The Complete Guide to Percentage Calculations

Percentages look like four different problems — of, change, reverse, comparison — but they are one idea: a fraction of 100. Master the four formulas below and you can read any percentage claim critically.

1. Percentage of a number

Result = Number × Percent ÷ 100

18% of 250 = 250 × 18 ÷ 100 = 45

2. Percentage change

Change % = (New − Old) ÷ Old × 100

46000 vs 40000: (46000 − 40000) ÷ 40000 = 15%

This is the formula behind every "up 15%" headline. The trap: change is always relative to the starting value, so an increase of 50% followed by a decrease of 50% does not return to the start (100 → 150 → 75).

3. Reverse percentage

Original = Final ÷ (1 − Percent ÷ 100)

After a 25% discount you pay 60:
60 ÷ 0.75 = 80

Reverse percentages appear everywhere: "price includes 20% VAT, what is the pre-tax amount?", "this is 30% off — what was the original price?".

4. X is what percent of Y

Percent = X ÷ Y × 100

42 out of 50 = 42 ÷ 50 × 100 = 84%

The mental-math shortcuts

• 10% is the number divided by 10 (decimal move).
• 5% is half of 10%.
• X% of Y = Y% of X (swap when one is easier).
• Estimate with rounding, then refine.