Net To Gross Calculator

Which way the percentage points

Look at the label on the second box. It says percentage tax (from net), and that parenthesis is doing a lot of work.

It means the rate you type is a percentage of the net amount, applied on top of it. Net 100 at 20 percent gives you 20 of tax and a gross of 120.

That is how value added tax, goods and services tax and sales tax all work. The rate sits on top of a price that was quoted without it.

It is not how income tax works. Income tax rates are a share of the gross, taken out of it. If your rate is 20 percent of gross and you take home 100, your gross was 125, not 120.

Two conventions, both called a percentage tax, running in opposite directions. This calculator does the first one. The section below on the other kind tells you how to handle the second, and why the gap between them is bigger than it looks.

Two boxes, three answers

1. Net amount. The figure before tax is added. On an invoice this is the price you actually charge for the work.
2. Percentage tax (from net). The rate applied to that net figure. Twenty for a standard UK VAT rate, thirteen for Nepali VAT, eighteen for a common Indian GST slab.

You get back three things.

Gross amount is the total, net plus tax, which is what the customer pays.

Tax amount is the money itself, which is the figure that goes on the tax line of an invoice and eventually to the revenue authority.

Percentage tax (from gross) is the same tax expressed as a share of the total instead of a share of the net. It is the least obvious of the three and the most useful, and it gets its own explanation below.

Adding it on, then looking back

Two steps forward, one step back.

Tax = net × rate ÷ 100

Gross = net + tax

Then the third result asks a different question about the same two numbers:

Rate on gross = tax ÷ gross × 100

That last figure is always smaller than the rate you typed, because it divides the same tax by a bigger number. And it is genuinely useful, because it is the number you need whenever you are working backwards from a total.

Twenty percent on the net comes out as 16.667 percent of the gross. Anyone who has done UK bookkeeping will recognise that as the VAT fraction of one sixth: to pull the tax out of a VAT inclusive total at the standard rate, you divide by six.

This is also where the most common tax arithmetic mistake lives. Given a gross of 120 that includes 20 percent VAT, people take 20 percent off it, get 96, and are wrong. The tax was never 20 percent of 120. It was 20 percent of 100.

The result is printed to five decimal places, which looks excessive until you notice that several of these fractions do not terminate. Sixteen point six six seven recurring is the honest answer to a very common rate.

A hundred at twenty percent

Net 100, rate 20 percent.

• Tax: 100 × 20 ÷ 100 = 20.00
• Gross: 100 + 20 = 120.00
• Rate on gross: 20 ÷ 120 = 16.667 percent

A few common rates, so you can see the second column diverge from the first:

The two columns start close and separate as the rate climbs. At 5 percent the difference is a quarter of a point. At 30 percent it is nearly seven.

Which is why the distinction matters more the higher the rate. On small percentages you can be sloppy and stay roughly right. On large ones you cannot.

The other kind of gross up, and how to spot it

Now the important part, because using this tool for the wrong kind of tax gives you an answer that is confidently wrong.

When a deduction is taken out of a larger figure rather than added on top, the rate is a share of the gross. Income tax withholding works this way. So do most statutory payroll deductions.

If you want to work backwards from a net to a gross under that convention, the formula is a division rather than an addition:

Gross = net ÷ (1 - rate ÷ 100)

On a net of 100 at 20 percent, that is 100 divided by 0.80, which is 125, with 25 of tax.

Compare that with the 120 this calculator returns. Same net, same headline percentage, five units apart, and the gap widens fast:

At a 30 percent rate the added-on-top answer is 9 percent short of the taken-out-of-gross one. On a payroll gross up that is a real shortfall in somebody's pay packet.

Here is the useful part though. You can still use this calculator for the payroll direction, you just have to convert the rate first, and the conversion is the third output on this page.

A rate of 20 percent of gross is a rate of 25 percent of net. Enter 25 here and you get a gross of 125 with 25 of tax, which is the correct payroll answer, and the third result will read back 20 percent of gross, confirming it.

The two conversions, so you have them both:

Rate on net = rate on gross ÷ (1 - rate on gross)

Rate on gross = rate on net ÷ (1 + rate on net)

A word of caution on real payroll, though. Actual take home pay is rarely one flat percentage. Progressive bands, allowances, thresholds and separate social security contributions mean the effective rate on the last unit of pay is not the effective rate on the whole. A single rate gross up is a reasonable estimate for a bonus inside one band and a poor model for a whole salary.

You have met this arithmetic before

Look at those two conversion formulas again and something might feel familiar.

Rate on gross = rate on net ÷ (1 + rate on net)

Now here is the relationship between markup and margin in retail pricing:

Margin = markup ÷ (1 + markup)

Identical. Not similar, identical.

Which is not a coincidence. Both are the same question in different clothing: I have a percentage measured against the smaller of two numbers, and I want it measured against the larger.

In pricing, the smaller number is the cost and the larger is the selling price. Markup divides by cost, margin divides by price. In tax, the smaller is the net and the larger is the gross.

So a 20 percent markup gives a 16.67 percent margin, and a 20 percent tax on net is 16.67 percent of gross. Same fraction, same reason.

Worth knowing because it means the intuition transfers. Anyone who has internalised that markup is always the bigger number will find the tax version obvious, and vice versa. If it helps, the margin calculator prints both percentages side by side for the pricing version of the same problem.

Which convention belongs where

A short guide to which side of the line you are on.

Added on top, so use this calculator directly:

• Value added tax and goods and services tax, everywhere they apply. VAT is charged on the net price, then added.
• Sales tax on a quoted pre-tax price.
• Service charges and levies expressed as a percentage of the bill before them.
• Any invoice where you have set your fee and the tax goes on afterwards.

Taken out of the total, so convert the rate first:

• Income tax withholding on wages.
• Statutory payroll deductions such as social security and provident fund contributions.
• Withholding tax on contractor or professional payments.
• Any deduction quoted as a percentage of the gross figure.

The quickest test when you cannot tell: ask what the percentage is being applied to. If it is applied to the smaller figure and then added, this tool does it directly. If it is applied to the larger figure and then subtracted, convert first.

And if you are on the invoicing side, keep the sanity check simple. Your gross should always equal net plus tax, and your tax as a share of gross should always be less than your headline rate. If either fails, one of the two numbers is on the wrong basis.

Questions people ask

Is the percentage taken from the net or the gross?

From the net. The rate you type is applied to the net figure and added on top, which is how VAT, GST and sales tax work. The third result then shows what that same tax is as a share of the gross.

How do I convert net to gross?

Multiply the net by the rate to get the tax, then add it. Net 100 at 20 percent gives 20 of tax and a gross of 120.

Can I use this for take home pay?

Not directly, because income tax is a share of the gross rather than something added to the net. Convert the rate first: divide it by one minus itself. A 20 percent rate of gross becomes 25 percent of net, and entering 25 gives the correct gross of 125.

Why is the percentage from gross lower than the one I entered?

Because it divides the same tax by a larger number. Twenty on 100 is 20 percent, and the same 20 on a gross of 120 is 16.667 percent.

What is the VAT fraction?

The share of a tax inclusive total that is tax. At a 20 percent rate it is 16.667 percent, or one sixth, which is why UK bookkeepers divide a gross figure by six to extract the VAT.

Why can I not just take 20 percent off a gross figure?

Because the tax was 20 percent of the net, not of the gross. Taking 20 percent off 120 gives 96, which was never the net amount. Divide by 1.20 instead, or use the from-gross percentage this tool returns.

Does the difference between the two conventions matter much?

It grows with the rate. At 10 percent the two methods differ by about 1 on a net of 100. At 30 percent they differ by nearly 13, which is 9 percent of the correct figure.

Is this related to markup and margin?

It is the identical piece of arithmetic. Converting a rate on net to a rate on gross uses exactly the formula that converts a markup into a margin, because both move a percentage from the smaller base to the larger one.

References

The convention of applying a rate to a net figure and adding it to reach a gross total is how value added tax and goods and services tax operate, and it produces the tax-inclusive fraction used to extract tax from a gross amount. The contrasting convention, where a rate is applied to the gross and withheld from it, is how employment tax withholding operates, as set out in the Internal Revenue Service's employer guidance. The relationship between a percentage measured against the smaller base and the same percentage measured against the larger one is the same relationship that holds between markup and gross margin, and follows the treatment published by the US Chamber of Commerce and the Corporate Finance Institute, with gross profit defined as receipts less cost of goods sold in IRS Publication 334.

1. Internal Revenue Service, Publication 15 (Circular E), Employer's Tax Guide. https://www.irs.gov/publications/p15
2. US Chamber of Commerce, Pricing Markups Explained: Definition and Similar Terms. https://www.uschamber.com/co/start/strategy/what-are-pricing-markups
3. Corporate Finance Institute, Markup: How to Calculate Markup and Markup Percentage. https://corporatefinanceinstitute.com/resources/accounting/markup/
4. Internal Revenue Service, Publication 334: Tax Guide for Small Business. https://www.irs.gov/publications/p334