GST maths NZ: add, remove, and the 3÷23 formula
New Zealand GST is 15% on most taxable supplies. The maths is three moves: add GST to an exclusive price, split GST out of an inclusive total, or find the exclusive amount left after tax. Inland Revenue (IRD) publishes the same methods in GST guide IR375 and on its calculating your GST page.
This guide is for beginners reading the GST Basics Guide who want the formulas, not just a button. Worked examples, a quick reference table, and practice questions follow IRD for the 2026/27 year (1 April 2026 to 31 March 2027). GSTCalc.nz is not IRD and this is not tax advice.
What GST means in maths (not geometry)
GST stands for Goods and Services Tax. In a New Zealand business or school commerce context, GST maths means calculating tax on money amounts. It is not the geometry term for straight lines meeting at a point.
Once you are GST registered you use these sums on invoices, receipts, and returns. Registration rules sit in the GST Basics Guide and how to register for GST in NZ. When you just need a fast answer, the free GST calculator on the homepage runs the same IRD maths in your browser.
Exclusive vs inclusive: the two price types
Every GST sum starts by naming which number you hold.
- GST exclusive: the price before 15% tax. IRD’s adding example uses $100 for headphones with no GST yet.
- GST inclusive: the price the customer pays when GST is already inside the total. IRD’s removing example uses $115 inclusive.
- GST amount only: the tax part, often shown on a tax invoice or in Box 5 style thinking before you file.
On IRD charging GST, a registered business either adds GST on top of its prices ($100 plus GST equals $115) or treats the price received as already including GST (where $100 inclusive contains 3/23 of $100, or $13.04, as GST). The fraction method works whenever the total already includes the standard 15% rate.
GST maths formula quick reference
| You want to | Formula (15% rate) | IRD example |
|---|---|---|
| Add GST to an exclusive price | Exclusive × 1.15 or Exclusive × 0.15, then add |
$100 × 0.15 = $15 → $115 inclusive |
| Find GST inside an inclusive price | Inclusive × 3 ÷ 23 | $115 × 3 ÷ 23 = $15 GST |
| Find exclusive from inclusive | Inclusive ÷ 1.15 or Inclusive minus GST from 3÷23 |
$115 minus $15 = $100 exclusive |
Source: IRD calculating your GST and GST guide IR375. Round money answers to the nearest cent unless IRD asks otherwise on a specific form.
How to add GST in maths
To add GST, multiply the exclusive amount by the rate. At 15% you can use 0.15 or divide by 100 then multiply by 15. Then add that GST to the exclusive price.
GST: $250.00 × 0.15 = $37.50
Inclusive price: $250.00 + $37.50 = $287.50
Shortcut: $250.00 × 1.15 = $287.50
That matches IRD’s headphone example: $100 exclusive, $15 GST, $115 inclusive. Use the GST invoice generator when you need a PDF that shows exclusive, GST, and inclusive lines together.
How to find GST in an inclusive price (3÷23)
When the total already includes GST, multiply by 3 and divide by 23. IRD recommends this over “divide by 1.15 then subtract” for finding the GST component because the fraction stays exact on paper.
GST: $115.00 × 3 ÷ 23 = $15.00
Exclusive: $115.00 minus $15.00 = $100.00
That is the full IRD “Arthur and Hine” worked example on calculating your GST. The same steps appear in IR375.
Where the 3÷23 fraction comes from
The GST part of an inclusive price is not “15% of the total”. It is 15% of the hidden exclusive base. As a share of the inclusive total:
So GST equals inclusive × 3 ÷ 23. Dividing an inclusive price by 1.15 to get the exclusive amount is still valid. It is the same mathematics rearranged. IR375 prefers 3÷23 for the GST line because long division by 1.15 invites rounding drift unless you keep enough decimal places.
Work back from the GST amount alone
If you only know the GST figure on a receipt or tax invoice, you can rebuild the prices around it. The GST exclusive price is the GST amount times 100 divided by 15. The GST inclusive total is the GST amount times 115 divided by 15.
Worked example. A receipt shows a GST line of $34.50 but no other breakdown.
GST inclusive total: $34.50 × 115 ÷ 15 = $264.50
Check: $264.50 × 3 ÷ 23 = $34.50 GST
One more shortcut for pen and paper work. Starting from a GST exclusive price, the GST is that price times 3 divided by 20, sometimes called the 3/20 rule. It is the mirror of 3÷23, which starts from a GST inclusive total.
Check: $140.00 × 0.15 = $21.00
IRD sets out the 3 divided by 23 extraction formula in the GST return instructions and in GST guide IR375. The rate is 15 percent for the 2026/27 tax year.
Why subtracting 15% from the total is wrong
A common GST maths mistake is taking 15% off an inclusive price and calling that the GST. That calculates 15% of the wrong base.
Wrong exclusive: $115.00 minus $17.25 = $97.75 (not $100.00)
Right: $115.00 × 3 ÷ 23 = $15.00 GST
The error shows up when bookkeepers “remove GST” with a flat 15% discount on receipts. Always check whether the starting number is exclusive or inclusive first. More traps are listed in 10 common GST mistakes in NZ.
Worked GST maths examples
| Exclusive | GST (× 0.15) | Inclusive (× 1.15) | Check: inclusive × 3 ÷ 23 |
|---|---|---|---|
| $50.00 | $7.50 | $57.50 | $7.50 |
| $200.00 | $30.00 | $230.00 | $30.00 |
| $1,000.00 | $150.00 | $1,150.00 | $150.00 |
| $2,000.00 | $300.00 | $2,300.00 | $300.00 |
Large purchase? A $2,300 inclusive invoice contains $300 GST under 3÷23. That is the input tax you may claim if the supply is taxable and you hold taxable supply information. Import border maths uses a different calculator: import duty calculator.
GST maths practice questions and answers
Use these as a mini worksheet. Round to the nearest cent.
Question 1: Add GST
A tradie quotes $480.00 exclusive for labour. What is the GST inclusive price?
Answer: GST = $480.00 × 0.15 = $72.00. Inclusive = $480.00 × 1.15 = $552.00.
Question 2: Find GST only
A receipt total is $57.50 inclusive. How much of that is GST?
Answer: $57.50 × 3 ÷ 23 = $7.50 GST.
Question 3: Find the exclusive amount
An invoice total is $1,150.00 inclusive. What is the pre tax price?
Answer: GST = $1,150.00 × 3 ÷ 23 = $150.00. Exclusive = $1,150.00 minus $150.00 = $1,000.00. Check: $1,150.00 ÷ 1.15 = $1,000.00.
Question 4: Spot the wrong method
A student says GST on $230.00 inclusive is $34.50 because 15% of $230.00 is $34.50. What should the GST be?
Answer: Correct GST = $230.00 × 3 ÷ 23 = $30.00. The student subtracted 15% of the inclusive price, not the GST component.
Question 5: Net GST on a return (simple)
In one two monthly period you collected $900 GST on sales and paid $400 GST on expenses. How much GST is payable?
Answer: Output tax $900 minus input tax $400 = $500 payable. myIR does this aggregation when you file. Step by step filing is in how to file your GST return in myIR.
GST maths on expenses and mixed business use
GST registered businesses run the same formulas on supplier receipts as on sales. The GST you pay on purchases is called input tax. The GST you collect from customers is called output tax. On the return, input tax is subtracted from output tax to get the net GST for the period.
Worked example. You buy a laptop for $1,150.00 GST inclusive and use it fully for the business.
That $150 is claimed as an input tax credit on the return, reducing the net GST you owe.
If an expense is partly business and partly personal, you may only claim the business share. Work the full GST with 3÷23 first, then multiply by the business percentage. IRD confirms this on its calculating GST page.
Total GST: $230.00 × 3 ÷ 23 = $30.00
Claimable: $30.00 × 0.60 = $18.00
If the input tax for the period is bigger than the output tax, the difference comes back to you as a refund rather than a payment. Example: you collected $1,500 GST on sales and paid $1,800 GST on expenses, so IRD owes you a $300 refund for the period.
Supplies where the 15 percent maths does not apply
Skip the 15 percent formulas entirely for zero rated and exempt supplies. These have no 15 percent to add, and running the maths on them creates wrong invoice figures.
Zero rated supplies are charged at 0 percent GST, but the supplier can still claim input tax credits on related expenses. Typical examples are exported goods, going concern sales, international transport, and certain land transactions. Zero rating is covered in sections 11 and 11A of the Goods and Services Tax Act 1985.
Exempt supplies have no GST charged at all, and the supplier cannot claim input tax credits on related expenses. Typical examples are residential rent and most financial services.
The practical test before any GST sum: is this a standard taxable supply at 15 percent? If the answer is zero rated or exempt, no GST is added and no GST credit is claimed on that line.
When to do GST maths by hand vs calculator
Manual maths helps you sanity check supplier invoices and train staff. A calculator or accounting software is faster at scale. IRD says most people file in myIR, which calculates the return totals once you enter your figures. You still need to understand add vs remove so Box entries and taxable supply information make sense.
Accounting basis (invoice vs payments) changes when GST hits the return, not the 15% formulas. Compare bases in invoice basis vs payments basis. Secondhand goods from private sellers use the same 3÷23 fraction for a special credit: see GST on second hand goods NZ.
GST formulas for Excel and Google Sheets
The core GST formulas drop straight into Excel or Google Sheets with cell references, so one column of amounts can generate the full breakdown. Assume the amount sits in cell A1.
- Add GST to a GST exclusive price:
=A1*0.15gives the GST,=A1*1.15gives the GST inclusive total - GST inside a GST inclusive total:
=A1*3/23gives the GST amount - GST exclusive from a GST inclusive total:
=A1/1.15 - GST exclusive from the GST amount alone:
=A1*100/15 - GST inclusive total from the GST amount alone:
=A1*115/15 - GST on hourly work: hourly rate in A1, hours in B1, use
=A1*B1*0.15
Spreadsheet tip: wrap invoice figures in ROUND to keep cents clean, for example =ROUND(A1*1.15,2). This avoids the long decimals that appear when you divide by 1.15 directly.
The 10 percent plus 5 percent mental maths trick
For a quick check without a calculator, work 15 percent as 10 percent plus half again, which is 5 percent. Ten percent is easy: move the decimal point one place left.
Ten percent is $115.00. Half of $115.00 (5 percent) is $57.50.
Add them: $115.00 + $57.50 = $172.50 GST
Check: $1,150.00 × 0.15 = $172.50
For removing GST mentally, 3÷23 works on friendly totals too. Example: $230.00 inclusive. Divide by 23 to get $10, times 3 to get $30 GST. Round money answers to the nearest cent when the total is not friendly.
How to quote and display prices: GST inclusive or GST exclusive
Always state clearly whether your quote is GST inclusive or GST exclusive, because the two numbers differ by 15 percent and confusion here causes invoice disputes. Only businesses registered for GST can add GST to their prices at all.
The NZ convention: prices shown to consumers are normally GST inclusive, so shoppers see the final price. Business to business quotes are often stated GST exclusive, with the GST line shown separately, because a GST registered buyer may reclaim that GST as input tax.
Worked example. A Wellington graphic designer quotes $3,000.00 GST exclusive for a branding project.
GST inclusive total: $3,000.00 × 1.15 = $3,450.00
Write the quote as: "$3,000 + GST ($3,450 total)"
Both price types are visible and nobody has to guess.
FAQs
What is the GST maths formula in New Zealand?
Add: exclusive × 1.15. Find GST in a total: inclusive × 3 ÷ 23. Find exclusive: inclusive ÷ 1.15.
Why 3÷23 and not divide by 7.666…?
3÷23 is the exact fraction form of 15÷115. It avoids rounding errors on cents.
What does GST stand for in maths?
Goods and Services Tax. In NZ business maths it is the 15% consumption tax on taxable supplies.
How do I find GST in maths from a total?
Multiply the inclusive total by 3, divide by 23, round to cents. IRD publishes this on calculating your GST.
Is the homepage calculator different from these formulas?
No. The homepage tool applies the same ×1.15 and 3÷23 rules. This guide explains the steps behind the tool.
How do I do GST maths in Excel?
Put the amount in a cell, say A1, and use =A1*1.15 to add GST to a GST exclusive price, or =A1*3/23 to extract the GST from a GST inclusive total. Wrap results in ROUND, for example =ROUND(A1*1.15,2), to keep cents clean on invoices. The same formulas work in Google Sheets.
I only know the GST amount. How do I find the price?
Multiply the GST amount by 100 then divide by 15 for the GST exclusive price, or multiply by 115 then divide by 15 for the GST inclusive total. For example, a $34.50 GST line sits on a $230.00 exclusive price and a $264.50 inclusive total.
Can I claim GST on an expense that is partly personal?
You can only claim the business use share. Work the full GST with 3÷23 first, then multiply by the business percentage. A $230 GST inclusive bill that is 60 percent business use contains $30 GST, so $18 is claimable. Fully personal expenses get no claim.