vs. Traditional Calculator

Roth or traditional: which leaves you more after tax?

At the same take-home cost, the account whose tax rate is lower wins. If your traditional withdrawals will be taxed at a lower rate than the rate a traditional contribution saves you today, traditional leaves more; if at a higher rate, Roth leaves more; if the two rates are equal, they tie to the cent. This calculator puts dollar figures on that for your contribution, years and return in a 401(k), 403(b) or IRA. It also shows the break-even tax rate and how the answer shifts if your guess about future tax rates turns out wrong.

It compares after-tax dollars: a traditional balance still owes income tax and a Roth balance doesn’t, so comparing the balances before tax flatters the traditional account. The calculator works on one of two bases and names the one it used in the headline:

• Same take-home cost (the default): a Roth contribution comes out of taxed pay, so an equal hit to your paycheck buys a smaller Roth contribution. $7,500 into a traditional account costs $5,850 of take-home pay at a 22% rate, the same as $5,850 into a Roth.
• Same amount in each account: for when you would contribute the same dollars either way, usually the maximum. The traditional saver’s tax saving then goes into an ordinary taxable account.

How to use the calculator

• Comparison basis: choose one of the two above. If you are unsure, keep same take-home cost.
• Traditional contribution: the pre-tax pay you would put in the traditional account. Enter it per year, or per paycheck with the frequency next to it ($300 every 2 weeks is $7,800 a year). Leave out any employer match.
• Tax rate now: the rate a traditional contribution saves: your top federal bracket rate plus any state income tax the contribution avoids. Not your average rate (total tax ÷ income).
• Tax rate on retirement withdrawals: your estimate of the extra tax your traditional withdrawals will cause, as a share of them. The next sections explain how to estimate it.
• Years until withdrawal: how many yearly contributions go in before the money comes out, from 1 to 80.
• Annual return: the same investments in both accounts, for example 7%. It can be negative.
• Tax drag (same amount only): how many percentage points the taxable side account loses to tax on dividends and realized gains each year, for example 1.

Every change recalculates at once. The Try chips switch to a higher tax rate on withdrawals, the same rate now and later, or the same-amount case, each worked through below. To compare your own scenarios, such as retiring in a state with no income tax, press Save for comparison, change a rate and save again: each saved column shows its change from the first.

How Roth vs. traditional is calculated

Both accounts get a contribution at the end of each year for $n$ years and grow at the same return $r$. One dollar paid in that way grows to the factor $G$, the future value of an ordinary annuity. The traditional account pays tax at the end; the Roth pays it at the start:

$$G = \frac{(1 + r)^n - 1}{r}, \qquad A_{\text{trad}} = C\,G\,(1 - t_{\text{later}}), \qquad A_{\text{Roth}} = C\,(1 - t_{\text{now}})\,G$$

• $C$ is the traditional contribution a year, in pre-tax dollars.
• $G$ is the growth factor; with a 0% return it is simply $n$.
• $t_{\text{now}}$ is your tax rate today, the tax a traditional contribution avoids; $t_{\text{later}}$ applies to the traditional withdrawals.
• $A_{\text{trad}}$ and $A_{\text{Roth}}$ are the after-tax values when everything comes out at the end.

Divide one by the other and $C$ and $G$ cancel: the Roth ends at $(1 - t_{\text{now}}) \div (1 - t_{\text{later}})$ times the traditional result, whatever the contribution, return or number of years. Those only change the size of the gap in dollars.

On the same-amount basis the Roth gets the full $C$, so $A_{\text{Roth}} = C\,G$. The traditional side adds a taxable account that receives $C\,t_{\text{now}}$ at the end of each year and grows at the return minus the drag.

Worked example: 22% now, 12% or 24% later

A saver puts $7,500 a year of pre-tax pay into a traditional 401(k), where it saves tax at 22%. The example assumes a 7% return for 30 years, and a 12% tax rate on the withdrawals. These are example assumptions, not forecasts.

1. Growth factor: $G = (1.07^{30} - 1) \div 0.07$, which comes to 94.46078632.
2. Traditional balance: $7,500 × 94.46078632 = $708,455.90, from $225,000.00 of contributions.
3. Tax on the way out: $708,455.90 × 0.12 = $85,014.71, leaving $623,441.19.
4. Roth contribution at the same take-home cost: $7,500 × (1 − 0.22) = $5,850.00 a year, $175,500.00 in all.
5. Roth balance, tax-free: $5,850.00 × 94.46078632 = $552,595.60.
6. The traditional account leaves $623,441.19 − $552,595.60 = $70,845.59 more after tax.

As a check, 0.78 ÷ 0.88 = 0.886364, and $552,595.60 is that share of $623,441.19. In a spreadsheet, =FV(0.07, 30, -7500) returns the same $708,455.90 traditional balance.

Now suppose the withdrawals are taxed at 24% instead. The tax becomes $170,029.42, the traditional account keeps $538,426.48, and the Roth leaves $14,169.12 more. Nothing else changed; the order of the two rates decided the winner.

What tax rate should I enter for retirement?

Enter the extra tax your traditional withdrawals would cause, divided by the withdrawals. That is usually lower than your top bracket rate in retirement, for two reasons. Income is taxed in layers, and a bracket’s rate applies only to the part of income inside it. And the standard deduction shelters the first slice of income from tax altogether, so part of your withdrawals may fall in the untaxed or low layers.

The rate can also be higher than it looks. If a pension or large pre-tax balances will already use up the low layers, each withdrawn dollar is taxed at your top rate. Other income also counts toward the test that decides how much of your Social Security benefits are taxed, so withdrawals can pull more benefits into tax. Add any state income tax you expect to pay where you will live then.

For today’s rate, the question is the reverse: what does the contribution take off the top of your income? For most people that is their marginal bracket rate plus state tax. A contribution large enough to reach down into the next bracket saves a blend of the two rates.

The break-even tax rate, explained

The break-even tax rate on withdrawals is the rate at which both routes leave the same after-tax money. Above it the Roth leaves more; below it the traditional account does. On the same take-home cost basis it is always your tax rate now: 22% in the example.

The what-if table under the steps reruns the calculation at your rate on withdrawals 5, 10 and 15 points either way, plus the break-even rate. For the example, each 5 points moves the traditional result by $708,455.90 × 0.05 = $35,422.79, while the Roth stays at $552,595.60:

Investing the tax saving: when you contribute the maximum

If you would put the same dollars in either account, usually because you contribute the most your plan or IRA allows, the Roth holds more after-tax money. Contribution limits are dollar amounts, and a Roth dollar carries no tax bill while part of every traditional dollar belongs to the IRS. To match the Roth’s cost, the traditional saver has to invest the tax saving somewhere else: in an ordinary taxable account, where dividends are taxed each year and gains when sold.

Choose same amount in each account for this. With the example’s $7,500, 22% now and 22% on withdrawals, and 1 point of tax drag:

1. Roth: $7,500 × 94.46078632 = $708,455.90, tax-free.
2. Traditional: $708,455.90 taxed at 22% leaves $552,595.60.
3. Side account: the tax saving, $7,500 × 0.22 = $1,650.00 a year, grows at 7% − 1 point = 6% to $130,446.01.
4. Traditional total: $552,595.60 + $130,446.01 = $683,041.61, so the Roth leaves $25,414.29 more even though the two tax rates are equal.

The break-even tax rate falls to $130,446.01 ÷ $708,455.90 = 18.41%: the traditional route now wins only if withdrawals are taxed below that. With no drag, the side account would grow as fast as the retirement accounts and the two would tie again. The calculator shows the side account before any tax on selling it; a sale would tax the gains not yet taxed and widen the Roth’s lead.

Reading the result

• The headline names the account that leaves more after tax, by how much, and the basis used.
• The tiles give each route’s after-tax total and the break-even tax rate, then each account’s yearly contribution with the take-home pay it costs, and the tax on the traditional withdrawals (or, with the same amount in each, the side account).
• How this was calculated walks through the arithmetic with your own figures, down to the spreadsheet formula.
• After tax at other tax rates on withdrawals is the what-if table. Its 50/50 split column puts half of the contribution in each account, which always lands halfway between the two.
• Year by year shows each account as if everything came out at the end of that year, taxed at your rate on withdrawals. Download it as a CSV file; the chart draws the same numbers.

What this calculator leaves out

These results are educational estimates, not tax advice. The model is deliberately simple, so check these separately:

• Contribution and income limits. None are applied. Limits are dollar amounts adjusted over time, Roth IRA contributions can be limited by income, and a traditional IRA deduction can be limited if you have a workplace plan. The IRS pages in the sources list the current figures.
• Brackets. Every withdrawal is taxed at your single rate on withdrawals, although real withdrawals spread over many years and fill the brackets from the bottom.
• State tax and moves. Include state tax in both rates; a move to a state with a different tax in retirement changes the later rate.
• Withdrawal rules. Traditional accounts have required minimum distributions, which can force taxable income; Roth IRAs and designated Roth accounts have none during the owner’s life. Roth earnings are tax-free only in a qualified distribution, which generally needs a five-year holding period and age 59½, disability or death.
• The employer match, which depends on how much you contribute, not on the account type.
• Fees and payroll taxes. Both accounts are assumed to cost the same; Social Security and Medicare taxes apply to both kinds of contribution alike.

Common mistakes when comparing Roth and traditional

• Putting the same dollars in both and calling it a fair test. $7,500 in a Roth costs $1,650 more take-home pay a year than $7,500 in a traditional account at 22%. Unless you are at the limit, compare at the same take-home cost, or count the extra saving with the same-amount basis.
• Using your average tax rate for today. A traditional contribution comes off the top of your income, so it saves your marginal rate, not total tax ÷ income.
• Assuming your top bracket in retirement. Withdrawals are partly taxed in the lower layers, so the rate on them is often lower. Use the what-if table to see how much the answer depends on it.
• Adding state tax on one side only. If the contribution saves state tax now, the withdrawals will probably owe state tax later too, unless you plan to move.
• Counting the employer match as your contribution. It usually goes into a pre-tax account whichever you choose.
• Typing a monthly or per-paycheck amount as yearly. Pick the frequency next to the contribution; the steps show the yearly total the calculator used.
• Confusing the break-even tax rate with a withdrawal rate. The break-even is a tax rate on withdrawals, not the share of your savings you take out each year.