Guide · 4 min read
How to Calculate Percentage: Discounts & Change
Percentage math made plain: find X% of Y, reverse-engineer shares, compute discounts, and get increase vs decrease right.
Last updated: 2026-10-07
Tools for this guide
The short answer
Three questions cover nearly all percentage math: X% of Y is (X ÷ 100) × Y; X as a share of Y is (X ÷ Y) × 100; change between two values is (new − old) ÷ old × 100.
Run any of them in the Percentage Calculator with the working shown, or price a sale directly in the Discount Calculator. Both compute instantly in your browser with nothing stored.
The three calculations, with examples
Finding a portion: 20% of a $500 repair quote is 0.20 × 500 = $100 deposit. Finding a share: 42 marks out of 60 is 42 ÷ 60 × 100 = 70%. Finding change: an hourly rate rising from $22 to $24 grew by (24 − 22) ÷ 22 × 100 ≈ 9.1%.
Notice each answers a different question — portion, share, or movement — and each needs different inputs. Most percentage mistakes are simply the wrong mode, so name the question before reaching for numbers.
Discounts without the regret
A single discount is one multiplication: price × (1 − discount). At 30% off $120, that is 120 × 0.70 = $84. Check the store's claim the same way before trusting the shelf tag.
Stacked discounts multiply, never add: 20% off followed by 10% off means paying 0.80 × 0.90 = 0.72 of the price — 28% off total, not 30%. Tax applies to the discounted price in most places, so apply tax last in your mental math.
Increase, decrease and points
Percent change always divides by the starting value, which is why up-then-down rarely cancels: +25% followed by −25% leaves you at 93.75% of the start, not 100%. Investments, prices and grades all behave this way.
Keep percentage points separate from percent: a rate moving from 4% to 6% rose 2 percentage points but 50% in relative terms. News about interest and inflation mixes these constantly — now you can tell which one is meant.
Tipping and splitting notes
Standard tips run 15–20% depending on service and country: on a $64 bill, 20% is $12.80 for a $76.80 total. The Tip Calculator splits this across diners including tax handling, so groups stop doing phone math at the table.
On phones, run the numbers in the browser tool rather than the system calculator: seeing the mode and the working together catches the classic error of tipping on the taxed total when you meant the subtotal. On desktop, the same pages handle invoices, quotes and grade sheets identically.
Frequently asked questions
What is 20% of 500?
100 — multiply 500 by 20/100. In general, X% of Y means (X ÷ 100) × Y. The Percentage Calculator runs all three percentage question types with the working shown.
How do I reverse it — what percent is X of Y?
Divide the part by the whole and multiply by 100: 42 out of 60 is (42 ÷ 60) × 100 = 70%. Use this for exam scores, budget shares and completion rates.
How do discounts work with percentages?
A 25% discount means you pay 75%: multiply the price by 0.75. On $80 that is $60, saving $20. For stacked deals, apply them sequentially — 20% then 10% is not 30% off.
Increase versus decrease — which base?
Always the original value: change equals (new − old) ÷ old × 100. A rise from 22 to 24 is +9.1%, while a fall from 24 to 22 is −8.3% — same two numbers, different bases, different answers.
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