How to work out percentages: change, discounts, tax and margin

Guide · Updated 2026-11-10

Six percentage sums in one place: a share of an amount, one number as a percent of another, percent change, adding or removing a percent, stacked discounts, and markup versus margin.

Open the Percentage calculator Free, in your browser, nothing uploaded.

A percentage is a fraction with 100 on the bottom, yet a few sums trip people up again and again: a pay rise, a price with tax already in it, two discounts in a row, or a shop owner’s profit. The percentage calculator puts six of these sums side by side in tabs, for shoppers, students, workers and small sellers. When the percent is a sales tax with a known rate, the sales tax handles it directly, and once you know your margin, break-even tells you how many sales cover your costs.

What it is

“Per cent” means “out of a hundred”. So 15% is 15 out of 100, or 0.15. Each tab is one short formula; the letters stand for the boxes you type into.

• X% of Y = X ÷ 100 × Y. For example, 20% of 45 is 9.
• X is what % of Y = X ÷ Y × 100. A score of 9 out of 45 is 20%.
• % change from an old value A to a new value B = (B − A) ÷ A × 100. The old value is always the base.
• Add a percent: amount × (1 + p ÷ 100). Take it off: amount × (1 − p ÷ 100).
• Remove a percent that is already included: amount ÷ (1 + p ÷ 100). This is how you find a price before tax.
• Stacked discounts: multiply what each discount leaves. With discounts d₁, d₂, d₃, the share left is (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100), and the true total discount is 1 minus that, as a percent.
• Markup = profit ÷ cost × 100. Margin = profit ÷ selling price × 100. Profit is selling price minus cost.

The big lesson hidden in these formulas is that a percent always belongs to a base. Change the base and the same profit or change gives a different percent.

How to use it

1. Choose the tab that matches your question. Each one opens with example numbers already in the boxes, so you can see the format.
2. Replace the example numbers with your own. The answer updates as you type; there is no button to press.
3. In Add or remove %, use the What to do menu to choose: add the percent, take the percent off, or find the original when the amount already includes it.
4. In Stacked discounts, fill in the first two discounts. A third discount and the original price are optional; add the price to see the final price and how much you save.
5. Read the sentence under the big answer. It repeats your question in words, so a box filled in the wrong way round stands out.

A worked example

Priya runs a small online shop and has a busy month of percentage questions.

Her pay from a part-time job went from 2,400 to 2,580 a month. In % change, From = 2,400 and To = 2,580. The change is (2,580 − 2,400) ÷ 2,400 × 100 = 180 ÷ 2,400 × 100 = +7.5%.

A supplier’s invoice says 1,180 including 18% tax. In Add or remove %, Amount = 1,180, Percent = 18, and she picks “Amount already includes it”. The price before tax is 1,180 ÷ 1.18 = 1,000, and the tax part is 180. (Taking 18% off 1,180 would give 967.60, which is wrong, because the tax was worked out on 1,000, not on 1,180.)

A clearance sale. She plans 25% off, then a further 20% off, then 10% off at checkout. The share left is 0.75 × 0.80 × 0.90 = 0.54, so the total discount is 46%, not 55%.

Pricing a mug. Each mug costs her 45 and she sells it for 60. Profit is 15. Markup is 15 ÷ 45 × 100 ≈ 33.33%; margin is 15 ÷ 60 × 100 = 25%. The same 15 of profit looks bigger next to the smaller cost.

Where it is used

• Shopping. Check whether “an extra 20% off sale prices” is as good as it sounds.
• Work and pay. Turn a raise into a percent, or check a commission at a given rate.
• Retail and small business. Set prices from a target margin, and stop markup and margin being mixed up between a seller and a buyer.
• School and exams. Marks as a percent, percentage error in a science practical, or growth from one year to the next.

Common mistakes

• Using the wrong base for change. A fall from 100 to 80 is 20%, but the rise back from 80 to 100 is 25%. Always divide by the starting value.
• Taking a percent off to remove tax. If tax is already in the price, divide by (1 + rate), as in the invoice above. Subtracting the rate from the total removes too much.
• Adding discounts together. Two discounts of 50% are 75% off, not free. Use the Stacked discounts tab.
• Treating markup as margin. A 33% markup is only a 25% margin. Decide which one you are talking about before you agree a price.
• Mixing “percent” and “percentage points”. A rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate itself.

Questions people ask

Why does a 10% rise followed by a 10% fall not get me back where I started? The fall is taken from the bigger number. 100 rises to 110, and 10% of 110 is 11, so you end at 99.

Can a percent change be more than 100%? Yes. Going from 20 to 50 is a rise of 150%. A fall, though, can never be more than 100%, because that would take you below zero.

What tax rate should I type? Sales and value-added tax rates differ by country, region and product, and they change. Check the official source, such as your tax authority’s website, for the rate that applies to you.

This article is general education, not financial or tax advice.