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% Percentage Calculator

Three essential percentage calculations in one tool: find a percentage of a number, calculate percentage change between two values, or find what percent one number is of another.

⚙️ Full calculator functionality for this tool is being added. The SEO content and structure are complete.

Three Ways to Calculate Percentages

The word "percentage" covers three different types of calculations that people confuse constantly. This calculator handles all three — switch between tabs above to use whichever you need.

  • Type 1 — Percent of a number: "What is 15% of $80?" → 0.15 × 80 = $12.00
  • Type 2 — Percentage change: "A stock went from $50 to $65 — what % increase is that?" → (65−50)/50 × 100 = +30%
  • Type 3 — What percent is X of Y: "42 is what percent of 168?" → 42/168 × 100 = 25%

The Percentage Formula

Core Percentage Formulas Part = (Percent / 100) × Whole Percent Change = (New − Old) / |Old| × 100 Percent of = (Part / Whole) × 100

Percentage Increase vs Percentage Difference

Percentage increase/decrease compares a new value to a specific original value and has a direction (positive = increase, negative = decrease). A price going from $100 to $125 is a 25% increase. Percentage difference compares two values without implying direction and uses the average as the denominator: |A−B| / ((A+B)/2) × 100. For comparing two alternatives without a clear "original" value, use percentage difference.

Common Percentage Mistakes to Avoid

  • Asymmetry of percentages: A 50% decrease followed by a 50% increase does NOT return to the original. $100 → $50 → $75. You need a 100% gain after a 50% loss to break even.
  • Percent vs percentage points: If interest rates rise from 2% to 3%, that's an increase of 1 percentage point, but a 50% increase in the rate. Both statements are correct but mean very different things.
  • Base confusion: "20% off, then 20% off again" is NOT 40% off. It's 20% off the already-reduced price: 0.8 × 0.8 = 0.64, so 36% total reduction.

Percentage Calculations in Real Life

Percentages appear everywhere: discounts and sales (20% off a $79.99 item = $63.99), tax calculations (use our sales tax calculator), investment returns (see our investment calculator), grade calculations (see our grade calculator), and tip calculations (15% tip on $47.80 = $7.17). Mastering the three formulas above handles virtually every percentage question you'll encounter.

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Frequently Asked Questions

Common questions about how do i calculate... and more.

How do I calculate a percentage of a number?

To find a percentage of a number, multiply the number by the percentage divided by 100. Formula: Result = (Percentage ÷ 100) × Number. Examples: 20% of 150 = 0.20 × 150 = 30. 7.5% of $240 = 0.075 × 240 = $18. 1% of any number = that number ÷ 100 (so 1% of 3,500 = 35). You can also use a quick mental trick: 10% is always the number with the decimal moved one place left, then multiply or divide from there (10% of 450 = 45; 5% = 22.5; 20% = 90).

How do I calculate the percentage change between two numbers?

Percentage change = (New Value − Old Value) / |Old Value| × 100. If the result is positive, it's an increase; if negative, a decrease. Example: a salary went from $55,000 to $62,000. Change = (62,000 − 55,000) / 55,000 × 100 = 7,000 / 55,000 × 100 = 12.73% increase. A stock dropped from $85 to $72: (72 − 85) / 85 × 100 = −13/85 × 100 = −15.3% decrease. Always divide by the original value, not the new one — that's the most common mistake.

What is the percentage difference between two numbers?

Percentage difference is used when there's no clear "original" value — you just want to know how different two numbers are relative to their average. Formula: |A − B| / ((A + B) / 2) × 100. Example: comparing two prices, $45 and $55. Difference = |45−55| / ((45+55)/2) × 100 = 10/50 × 100 = 20% difference. This is different from percentage change. Use percentage change when comparing old vs new; use percentage difference when comparing two alternatives without a defined baseline.

How do I calculate a percentage increase or discount?

For a percentage increase: New Value = Original × (1 + Percentage/100). Example: $80 + 25% = $80 × 1.25 = $100. For a percentage discount: Sale Price = Original × (1 − Discount/100). Example: $120 with 30% off = $120 × 0.70 = $84. To find the discount amount: $120 × 0.30 = $36. Quick mental check: if you're taking 15% off a $60 item, 10% = $6, 5% = $3, so 15% = $9 off, final price = $51.

How do I reverse a percentage (find the original price before discount)?

To reverse a percentage, divide by the multiplier. If a price after 20% discount is $64, the original was $64 ÷ 0.80 = $80 (because $80 × 0.80 = $64). The formula: Original = Final ÷ (1 − Discount/100). For a tax-included price: if $108 includes 8% tax, the pre-tax price = $108 ÷ 1.08 = $100. The most common mistake is subtracting the percentage directly from the discounted price — that gives the wrong answer because the percentage was applied to the original, not the final price.