To calculate gross from net, divide the net amount by (1 minus the deduction rate). If you received $80 after a 20% deduction, the gross amount is $80 / (1 – 0.20) = $80 / 0.80 = $100. This single formula works whether you’re reversing taxes on a paycheck, backing out sales tax from a total price, or finding gross revenue from net profit figures. The key is knowing what rate was taken out.
The Core Formula
The gross-up formula is:
Gross = Net / (1 – deduction rate)
The “deduction rate” is whatever percentage was subtracted to arrive at the net figure, expressed as a decimal. A 25% tax rate becomes 0.25. A 7% sales tax becomes 0.07. Plug it in and divide.
This works because the net amount represents only the remaining percentage of the gross. If 20% was removed, the net is 80% of gross. Dividing the net by 0.80 reverses the math and recovers the original gross figure.
Why You Can’t Just Add the Percentage Back
A common instinct is to take the net amount and add the percentage on top. If you netted $1,000 after a 20% deduction, you might think the gross was $1,000 + 20% = $1,200. But that’s wrong. Twenty percent of $1,200 is $240, which would leave you with $960, not $1,000.
The correct calculation: $1,000 / (1 – 0.20) = $1,250. Check it: 20% of $1,250 is $250, and $1,250 – $250 = $1,000. The difference between $1,200 and $1,250 may seem small, but on larger amounts it grows quickly. On a $50,000 net figure, adding 20% gives you $60,000 while the correct formula gives you $62,500, a $2,500 gap.
Grossing Up a Paycheck
Employers use this formula when they want an employee to receive a specific take-home amount. If a company promises a $100,000 net relocation bonus and the combined tax rate on that payment is 20%, the company needs to pay $125,000 gross so that after $25,000 in taxes, the employee actually receives $100,000.
For payroll, the tricky part is determining the right deduction rate. A paycheck has multiple layers of withholding: federal income tax, state income tax (in most states), Social Security tax, and Medicare tax. To gross up accurately, you need to combine all applicable rates into a single total rate. If federal withholding is 22%, state tax is 5%, Social Security is 6.2%, and Medicare is 1.45%, the combined rate is 34.65%. Your formula becomes:
Gross pay = Net pay / (1 – 0.3465)
So if you want to take home $3,000 per paycheck and your combined rate is 34.65%, you’d need a gross of $3,000 / 0.6535 = approximately $4,592.
Keep in mind that federal income tax withholding isn’t a single flat rate for most people. It follows a bracketed structure, so the effective rate on your paycheck depends on your filing status, number of allowances, and income level. If you’re doing a rough estimate, use the rate shown on your most recent pay stub (total taxes withheld divided by gross pay) as a reasonable approximation.
Removing Sales Tax From a Total Price
If you have a receipt total that includes sales tax and you need the pre-tax price, the same formula applies. Say you paid $107 for something in a jurisdiction with a 7% sales tax. The pre-tax price is $107 / (1 + 0.07). Notice the sign flips here: with sales tax, the tax was added to the net price, not subtracted from a gross amount. So you divide by (1 + tax rate) instead of (1 – tax rate).
$107 / 1.07 = $100. The tax portion was $7, and the base price was $100.
This same approach works for value-added tax (VAT) in countries that include tax in the sticker price. If a product costs €120 including 20% VAT, the pre-tax price is €120 / 1.20 = €100.
Gross Revenue From Net Profit
In a business context, “gross” and “net” refer to different levels of a company’s income statement. Gross earnings equal total revenue minus the cost of goods sold (the direct costs of producing whatever the company sells). Net income is what remains after subtracting all additional expenses: rent, utilities, salaries, loan payments, taxes, and everything else.
If you know the net profit and want to find the gross revenue, you need to know the total expenses that were deducted. The relationship is:
Gross revenue = Net profit + Total expenses
This is simpler addition rather than the division formula, because business expenses aren’t a single percentage rate applied uniformly. They’re a collection of fixed and variable costs. If a business reported $200,000 in net profit and had $800,000 in total expenses (cost of goods, operating costs, taxes), gross revenue was $1,000,000.
To go from net income to gross profit specifically, add back the operating expenses, interest, and taxes, but not the cost of goods sold. Gross profit sits between total revenue and net income on the income statement, capturing only the direct production costs.
Quick Reference for Common Rates
- 10% deduction rate: Divide net by 0.90 (a $900 net = $1,000 gross)
- 15% deduction rate: Divide net by 0.85 (a $850 net = $1,000 gross)
- 20% deduction rate: Divide net by 0.80 (a $800 net = $1,000 gross)
- 25% deduction rate: Divide net by 0.75 (a $750 net = $1,000 gross)
- 30% deduction rate: Divide net by 0.70 (a $700 net = $1,000 gross)
- 35% deduction rate: Divide net by 0.65 (a $650 net = $1,000 gross)
When Multiple Deductions Apply Separately
Sometimes deductions aren’t all calculated on the same base amount. For example, one tax might be calculated on gross pay while another is calculated after a pre-tax retirement contribution is removed. In cases like these, you can’t simply add the rates together and use one division. You need to work backward through each deduction in reverse order.
Start with your net amount and reverse the last deduction that was applied. Then take that result and reverse the next deduction, working your way back up to the original gross. If your net pay of $2,800 had a 5% state tax applied after a 22% federal withholding, first reverse the state tax ($2,800 / 0.95 = $2,947.37), then reverse the federal ($2,947.37 / 0.78 = $3,778.68). This layered approach gives a more accurate result than combining rates when deductions are applied sequentially rather than simultaneously.