How to Calculate Percentages: 7 Types with Formulas & Examples

Percentages appear everywhere — tax, tips, discounts, pay rises, test scores. Yet most people only know one formula. This guide covers all 7 types of percentage calculation with plain-language formulas and worked examples.

The 7 types of percentage calculation

1. X% of Y (percentage of a number)

Formula: Result = (X ÷ 100) × Y

Example: What is 15% of 240? → (15 ÷ 100) × 240 = 36

Use this for: calculating VAT, tips, commission, discounts in absolute terms.

2. X is what % of Y?

Formula: Percentage = (X ÷ Y) × 100

Example: 45 is what % of 180? → (45 ÷ 180) × 100 = 25%

Use this for: test scores, market share, budget allocation.

3. Percentage increase

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

Example: Price went from $80 to $100 → ((100 − 80) ÷ 80) × 100 = 25% increase

4. Percentage decrease

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

Example: Sales fell from 500 to 425 → ((500 − 425) ÷ 500) × 100 = 15% decrease

5. Value after a percentage change

Increase: New value = Old × (1 + Rate/100)
Decrease: New value = Old × (1 − Rate/100)

Example: $200 after a 12% increase → 200 × 1.12 = $224

6. Reverse percentage (find the original value)

If you know the final value after a percentage change and want the original:

Formula: Original = Final ÷ (1 ± Rate/100)

Example: A product is $85 after a 15% discount — what was the original price?
→ 85 ÷ (1 − 0.15) = 85 ÷ 0.85 = $100

This is one of the most commonly miscalculated formulas. People subtract 15% from $85 and get $72.25 — that is wrong. You must divide by the remaining fraction.

7. Tip calculator with bill split

Formula: Tip = Bill × (Tip% ÷ 100) → Per person = (Bill + Tip) ÷ Guests

Example: $120 bill, 18% tip, 4 people:
Tip = $21.60 → Total = $141.60 → Per person = $35.40

Common percentage mistakes

• Adding percentages directly: 20% off + 10% extra is NOT 30% off — it is 28%. Apply them sequentially: × 0.80 × 0.90 = × 0.72 = 28% off.
• Reversing a percentage incorrectly: To undo a 20% increase, do not subtract 20% — divide by 1.20. To undo a 20% discount, divide by 0.80.
• Percentage points vs percentage change: Going from 10% to 12% is a 2 percentage-point increase but a 20% relative increase.