How to Calculate Discounts, Tax, and Tips
Discounts, tax, and tips are all percentages, but they apply to different amounts and in a particular order. A sale price is the original price minus a percentage of that price. Tax is usually added to the price you pay. A tip is a percentage of the bill before or after tax, depending on the convention. Mixing the order changes the answer.
The Percentage Calculator handles the arithmetic. The examples below show which number to put in.
Quick answer
For a discount, multiply the original price by the discount rate and subtract it, or multiply by one minus the rate. For tax, multiply the price by one plus the tax rate. For a tip, multiply the bill by the tip rate and add it. When several percentages apply, do them one at a time and keep the order explicit.
Discounts
A 25 per cent discount on 800 is 200, so the sale price is 600. The short method is 800 times 0.75, which gives 600 directly. The short method is less error-prone because it avoids a subtraction, but both are valid. If the discount is 25 per cent and then a further 10 per cent, the second discount applies to 600, not 800: 600 times 0.90 is 540.
Do not add the two discounts and apply 35 per cent to the original. That gives 520, which is less than the correct 540. Successive percentages always apply to the new amount, not the original. This is the same compounding effect that makes a percentage increase followed by a percentage decrease fail to return to the start.
Tax
If the tax rate is 12 per cent and the price is 1,000, the tax is 120 and the total is 1,120. The short method is 1,000 times 1.12. If you know the total and need the pre-tax price, divide by 1.12 rather than subtracting 12 per cent of the total. Subtracting 12 per cent of 1,120 gives 985.60, which is too low; the tax was 12 per cent of 1,000, not of 1,120.
In some countries, displayed prices already include tax; in others, tax is added at checkout. The same percentage produces a different final number depending on which convention applies. Read the invoice or the price label before assuming.
Tips
A 15 per cent tip on a 1,200 bill is 180, so the total is 1,380. To split the bill, divide the total by the number of people. Decide first whether the tip is based on the pre-tax or post-tax amount. Either can be the local convention, but the group should agree before the bill is divided.
For a quick estimate, 10 per cent is easy to move one decimal place, and 5 per cent is half of that. A 15 per cent tip is 10 per cent plus 5 per cent. A 20 per cent tip is double 10 per cent. These mental shortcuts are useful for checking a calculator result.
Keep the order visible
Write the steps as a list: original price, discount, discounted price, tax, total, tip, split. That list makes it obvious which amount each percentage applies to. If the numbers look wrong, the list shows where the error entered.
Use the Percentage Calculator for each step, and round only at the end. Rounding the intermediate values can change the final total by a few units. For the basic part-over-whole formula, read How to Calculate a Percentage of a Total. For percentage change, see Percentage Increase, Decrease, and Difference Explained.
Common questions
Do successive discounts add together?
No. A 25 per cent discount followed by a further 10 per cent does not equal 35 per cent off. The second discount applies to the already discounted price, so 800 becomes 600, then 540. Adding the rates would give 520, which is too low.
Should tax be calculated before or after a discount?
Usually the discount is applied first, and tax is calculated on the discounted price. The rule depends on the jurisdiction and the wording of the invoice. If you are checking a receipt, apply the order shown on the document rather than assuming.
How do I work out a tip quickly?
Ten per cent is one decimal place to the left, and five per cent is half of that. For 15 per cent, add the two. For 20 per cent, double the 10 per cent figure. Check the total against the bill before adding it to the amount you pay.