Percentage Calculator
All percentage calculations in one place — find a percentage, calculate percentage change, or reverse a discount.
Percentage Calculations — The Complete Guide
Percentages are one of the most universally useful mathematical tools — used in finance, health, science, everyday shopping, and statistics. Despite their ubiquity, many people struggle with less common percentage calculations like percentage change, reverse percentages, and percentage difference vs percentage change. This guide covers all the core types clearly.
Type 1 — Finding a Percentage of a Number
This is the most common calculation: "What is 15% of $85?" Formula: (percentage ÷ 100) × number = result. 15% of $85 = 0.15 × 85 = $12.75. Practical uses: calculating tips, discounts, tax amounts, commission on sales, interest on a balance.
Type 2 — What Percentage Is X of Y?
For questions like "30 is what percentage of 120?" Formula: (X ÷ Y) × 100 = percentage. 30 ÷ 120 × 100 = 25%. Practical uses: test scores (you got 34 out of 40 — what percentage?), market share calculations, body fat percentage, understanding what fraction a number represents.
Type 3 — Percentage Change
Percentage change measures how much a value increased or decreased relative to its starting point. Formula: ((New − Old) ÷ Old) × 100. Important: percentage increase and percentage decrease are not symmetric. A 50% decrease from $100 gives $50; a 50% increase from $50 gives $75, not $100. This asymmetry trips up many people when comparing prices or investment returns.
Type 4 — Reverse Percentage (Finding the Original)
When you know the final value after a percentage change and need the original: for increases, divide by (1 + rate). For decreases, divide by (1 − rate). Example: a shirt costs $42.50 after a 15% discount. Original price = $42.50 ÷ 0.85 = $50. This is useful for finding pre-tax prices, pre-discount original prices, or pre-markup wholesale prices.
Common Percentage Mistakes
- Percent vs percentage point: "Interest rates rose 2%" (from 3% to 3.06%) vs "rose 2 percentage points" (from 3% to 5%) — very different meanings.
- Percentage of vs percentage more than: "A is 150% of B" means A = 1.5B. "A is 150% more than B" means A = 2.5B.
- Averaging percentages: You cannot simply average two percentages when the base numbers differ.
Percentages — FAQ
How do you calculate a percentage increase?
Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100. Example: salary increased from $50,000 to $54,000: ((54,000 − 50,000) ÷ 50,000) × 100 = 8% increase. For a quick mental check: find how much it increased ($4,000), divide by the original ($50,000 = 0.08), multiply by 100 = 8%.
How do you calculate a discount?
Discounted price = Original × (1 − discount rate). For a 30% discount on $80: $80 × 0.70 = $56. To find the discount amount: $80 × 0.30 = $24. To reverse — find original price from discounted price: $56 ÷ 0.70 = $80. Our reverse percentage calculator (Type 4 above) handles this instantly.
What is the difference between percentage and percentage point?
A percentage point is an absolute difference between two percentages. If unemployment goes from 4% to 6%, it rose 2 percentage points — but that's a 50% increase in the rate (2 ÷ 4 × 100 = 50%). This distinction is critical in economics, polling, and medical statistics. When a study says a drug "reduced risk by 30%," it may mean from 10% to 7% (3 percentage points) — which sounds less dramatic than "30%" but is the same fact expressed differently.
How do you add a percentage to a number?
To add X% to a number: multiply by (1 + X/100). Adding 20% to $50: $50 × 1.20 = $60. This is the same as finding 20% of $50 ($10) and adding it, but the multiplication method is faster for complex numbers. Practical uses: adding sales tax to a price, calculating a price after a markup, finding a total with gratuity included.