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% of Number

What is X% of Y?

% Change

From X to Y is what %?

X is % of Y

X is what % of Y?

Reverse %

Y after X% = Z, find Y

Everything You Need to Know About Percentage Calculations

Percentages are one of the most universally encountered forms of mathematics, appearing in everyday situations from calculating a restaurant tip to understanding quarterly revenue growth, from figuring out how much a sale price saves you to analyzing data in scientific research. The word "percent" comes from the Latin "per centum," meaning "per hundred" — a percentage is simply a number expressed as a fraction of 100. Despite this seemingly simple concept, percentage calculations span a surprising range of scenarios, each with its own formula and nuance.

The most common calculation is finding a percentage of a number: "What is 15% of 340?" This is straightforward — multiply 340 by 0.15 (or equivalently, multiply by 15 and divide by 100) to get 51. This type of calculation is used for tips (15–20% of a restaurant bill), commission (sales agent earns 8% of total sales), discounts (30% off a product price), and tax calculation (applying a fixed percentage to a subtotal). Our calculator handles this in Mode 1 with instant results.

Percentage change is critically important in finance, analytics, and business reporting. The formula is: ((New Value − Old Value) ÷ Old Value) × 100. A positive result indicates a percentage increase; a negative result indicates a decrease. This is used to report growth metrics (monthly active users grew 18%), stock price movements (shares fell 4.2%), inflation rates, and year-over-year business performance comparisons. A common mistake is confusing percentage change with percentage point change — a rate rising from 10% to 15% is a 5 percentage point increase but a 50% increase in the rate itself.

Reverse percentage calculation is less intuitive but equally important, especially for tax-inclusive pricing. If a product costs £120 including 20% VAT, the pre-tax price is not £120 × 0.80 = £96. The correct approach is £120 ÷ 1.20 = £100. The difference matters significantly in accounting, tax filing, and invoice reconciliation. Mode 4 of our calculator handles reverse percentage accurately using the correct formula.

Common Percentage Use Cases

  • Discount calculation — 30% off a £250 item = £250 × 0.30 = £75 savings → You pay £175
  • Tax calculation — Item costs £100, 10% GST = £100 × 1.10 = £110 total
  • Grade/score percentage — Scored 47 out of 60 = (47÷60) × 100 = 78.3%
  • Salary increase — Salary goes from £40,000 to £44,000 = 10% increase
  • Commission — Sold £15,000, earn 5% commission = £750
  • Body weight change — Lost 4kg from 80kg = 5% reduction
  • Investment return — Invested £5,000, now worth £6,200 = 24% return

Percentage Formulas Quick Reference

  1. X% of Y = (X ÷ 100) × Y
  2. Percentage change = ((New − Old) ÷ Old) × 100
  3. X is what % of Y = (X ÷ Y) × 100
  4. Reverse % = Final Value ÷ (1 + percentage/100)

All calculations are performed instantly in your browser. No data is sent to any server, and results are accurate to multiple decimal places for maximum precision.

Frequently Asked Questions

To find X% of Y, multiply Y by X and divide by 100. For example, 20% of 150 = (20 × 150) ÷ 100 = 30. Our calculator handles this in Mode 1 automatically.

Percentage change = ((New Value - Old Value) ÷ Old Value) × 100. Positive = increase, negative = decrease. For example, from 80 to 100: ((100-80)÷80)×100 = 25% increase.

Reverse percentage finds the original value before a percentage was applied. For example, if a price after 20% VAT is £120, the original price = 120 ÷ 1.20 = £100. Use Mode 4 (Reverse %) in our calculator.

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