Roth IRA Calculator

balance before tax = initial balance × (1 + i)^n + (pre-tax contribution ÷ 12) × ((1 + i)^n − 1) ÷ i | traditional: what you keep = balance before tax × (1 − retirement tax rate) | Roth: what you keep = balance before tax × (1 − current tax rate) | difference (Roth − traditional) = balance before tax × (retirement tax rate − current tax rate)

Pre-tax contribution

The amount of gross income you are directing at retirement each year, before any tax. This is deliberately NOT how much lands in the Roth: the Roth receives this figure minus the tax on it, which is the entire difference between the two paths. Entering what you actually transfer into the Roth would compare a pre-tax figure with an after-tax one and manufacture a difference that is not there.

Current tax rate

The rate the contribution is taxed at on the way into a Roth, and the rate the traditional path would have deducted it at instead. It multiplies the whole accumulated balance on the Roth side, which is what makes the two paths comparable: neither account is special, they simply apply their rate at opposite ends.

Retirement tax rate

The rate applied to the entire balance when a traditional IRA is drawn down. Everything about the decision turns on how this number compares with the one above it, and nothing turns on how large either is — a ten-point gap in either direction is worth the same money.

i

Return per period, the annual return divided by twelve. Both paths use the same rate for the same number of periods, which is why the return drops out of the difference entirely: it scales the balance, and the balance is what the two tax rates are applied to.

n

Number of periods, years times twelve. It drops out of the comparison in the same way the return does, and it is the only reason the difference grows over time — the gap between the rates is fixed, but the balance it multiplies is not.

Initial balance

What is already saved, treated as pre-tax money on both sides. Strictly this is an assumption about money whose tax status you may not know — an existing Roth balance is already after-tax, and putting it here overstates the tax that will be paid on it. Treat the figure as fresh pre-tax savings, or set it to zero.

Use it when the question is which account to put the next contribution into, and use it for the negative result too: at equal tax rates the page says the choice does not matter, and that answer is worth more than a confident one in either direction. It does not model the eligibility rules that decide whether you may contribute to a Roth at all, and it does not put a value on the Roth's freedom from required distributions — both are in the limitations.

1. The same tax rate going in and coming out

   1. The balance either path reaches before tax is the same: 10,000 × 4.46497 + (7,000 ÷ 12) × 692.994 = 448,896.18.
   2. Traditional: the whole balance is taxed at 22% on withdrawal, 448,896.18 × 0.78 = 350,139.02.
   3. Roth: the contributions were taxed at 22% on the way in, so 22% of the same final balance never arrives — 448,896.18 × 0.78 = 350,139.02.
   4. Difference: 350,139.02 − 350,139.02 = 0.

   Zero, exactly, and not by coincidence. Multiplying by (1 − 0.22) before twenty-five years of growth gives the same answer as multiplying after, because multiplication is commutative — the compounding never gets a chance to prefer either side.

2. A higher rate at retirement

   1. Balance before tax is unchanged at 448,896.18.
   2. Roth keeps 448,896.18 × 0.78 = 350,139.02, because the rate that applies to it is the one on the way in.
   3. Traditional keeps 448,896.18 × 0.68 = 305,249.40.
   4. Difference: 350,139.02 − 305,249.40 = 44,889.62.

   The 44,889.62 is exactly 448,896.18 × 10%, the gap between the two rates. The size of the balance decides how much a ten-point gap is worth, and the gap decides which way it points — the two never mix.

3. A lower rate at retirement

   1. Balance before tax is still 448,896.18.
   2. Roth keeps 448,896.18 × 0.78 = 350,139.02 — the Roth figure does not move at all, because the rate that applies to it is the current one.
   3. Traditional keeps 448,896.18 × 0.88 = 395,028.64.
   4. Difference: 350,139.02 − 395,028.64 = −44,889.62.

   The sign flips and the magnitude does not: same ten points, opposite direction, and the negative figure means the traditional account wins by that much. Notice that the Roth column has been identical in all three cases so far — in this comparison it is the traditional side that moves.

4. No tax at either end

   1. With no tax on either side, both paths keep the whole balance: 448,896.18.
   2. Difference: 0.

   A degenerate case that is still worth running once, because it shows the identity does not depend on the rates being equal and non-zero — it depends only on their difference. Any pair with the same value on both sides gives zero, including zero itself.

5. A zero return, with the rate rising

   1. No growth, so the balance before tax is just what went in: 10,000 + 7,000 × 25 = 185,000.
   2. Roth keeps 185,000 × 0.78 = 144,300.
   3. Traditional keeps 185,000 × 0.68 = 125,800.
   4. Difference: 144,300 − 125,800 = 18,500, which is 185,000 × 10%.

   With no growth the difference is smaller in dollars than in the case with growth, and it is the same ten points — which is the cleanest demonstration that the gap multiplies the balance and nothing else. Compounding does not make the Roth better; it only makes whatever the rate gap already decided more expensive.

The contribution is a pre-tax figure, and the Roth side of the page taxes it before the money goes in. That is the honest way to compare the two accounts, but it means the field is not asking how much you transfer into a Roth — a real Roth contribution is made out of income you have already paid tax on, and the amount that lands is the after-tax part of what you enter here. The eligibility rules for contributing to a Roth at all are not modelled. Direct Roth contributions are limited by modified adjusted gross income and phase out above a threshold, and the annual contribution ceiling applies to the two account types together rather than separately; the IRS pages in the references have the current figures. This page assumes you may contribute and asks only what happens if you do. The freedom from required distributions on a Roth is real and is not in the arithmetic. A traditional IRA must begin distributing at a set age whether or not you want the money, so its balance cannot compound untouched indefinitely, while a Roth can — this makes the difference shown here a lower bound on the Roth's advantage, though by how much depends on what you would have done with a forced distribution. The existing balance is treated as pre-tax on both sides. If part of it is already a Roth balance, the page overstates the tax that will be paid on it. A single rate now and a single rate later stands in for a lifetime of progressive brackets, and state and local tax is ignored entirely — in places where the two account types are treated differently at the state level, the direction of the answer can differ from the federal one shown here. The additional tax on early distributions is not modelled on either side, and neither is the qualified-distribution requirement: this page assumes the withdrawal is a qualified one, and an unqualified Roth distribution can be taxed and penalised in ways that would erase the advantage shown.

Are the two accounts really identical when the tax rates match?

Yes, to the cent, and the arithmetic is not close — it is exact. Paying tax on the way in means multiplying the balance by (1 − rate) before it grows; paying on the way out means growing it first and multiplying by (1 − rate) afterwards. Multiplication commutes, so twenty-five years of compounding cannot prefer either order. Anyone who tells you the Roth wins because of tax-free growth is describing a real feature of the account and drawing a conclusion from it that the arithmetic does not support.

Then why does anyone say a Roth is better?

For three reasons that this page either computes or cannot. The one it computes is a rate gap: if your rate at retirement is lower than it is now, the traditional account wins by exactly that gap times the balance, and if it is higher the Roth wins by the same amount. The ones it cannot compute are that a Roth has no required distributions, so it can keep compounding where a traditional account is forced to pay out, and that a Roth's balance is more predictable because its tax has already been settled. Both are real; neither is a reason to expect the Roth to win on equal rates.

What counts as a qualified distribution?

This page assumes the withdrawal is qualified and does not test it. The conditions involve how long the account has been held and what event the money is being withdrawn for, and both the Roth IRA page and Publication 590-B in the references set them out. It matters because an unqualified distribution can be taxed and carry an additional tax, which would wipe out the advantage shown here — so a Roth's number is only as good as the assumption that you leave it alone until it qualifies.

What exactly am I entering in the contribution field?

Pre-tax income — the gross amount you are committing to retirement, before any tax is taken. The Roth side of the page then subtracts the tax from it and invests the rest, which is what actually happens to a Roth contribution. So the figure is not the amount that appears in your Roth account. If you entered the after-tax amount instead, the page would be comparing a pre-tax figure against an after-tax one, and the difference it reported would be an artefact of that mismatch rather than a fact about the accounts.

Does this model the income limits on Roth contributions?

No. Whether you may contribute directly to a Roth depends on your modified adjusted gross income, and the ability phases out above a threshold; the annual contribution ceiling also applies across both account types rather than separately. The IRS pages in the references have the current numbers. This page takes any contribution you enter, because eligibility is a different question from what a contribution becomes once it is in.

Does a Roth have required distributions?

No, and that is a genuine advantage this page cannot put a number on. A traditional IRA must start distributing at a set age whether or not you need the money, so its tax bill arrives on a schedule you do not control; a Roth is not subject to that while the owner is alive. The effect is to make the difference computed here a lower bound on the Roth's advantage — but the size of the effect depends on what you would have done with a distribution you were forced to take, which is a decision rather than an input.

How is this different from the IRA calculator?

That page follows one account; this one follows two from the same starting point, which is the only way the choice between them can be seen. Its central output is what a traditional IRA is worth after tax, and it is a good page for that. But a single account cannot show you that the two are identical at equal rates, because the identity only appears when both sides are computed — and that is the one fact most people arrive at this decision without.

• Roth IRAs — the account's own rules: contributions are made with after-tax money, qualified distributions are not taxed, and the income limits that decide who may contribute directly — Internal Revenue Service (United States)
• Publication 590-B (2025), Distributions from Individual Retirement Arrangements (IRAs) — what makes a distribution qualified, how a traditional IRA distribution is taxed as ordinary income, and the additional tax on early distributions — Internal Revenue Service (United States)
• Retirement plan and IRA required minimum distributions FAQs — the source for the one asymmetry this page cannot compute: the RMD rules do not apply to Roth IRAs while the owner is alive — Internal Revenue Service (United States)
• Planning for retirement — what the money is for, and why the account type is one of the smaller decisions in it; the consumer-facing version of the trade-off this page computes — Consumer Financial Protection Bureau (United States)
• 关于个人养老金有关个人所得税政策的公告 (Announcement No. 34 of 2022 on the individual income tax policy for private pensions, Ministry of Finance and State Taxation Administration, China; issued 3 November 2022) — the China-side analogue of the same three-stage shape: contributions deducted against income up to an annual ceiling, no individual income tax during the investment period, and the withdrawal taxed separately at 3% rather than added to comprehensive income — Ministry of Finance and State Taxation Administration, China