Gross-Up Calculator
↻ Updated 2026Work backwards from a net amount to the gross payment required to cover tax — the method employers use for relocation packages and tax-free bonuses.
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How to read a gross-up
Delivering $5,000 net at a 30% tax rate costs $7,142.86, not $6,500. The extra $642.86 is the answer to the question that makes gross-ups counter-intuitive: the money you add to cover the tax is itself taxable, so it needs covering too.
How to work backwards from a net amount to the gross
One division, and the whole difficulty is in believing it. To deliver a net amount N when a rate t will be withheld, you pay N ÷ (1 − t). Not N × (1 + t).
The reason is circular and that's precisely the point. Pay someone extra to cover their tax, and that extra is wages — so it's taxed too, and now there's a shortfall on the top-up. Top that up and the same thing happens again, smaller each time. Dividing by (1 − t) is the closed-form answer to that infinite regress: it's what the series converges to.
gross = net ÷ (1 − tax rate) tax withheld = gross − net check: gross × (1 − tax rate) = net the wrong way: gross = net × (1 + tax rate) ← always short
- net
- The exact amount the recipient must end up with — the promise you're working backwards from — a relocation allowance, a sign-on bonus, a referral payment
- tax rate
- The combined rate that will be withheld from the payment — federal supplemental (22% under $1M) + FICA (7.65%) + any state rate — 29.65% is the common US floor
- gross
- What the employer actually pays — net ÷ (1 − rate); always more than net + tax-on-net
- tax withheld
- Gross minus net — the employer's real cost of the gross-up — $2,142.86 on the defaults, to deliver $5,000
Watch the factor rather than the rate. At 30% the multiplier is 1 ÷ 0.7 = 1.4286, so every $1 of net costs $1.43. At 40% it's 1 ÷ 0.6 = 1.6667, and each $1 of net costs $1.67. At 50% it's exactly 2.00 — a dollar in hand costs two. The cost curve is a hyperbola, not a line, which is why relocation budgets get away from companies at high combined rates and why gross-ups of six-figure packages are negotiated so carefully.
The formula assumes the withholding is a flat percentage of the payment, which is exactly true for a US bonus withheld under the IRS percentage method and only approximately true otherwise. Progressive brackets, the Social Security wage base and the additional Medicare tax all make the real effective rate move with the size of the payment — see the limitations below. For the ordinary direction of travel, the take-home paycheck calculator starts from gross and works down.
Worked examples
Example: delivering exactly $5,000 net at a 30% tax rate
The calculator's defaults. An employer has promised an employee $5,000 in hand — a relocation allowance, say — and 30% will be withheld.
| Desired netthe promise | $5,000 |
| Combined tax ratefederal supplemental + FICA + state | 30% |
| Gross-up factor1 − 0.30 | ÷ 0.70 |
| Required gross payment$5,000 ÷ 0.70 | $7,142.86 |
| Tax withheld30% of $7,142.86 | $2,142.86 |
| Net delivered$7,142.86 × 0.70 — exactly on target | $5,000.00 |
$7,142.86 to hand over $5,000. The tax withheld — $2,142.86 — is 30% of the gross but 43% of the net, and that second number is the one a budget holder feels. Delivering $5,000 tax-free costs 43% more than $5,000, and at higher rates the gap widens sharply.
Example: the additive method, and the $450 hole it leaves
The intuitive approach: take $5,000, add 30% for tax, pay $6,500. Watch what the employee actually receives.
| Desired netunchanged | $5,000 |
| Additive 'gross-up'$5,000 + 30% of $5,000 | $6,500 |
| Tax withheld (30%)30% of $6,500, not of $5,000 | − $1,950 |
| Actually delivered$450 short of the promise | $4,550 |
| Correct gross$642.86 more than the additive answer | $7,142.86 |
The additive method lands $450 short — 9% of what was promised. The error is that the $1,500 added to cover tax was itself taxed at 30%, costing $450 that nobody budgeted for. This is the single most common payroll mistake in gross-ups, and it scales: at a 40% rate the same additive shortcut delivers $4,200 against a $5,000 promise.
Frequently asked questions
How do you gross up a bonus?
Divide the net you want to deliver by one minus the combined tax rate. For $5,000 net at 30%: $5,000 ÷ 0.70 = $7,142.86. Withhold 30% of that and exactly $5,000 lands.
The combined rate is where the judgement lies. For a US bonus under $1 million, federal supplemental withholding is a flat 22% (IRS Pub 15) and FICA is 7.65%, giving 29.65% before any state tax — which is why this calculator's 30% default is roughly the no-state-tax case. Delivering $5,000 net at 29.65% costs $7,107.32.
Why can't you just add the tax rate to gross up?
Because the money you add is wages, and wages are taxed. Add 30% to $5,000 and you get $6,500 — but the withholding is 30% of $6,500, which is $1,950, not the $1,500 you budgeted. The employee receives $4,550.
Chasing it doesn't help: top up the $450 and 30% of that is taxed too, leaving $135 short, then $40.50, and so on. That series converges to $7,142.86, which is exactly what $5,000 ÷ 0.70 gives you in one step. The division isn't a trick — it's the sum of the infinite top-ups, solved.
Is relocation reimbursement taxable income?
For almost everyone, yes. The Tax Cuts and Jobs Act suspended the moving-expense exclusion and deduction, and later legislation made the repeal permanent for civilians — so employer-paid relocation, whether it's reimbursed to you or paid directly to a moving company on your behalf, is wages in Box 1 of your W-2, subject to income tax and FICA.
Active-duty members of the armed forces moving under military orders remain the main exception, along with certain intelligence-community personnel. Everyone else's 'relocation package' is a taxable bonus with a specific purpose attached, which is exactly why gross-ups became standard practice in relocation — without one, a $10,000 moving allowance is a $7,000 moving allowance.
What is a tax gross-up on a relocation package?
It's the employer paying the tax on your relocation benefit so that the benefit arrives whole. Because relocation is taxable wages, a $5,000 allowance nets about $3,500 after withholding — the gross-up pays $7,142.86 instead, at a 30% rate, so that $5,000 actually reaches you.
The employer's cost is the interesting part: they're buying $5,000 of benefit for $7,142.86, a 43% premium. Practice varies — some employers gross up the whole package, some only the taxable components, some cap the gross-up at a fixed figure and let the employee absorb the rest. The number this page produces is the full gross-up. The FICA calculator covers the 7.65% component that applies no matter which state the move ends in.
Where a flat-rate gross-up stops being exact
The division is exact for a flat withholding rate. Real US payroll isn't flat, and the differences all push the same way: the rate you should have used isn't the rate you entered.
- One rate for everything — Federal supplemental withholding is genuinely flat at 22% under $1 million, so the formula holds well there. Nothing else is: state rates vary, several states set their own supplemental rate, and local income taxes don't appear at all. The answer is exactly as good as the rate you entered.
- The Social Security wage base isn't modelled — FICA is only 7.65% until wages reach $184,500, after which the 6.2% Social Security component stops and the marginal rate falls to 1.45%. Gross up a bonus for someone who has already crossed the base and this page overstates the required gross — the true combined rate on their payment is 6.2 points lower.
- The additional Medicare tax runs the other way — Above $200,000 for a single filer ($250,000 married filing jointly, $125,000 married filing separately), an extra 0.9% applies. For high earners the real combined rate is higher than a naive 29.65%, and the gross-up understates.
- Withholding isn't the tax — A gross-up delivers the net after withholding, which is not the same as making the payment tax-neutral over the year. If the employee's real marginal rate is 32%, a gross-up computed at 22% federal leaves them owing at filing on a payment they were told was tax-free — a distinction relocation policies frequently get argued over.
- Grossed-up pay is still pay — The full $7,142.86 is wages: it appears on the W-2, counts toward the wage base, and can affect income-tested calculations elsewhere on a return. The employee received $5,000 and is taxed on $7,142.86 having been credited with the withholding.
- ·IRS Publication 15 (Circular E) — Employer's Tax Guide — Supplemental-wage withholding and payroll tax rules
- ·IRS Topic 751 — Social Security & Medicare withholding rates
Rates, brackets and limits here are checked against primary sources. If a number still looks off, email support@realmoneyiq.com and we'll review and fix it.
RealMoneyIQ provides free educational calculators, not financial, tax, investment or legal advice. Results are estimates based on the assumptions you enter and publicly published rates; your actual outcome will differ. Always confirm decisions with a licensed professional who knows your full situation.