Percentage calculations show up everywhere — discounts while shopping, exam scores, tax rates, tips, interest rates, and statistics. Yet many people only remember one version of the formula and get stuck when a question is phrased differently. This guide covers every common type of percentage calculation, with the formula and a worked example for each.
Type 1: What is X% of a Number?
Formula: Result = (Percentage ÷ 100) × Number. Example: What is 20% of 150? Result = (20 ÷ 100) × 150 = 0.20 × 150 = 30.
Type 2: What Percent is X of Y?
Formula: Percentage = (X ÷ Y) × 100. Example: What percent is 45 of 180? Percentage = (45 ÷ 180) × 100 = 0.25 × 100 = 25%.
Type 3: Finding the Original Number
Formula: Original Number = Result ÷ (Percentage ÷ 100). Example: 30 is 20% of what number? Original Number = 30 ÷ (20 ÷ 100) = 30 ÷ 0.20 = 150.
Type 4: Percentage Increase or Decrease
Formula: % Change = ((New Value − Old Value) ÷ Old Value) × 100. Example: A price rises from £80 to £100: % Change = ((100 − 80) ÷ 80) × 100 = 25% increase. A price falls from £100 to £75: % Change = ((75 − 100) ÷ 100) × 100 = −25%, a 25% decrease.
Type 5: Calculating a Percentage of a Total From Several Parts
This comes up often in exam scores and surveys. Formula: Percentage = (Part ÷ Total) × 100, applied to each category. Example: Out of 600 exam marks, a student scores 450: Percentage = (450 ÷ 600) × 100 = 75%.
Quick Mental Math Tricks
- •To find 10% of any number, move the decimal point one place to the left (10% of 250 = 25).
- •To find 50%, simply halve the number.
- •To find 25%, halve it twice.
- •To find 1%, move the decimal two places left, then multiply by your target percentage (1% of 250 = 2.5, so 15% of 250 = 2.5 × 15 = 37.5).
- •To quickly estimate a tip, find 10% and then adjust: for a 20% tip, find 10% and double it.
Common Percentage Mistakes
- •Confusing percentage change with percentage points: going from 10% to 15% is a 5 percentage point increase, but a 50% relative (percentage) increase. These are not the same thing and are frequently mixed up in news and finance.
- •Forgetting that percentage decrease and increase are not symmetric: a 50% increase followed by a 50% decrease does NOT return you to the original number (100 → 150 → 75, not 100).
- •Using the wrong base: always divide by the original/old value, not the new value, when calculating percentage change.
Use the free CalcSphere Percentage Calculator to instantly solve any percentage problem — no manual formula needed.
Open Percentage Calculator →