How to Calculate Percentages

Three types of percentage calculation every student and professional needs — percentage of, percentage change, and reverse percentage.

QUICK ANSWER

Three key percentage formulas: (1) X% of Y = (X ÷ 100) × Y. (2) Percentage change = ((New − Old) ÷ Old) × 100. (3) Reverse percentage (find original) = Final ÷ (1 ± rate). Example: 25% of 80 = 20. A rise from $50 to $65 = 30% increase. A $119 price with 19% VAT included → original = 119 ÷ 1.19 = $100.

Type 1: Percentage of a Number

Formula: Result = (Percentage ÷ 100) × Whole

1
Convert the percentage to a decimal

Divide the percentage by 100. Quick trick: move the decimal point two places left. 25% → 0.25. 7.5% → 0.075. 100% → 1.0.

2
Multiply by the whole number

Multiply the decimal by the whole. 25% of 80: 0.25 × 80 = 20. Done.

3
Verify

Check: 20 ÷ 80 = 0.25 = 25%. ✓

Question Working Answer
15% of 200 0.15 × 200 30
8% of $750 0.08 × 750 $60
37.5% of 400 0.375 × 400 150
110% of 90 1.10 × 90 99
0.5% of 10,000 0.005 × 10,000 50

Type 2: Percentage Change (Increase or Decrease)

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

  • Positive result = increase. Negative result = decrease.
  • A stock goes from $80 to $100: ((100 − 80) ÷ 80) × 100 = 25% increase.
  • A salary drops from $60,000 to $54,000: ((54,000 − 60,000) ÷ 60,000) × 100 = −10% (10% decrease).

Type 3: Reverse Percentage (Find the Original)

Formula: Original = Final ÷ (1 + rate) for increases, or Final ÷ (1 − rate) for decreases.

  • Price after 20% VAT: £144 → Original = 144 ÷ 1.20 = £120.
  • Sale price after 30% off: $63 → Original = 63 ÷ 0.70 = $90.
  • Remember: DO NOT subtract 20% from £144 to find the original — that gives the wrong answer (£115.20 instead of £120).

How Percentage Display Differs by Country

Country How they write 25% Tax/VAT percentage examples
🇺🇸 USA 25% Sales tax 0–10.25% (state varies, not included in price)
🇬🇧 UK 25% VAT 20% (included in advertised price)
🇩🇪 Germany 25 % MwSt 19% (included in price; symbol has space before it)
🇫🇷 France 25 % TVA 20% (included in price)
🇮🇳 India 25% GST 5%/12%/18%/28% (included in price)
🇯🇵 Japan 25% Consumption Tax 10% (sometimes added at checkout)

Frequently Asked Questions

How do you calculate a percentage of a number? ▾
Divide the percentage by 100, then multiply by the whole. Example: 20% of 150 = (20 ÷ 100) × 150 = 0.20 × 150 = 30. Shortcut: move the decimal point two places left — 20% → 0.20, then multiply.
How do you calculate percentage change? ▾
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. Example: price rises from $50 to $65. Change = (65 − 50) ÷ 50 × 100 = 30% increase. If the result is negative, it is a decrease.
What is reverse percentage and how do you calculate it? ▾
Reverse percentage finds the original amount before a percentage was applied. Formula: Original = Final ÷ (1 ± percentage/100). Example: a $119 item includes 19% VAT. Original = 119 ÷ 1.19 = $100. Or: price fell 20% to $80. Original = 80 ÷ 0.80 = $100.
What number is X percent of Y? ▾
Formula: Result = (X ÷ 100) × Y. Example: What is 35% of 200? Result = (35 ÷ 100) × 200 = 0.35 × 200 = 70. So 35% of 200 is 70.
X is what percent of Y? ▾
Formula: Percentage = (X ÷ Y) × 100. Example: 45 is what percent of 180? = (45 ÷ 180) × 100 = 25%. So 45 is 25% of 180.
Do all countries use the % symbol the same way? ▾
The percent symbol (%) is universal. However, some countries also use per mille (‰ = per thousand, or 0.1%) and basis points (bps — used in finance; 1 bps = 0.01%). In Germany and other European countries, the symbol comes after the number with a space: 25 %. In the US/UK it is written directly: 25%.

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