Understanding discount and tax interactions
The table below illustrates how different discount and tax rates interact, using a £100 base price. Values are rounded to two decimal places.
| Original price | Discount | Tax | Final price | You save |
|---|---|---|---|---|
| £100.00 | 10% | 0% | £90.00 | £10.00 |
| £100.00 | 20% | 0% | £80.00 | £20.00 |
| £100.00 | 10% | 20% | £108.00 | £10.00 |
| £100.00 | 30% | 20% | £84.00 | £30.00 |
| £100.00 | 50% | 10% | £55.00 | £50.00 |
| £100.00 | 0% | 20% | £120.00 | £0.00 |
- Tax ordering convention: this calculator applies the discount before the tax (discount first, tax second). This is the standard retail convention in most jurisdictions, including UK VAT and US state sales tax on discounted goods. In some B2B trade contexts, tax may be applied to the list price before a trade discount. If your situation uses a different ordering, the 'beforeTax' figure can serve as an intermediate reference.
- Stacked discounts: two successive discounts do not add arithmetically. A 20% discount followed by a further 10% discount gives a total reduction of 28% (not 30%), because the second discount is applied to the already-reduced price. This calculator applies a single composite discount entered by the user; to model stacked discounts, apply them sequentially with separate calculations.
- The 'youSave' figure represents the pre-tax monetary saving versus the original list price. It does not account for tax that would have applied to the full price. If comparing total out-of-pocket cost versus buying at the full taxed price, calculate: (original price × (1 + taxPct/100)) − (finalPrice).
- This calculator is for informational purposes only. Tax rules vary by jurisdiction, product type and purchaser category. Consult a tax professional for decisions requiring precise tax treatment.
What is a discount calculator?
A discount calculator automates the two-step arithmetic of reducing a price by a percentage and, optionally, adding a tax to the reduced amount. In retail and e-commerce, prices are commonly listed before tax; the discount is applied to the pre-tax list price, and tax is then calculated on the discounted amount. This is the convention followed here.
A discount is a percentage reduction from the list price. A 30% discount on a £120 item reduces the price by £36, yielding a pre-tax price of £84. If a 20% sales tax then applies, it is calculated on £84 (£16.80), giving a final price of £100.80. The saving versus buying at full list price plus tax is the difference between the taxed list price and the taxed discounted price.
The order in which discount and tax are applied affects the final price only if the tax base differs. In most retail jurisdictions, tax applies to the final selling price (after discount). In some business-to-business contexts, tax may apply before a trade discount is subtracted — this calculator follows the more common retail convention (discount first, then tax) and notes where this matters.
How to use this discount calculator
- Enter the original (list) price of the item. Use the currency selector if needed.
- Enter the discount percentage. For example, enter 30 for a 30% discount.
- If a sales tax applies to your purchase, enter the tax rate as a percentage (e.g. 20 for 20% VAT or 8.5 for an 8.5% state sales tax). Leave this at 0 if there is no applicable tax.
- Read the final price after discount and tax, the amount saved compared with the full list price (before tax), and the post-discount, pre-tax price.
How the discount and tax calculation works
The calculation proceeds in two steps. First, the discount is applied to the original price by multiplying the price by (1 − discount/100). A 30% discount on £120 gives £120 × (1 − 0.30) = £120 × 0.70 = £84. This is the 'beforeTax' result shown by the calculator.
Second, if a sales tax rate is specified, it is applied to the discounted price: discounted price × (1 + taxPct/100). At a 20% tax rate, £84 × 1.20 = £100.80. This is the 'finalPrice'. The saving ('youSave') is the undiscounted list price minus the discounted pre-tax price: £120 − £84 = £36. Note that 'youSave' does not deduct any tax that would have been payable on the full list price; it represents the pre-tax reduction in price.
If tax were applied before the discount (a different convention), the arithmetic would differ. Applying 20% tax to £120 first gives £144, then a 30% discount gives £100.80 — the same final price in this case, but this will not always be true and the convention varies. This calculator uses the retail-standard 'discount first, then tax' order.
Câu hỏi thường gặp
How do I calculate a discounted price?
Multiply the original price by (1 − discount ÷ 100). For a 30% discount on £120: £120 × (1 − 0.30) = £120 × 0.70 = £84. Alternatively, calculate the discount amount (£120 × 0.30 = £36) and subtract it from the original price (£120 − £36 = £84). Both approaches give the same result.
Is tax applied before or after the discount?
In standard retail practice, sales tax (such as UK VAT or US state sales tax) is applied to the final selling price after any discount. This calculator follows that convention: the discount is applied first, reducing the price, and tax is then calculated on the reduced amount. If you need to model a different ordering — for example, tax applied to the list price before a trade discount — use the 'beforeTax' result as an intermediate value and perform the additional step manually.
How much do I save with a percentage discount?
The saving equals the original price multiplied by the discount percentage divided by 100. For a 25% discount on a £200 item: saving = £200 × 25 ÷ 100 = £50. This is the pre-tax saving. The 'You save' figure shown by this calculator represents the reduction in pre-tax price; it does not include any tax that would have applied to the undiscounted price.
What is the difference between 20% off and 20% tax added?
They are not symmetric. A 20% discount reduces a £100 price to £80 (saving £20). Adding 20% tax to £100 gives £120 (paying £20 extra). Applying both: £100 discounted by 20% = £80, then taxed at 20% = £96. The net effect of a 20% discount and a 20% tax is a final price of £96 — a 4% reduction from the original, not a 0% net change.
Do two successive discounts add up?
No. Two successive percentage discounts are not equivalent to their sum. A 20% discount followed by a 10% discount gives a total reduction of 28%, not 30%. The second discount is applied to the already-reduced price: £100 → £80 (after 20%) → £72 (after a further 10%). The combined discount factor is (1 − 0.20) × (1 − 0.10) = 0.72, equivalent to a single 28% discount.
How do I reverse a discount to find the original price?
Divide the discounted price by (1 − discount ÷ 100). If an item costs £70 after a 30% discount, the original price is £70 ÷ (1 − 0.30) = £70 ÷ 0.70 = £100. This reverse calculation is useful when only the sale price and discount rate are known.
Tài liệu tham khảo
- HM Revenue and Customs (HMRC). VAT Notice 700: The VAT Guide. gov.uk/government/publications.
- National Institute of Standards and Technology (NIST). NIST/SEMATECH e-Handbook of Statistical Methods. nist.gov.
- Lam G. Consumer Arithmetic and Percentage Calculations. In: Stewart S (ed.), Mathematics for the Practical Man. 4th ed. Van Nostrand, 1918. (Classic reference for commercial percentage methods.)