Everyday Percentage Math: Discounts, Markups, Percentage Changes, and Tips
Deconstruct $(B - A)/A \times 100$, consecutive percentage discount fallacies (30% + 20% ≠ 50%), gross margin vs markup, and mental calculation tricks.
Learn the mathematical difference between adding tax and extracting tax, reverse VAT formulas, multi-tier tax brackets, and invoice compliance.
Finance & Math technical reference asset
Value-Added Tax (VAT) and Goods and Services Tax (GST) are destination-based consumption taxes levied on goods and services in over 160 countries worldwide, including the EU, UK, Canada, Australia, Singapore, and India.
For business owners, freelancers, and consumers, knowing how to accurately add tax to a quote or reverse-calculate the pre-tax base price from a total receipt is essential for correct bookkeeping.
• Tax-Exclusive Price (Net Price): The base price of the item before any tax is added. B2B wholesale transactions are typically quoted exclusive of tax.
• Tax-Inclusive Price (Gross Price): The final checkout price that includes all applicable GST/VAT. Consumer retail prices (such as on supermarket shelves) are legally required to be displayed inclusive of tax in most jurisdictions.
To calculate the tax amount and total gross price from a net amount:
GST Amount = Net Price * (Tax Rate / 100)
Gross Price = Net Price + GST Amount
= Net Price * (1 + Tax Rate / 100)
Example ($500 base price at 18% GST):
GST Amount = 500 * 0.18 = $90.00
Gross Total = 500 + 90 = $590.00When you receive a total invoice of $590 and need to determine the original pre-tax base price and the tax paid:
Net Price = Gross Price / (1 + Tax Rate / 100)
GST Amount = Gross Price - Net Price
= Gross Price * [Tax Rate / (100 + Tax Rate)]
Example ($590 total receipt at 18% GST):
Net Price = 590 / (1 + 0.18) = 590 / 1.18 = $500.00
GST Amount = 590 - 500 = $90.00A very frequent accounting mistake is attempting to extract 18% tax from $118 by simply calculating $118 \times 0.18 = $21.24$, and subtracting: $118 - 21.24 = $96.76$.
This is mathematically incorrect because the 18% tax was originally added to the base price of $100 ($18 tax), not the final $118 total. Always divide by `1 + (Rate / 100)` to find the true base.
In a GST system, businesses claim Input Tax Credits on the tax paid for business purchases (laptops, software subscriptions, office rent) against the tax collected from client sales, paying only the net difference to the government.
Calculate inclusive and exclusive GST, VAT, and sales tax in seconds with Softnag’s GST Calculator.
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