What you can calculate

• Percentage of a number: sales tax, discounts, tips, exam score weighting.
• Increase by a percent: markups, salary raises, price inflation.
• Decrease by a percent: discounts, depreciation, markdowns.
• Percent change: comparing old vs new values for analytics and KPIs.
• What percent is A of B: contribution to total, completion progress, mix percentages.

Reference Table (Common Discounts)

Long‑Tail Use Cases

• "percentage increase calculator for salary raise 2025"
• "how to find what percent one number is of another fast"
• "discount calculator for online shopping 15 20 30 percent off"
• "percent change calculator for data analysis and KPIs"

Formulas (Quick Reference)

• a% of b = (a ÷ 100) × b
• Increase b by a% = b × (1 + a ÷ 100)
• Decrease b by a% = b × (1 − a ÷ 100)
• Percent change a → b = ((b − a) ÷ a) × 100
• What percent is a of b = (a ÷ b) × 100

Percent ↔ Decimal ↔ Fraction Table

Reverse Problems (Back‑Calculations)

• Find original price before discount: final = original × (1 − d). So original = final ÷ (1 − d). Example: $85 after 15% off → 85 ÷ 0.85 = $100.
• Find original before markup/VAT: final = base × (1 + r). So base = final ÷ (1 + r). Example: $118 inc. 18% tax → 118 ÷ 1.18 = $100.
• Two successive changes: +a% then −b% = multiply by (1 + a/100)(1 − b/100), not a − b net.

Real‑World Scenarios

• Shopping: Stacked discounts (e.g., 20% off then extra 10%) multiply, they do not add. 100 × 0.8 × 0.9 = 72 (28% total off).
• Finance: Annual growth vs monthly growth: 12×2% ≠ 24%; compound monthly: ×1.02^12 ≈ +26.8%.
• Analytics: When baseline is small, large % swings can be misleading—show absolute changes too.

Common Mistakes

• Adding percent increases directly instead of compounding.
• Using percent points vs percent change interchangeably (e.g., 5% → 7% is +2 percentage points, not +2%).
• Dividing by the wrong base in "what percent" problems.