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.
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: GST on imports 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.
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.
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.
Sources and verification
Last full check: 28 August 2026. This page was matched to IRD calculating your GST, charging GST, GST guide IR375, and the Goods and Services Tax Act 1985 on legislation.govt.nz.
GSTCalc.nz is a free New Zealand publisher of tax calculators and guides. Ads may fund the site. We are not Inland Revenue and this is not tax advice. Figures are working papers. Publisher details: About us and Contact. Privacy: Privacy policy.