How do you calculate 20% of a number?

To find 20% of a number: multiply it by 0.20 (or divide by 5). Example: 20% of £150 = £150 × 0.20 = £30. Formula: Result = (X ÷ 100) × Y. Quick tip: find 10% by moving the decimal left one place, then double it for 20%.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value to an original: ((New−Old)÷|Old|)×100. It has a reference point. Percentage difference compares two values with no reference: |A−B|÷((A+B)÷2)×100. Example: a price rising from $80 to $100 is a 25% change; the percentage difference between $80 and $100 is 22.22%.

How do you calculate percentage increase?

Percentage increase formula: New = Original × (1 + Rate÷100). Example: 100 increased by 25% = 100 × 1.25 = 125. To reverse: Original = New ÷ (1 + Rate÷100). This is used for UK/EU VAT-inclusive prices: pre-VAT = total ÷ 1.20 (20% VAT).

How do VAT and sales tax percentages work differently by country?

UK VAT is 20% and already included in displayed prices. EU VAT ranges 17–27%. US sales tax is added at checkout (0–10.25% by state). Canada has GST/HST (5–15%). Japan has 10% consumption tax. Australia has 10% GST. Always check whether a displayed price is tax-inclusive or tax-exclusive.

How do you calculate a percentage tip?

Tip = Bill × (Tip% ÷ 100). For 20% on a $80 bill: $80 × 0.20 = $16. Total = $96. Tip norms by country: US 18–22%, UK 10–15% (optional), Japan 0% (tipping is unusual), Australia rarely expected, UAE 10–15% in hotels/restaurants.

What is X% of Y when X and Y are in different units?

Percentages are dimensionless, so units do not change the formula. 20% of £150 = £30; 20% of 150 kg = 30 kg. The percentage operates on whatever unit Y is in.

Percentage Calculator

Six modes in one: find X% of Y, what % one number is of another, percentage change, percentage difference, percentage increase, and percentage decrease. Each result shows the formula and step-by-step working.

Quick Answer

X% of Y = (X÷100)×Y · X is what % of Y = (X÷Y)×100 · % Change = ((New−Old)÷|Old|)×100 · % Difference = |A−B|÷((A+B)÷2)×100 · % Increase = Original×(1+Rate÷100) · % Decrease = Original×(1−Rate÷100)

What is 20% of 150?

Percentage (%)

Of Number

All Six Percentage Formulas Explained

1. X% of Y — Find a Percentage of a Number

Formula: Result = (X ÷ 100) × Y

Example: 20% of £150 = (20÷100) × 150 = £30

Used for: sale discounts, VAT, tips, commissions. Quick shortcut: 10% = move decimal left; 5% = half of 10%; 15% = 10% + 5%.

2. X is What % of Y — Find the Percentage

Formula: Percentage = (X ÷ Y) × 100

Example: 30 out of 200 = (30÷200) × 100 = 15%

Used for: test scores, grade calculations, survey results. A US grade of 90% is an "A"; a UK degree with 70%+ is a First Class Honours.

3. Percentage Change — How Much Did It Change?

Formula: Change = ((New − Old) ÷ |Old|) × 100

Example: price from $80 → $100 = ((100−80)÷80) × 100 = +25% increase

Important: a 25% increase followed by a 20% decrease returns to the original — these are not symmetric.

4. Percentage Difference — Comparing Two Values

Formula: Difference = |A − B| ÷ ((A + B) ÷ 2) × 100

Example: 80 vs 100 → |80−100| ÷ 90 × 100 = 22.22%

Unlike percentage change, there is no "original" or "new" — both values are on equal footing. Used in science, quality control, and comparing prices across markets.

5. Percentage Increase — Apply an Increase

Formula: New = Original × (1 + Rate ÷ 100)

Example: salary of £40,000 increased by 5% = £40,000 × 1.05 = £42,000

Reverse (find original from new): Original = New ÷ (1 + Rate÷100). This is how you remove UK/EU VAT from a displayed price: divide by 1.20 for 20% VAT.

6. Percentage Decrease — Apply a Discount

Formula: New = Original × (1 − Rate ÷ 100)

Example: item priced at €200, 30% off = €200 × 0.70 = €140

Reverse (find original from discounted price): Original = Discounted ÷ (1 − Rate÷100).

Percentage in Different Countries

The arithmetic is universal, but real-world contexts vary:

Tax rates: UK VAT = 20% (included in prices). Germany/France = 19–20% (included). US sales tax = 0–10.25% (added at register). Canada GST/HST = 5–15%. Japan consumption tax = 10%. Australia GST = 10%.
Tipping: US 18–22% (expected), UK 10–15% (discretionary), Japan 0% (tipping is unusual), UAE 10–15%, Australia rare.
Grade systems: US: 90% = A, 80% = B. UK: 70%+ = First Class Honours, 60–69% = 2:1. Germany: 1.0 = top (inverted scale, 1–4). France: 16–20/20 = Très Bien.
Interest rates: Expressed as annual percentage (APR) everywhere, but compounding frequency varies — US often compounds monthly, UK often uses effective annual rate (EAR).

Percentage Change vs. Percentage Difference: Which to Use?

Use percentage change when there is a clear before-and-after (price yesterday vs today, salary before vs after a raise). Use percentage difference when comparing two equivalent values with no implied direction (comparing prices in two stores, measuring two slightly different quantities in an experiment).

Frequently Asked Questions

How do you find X% of a number quickly?

Move the decimal left one place to find 10%, then scale: 5% = half of 10%, 20% = double 10%, 25% = quarter the number, 1% = move decimal two places. Example: 15% of 80: 10% = 8, 5% = 4, total = 12.

Is a 50% increase followed by a 50% decrease back to the original?

No. Starting with 100: a 50% increase gives 150. A 50% decrease of 150 gives 75 — not 100. Percentage changes are multiplicative, not additive.

How do I remove VAT from a price?

Divide the VAT-inclusive price by (1 + VAT rate). For UK 20% VAT: pre-VAT price = total ÷ 1.20. Example: £120 ÷ 1.20 = £100 pre-VAT. Same logic applies to Australian GST (÷1.10) and Japanese consumption tax (÷1.10).

What is percentage difference used for in science?

Scientists use percentage difference to compare two experimental measurements with no clear "reference" value. Formula: |A−B| ÷ ((A+B)/2) × 100. This avoids the bias of picking one value as the "original".

Related Calculators

½ Fraction Calculator ➗ Long Division Calculator 🍽️ Tip Calculator 🧾 Tax Calculator 🎓 GPA Calculator 📊 Average / Mean Calculator