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Percentage Calculator

Four modes: find percentage, percentage change, what percent, and reverse percentage

%
15% of 200 = ?
Result
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15% of 200
(100 − 80) / 80 × 100 = ?
Percentage Change
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Increase / Decrease
Absolute change0
Change direction—
45 / 180 × 100 = ?
Percentage
—
X is this % of Y
%
▾
120 / 1.20 = ?
Original Value
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Before the % change

How to Calculate Percentages — All 4 Methods

Percentages appear in everyday life: sales discounts, tax rates, investment returns, test scores, and tip calculations. This calculator handles every common percentage problem instantly, with a clear formula shown for each result so you understand the math behind the answer.

Students use it to check homework. Shoppers use it to calculate discounts and final prices. Business owners use it to track margin changes and growth rates. The four modes cover every scenario: finding a percentage of a number, measuring change, expressing a ratio as a percentage, and working backwards from a changed value.

Four Percentage Formulas

1. What is X% of Y? → Y × (X / 100)
2. Percentage change → ((New − Old) / Old) × 100
3. X is what % of Y? → (X / Y) × 100
4. Original value before % change → Value / (1 ± percentage/100)

Practical Examples

• 30% off a $250 item → $250 × 0.70 = $175 (you save $75)
• Price increases from $80 to $100 → ((100−80)/80) × 100 = 25% increase
• You scored 42 out of 60 → (42/60) × 100 = 70%
• $120 after 20% increase → original was $120 / 1.20 = $100

When to Use This Calculator

Percentage calculations appear in virtually every area of life. Here are the situations where each of the four modes is most useful:

  • "What is X% of Y?" — Shopping and tips: A restaurant bill is $87.50. What is a 20% tip? 20% × $87.50 = $17.50. Total: $105. Also useful for calculating tax on purchases or finding 15% of your salary for savings.
  • "% Change" — Business metrics: Website traffic went from 8,200 visits last month to 11,480 this month. Percentage change = ((11,480 − 8,200) / 8,200) × 100 = +40%. Essential for monthly reports, investment tracking, and KPI analysis.
  • "X is what % of Y?" — Test scores and budgets: You scored 47 out of 65 on an exam: (47 / 65) × 100 = 72.3%. Or: you spent $1,340 of a $2,000 monthly budget — that's 67% used.
  • "Find Original Value" — Reverse discounts: A jacket costs $119 after a 30% off sale. Original price = $119 / (1 − 0.30) = $119 / 0.70 = $170. Also used to work backwards from VAT-included prices.

Common Percentage Errors to Avoid

The biggest mistake: subtracting a percentage twice. A 20% increase followed by a 20% decrease does NOT return to the original. Starting at $100: +20% = $120, then −20% of $120 = $96 — a net 4% loss. Percentage changes compound multiplicatively, not additively. Always use this calculator to verify.

Frequently Asked Questions

How do I calculate what percentage X is of Y? ▼
Formula: (X / Y) × 100. Example: 45 out of 180 → (45 / 180) × 100 = 25%. So 45 is 25% of 180. This is useful for test scores, survey responses, inventory counts, and any situation where you need to express a part as a share of the whole.
How do I calculate percentage increase or decrease? ▼
Percentage change = ((New − Old) / Old) × 100. Positive = increase, negative = decrease. Example: sales went from $5,000 to $6,500 → ((6500−5000)/5000) × 100 = 30% increase. If sales fell from $6,500 to $5,200 → ((5200−6500)/6500) × 100 = −20% decrease.
How do I find the original price before a discount? ▼
If you know the sale price and the discount percentage, the original is: Sale price / (1 − discount/100). Example: an item costs $70 after 30% off → original = $70 / 0.70 = $100. This works for any percentage subtraction, not just discounts.
What is the difference between percentage points and percent? ▼
Percentage points measure the absolute arithmetic difference between two percentages. If a tax rate rises from 20% to 25%, that's 5 percentage points — but a 25% relative increase. The word "percent" always describes a relative change; "percentage points" describes an absolute difference between two percentages.
How do I calculate a tip percentage? ▼
Multiply the bill amount by the tip rate divided by 100. For a 20% tip on a $85 bill: $85 × (20/100) = $17. Total with tip = $85 + $17 = $102. Quick mental math shortcut: 20% = double the 10% amount. 10% of $85 = $8.50, so 20% = $17.
How do I calculate compound percentage changes? ▼
For multiple consecutive percentage changes, multiply the factors together. Example: a price increases 10% then falls 10% — it does NOT return to original. It becomes Price × 1.10 × 0.90 = 0.99 × Price — a 1% net loss. Percentage changes compound multiplicatively, not additively.
How do I calculate a percentage of a percentage? ▼
To find a percentage of a percentage, convert both to decimals and multiply. Example: 30% of 40% = 0.30 × 0.40 = 0.12 = 12%. Real-world use: a retailer offers 30% off, then an extra 40% off the sale price. The combined discount is NOT 70% — it's 1 − (0.70 × 0.60) = 1 − 0.42 = 58% total discount. This is why "extra X% off sale items" deals are less dramatic than they appear. Always calculate the final price directly rather than adding percentages together.
How do I calculate a percentage increase to reach a target? ▼
To find the percentage increase needed to reach a target: ((Target − Current) / Current) × 100. Example: current revenue is $80,000, target is $100,000. Increase needed = ((100,000 − 80,000) / 80,000) × 100 = 25%. Useful for setting sales targets, budgeting, and performance goals. Reverse check: $80,000 × 1.25 = $100,000 ✓. Note that a 25% increase from $80K gets you to $100K, but a 25% decrease from $100K gives you $75K — not $80K. Percentage increases and decreases are not symmetric.
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