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Math & School
Percentage Calculator — Percent Of, Increase, Decrease & % Change
The everyday math behind discounts, tips, raises, grades and price changes
Percentage is the most-used piece of math in daily American life — it shows up in store discounts, sales tax, restaurant tips, credit card APR, commission, test grades, raises and the price changes you see on every receipt. It looks simple, yet it is also where people slip up most: mixing up an increase with a discount, adding percentages that don't add, or measuring change against the wrong starting number.
The core idea is straightforward: a percent is just a fraction of 100. X% of Y = (X ÷ 100) × Y. So 15% of $200 = (15 ÷ 100) × 200 = $30.
The four cases you'll use most:
Discount (percent off): final = original × (1 − X ÷ 100). A $200 jacket at 15% off = 200 × 0.85 = $170.
Increase (markup or raise): final = original × (1 + X ÷ 100). A $3,000 paycheck with an 8% raise = 3,000 × 1.08 = $3,240.
Percent change: ((new − old) ÷ old) × 100. A price that goes from $80 to $100 → ((100 − 80) ÷ 80) × 100 = +25%.
Reverse percentage: find the whole when you know the part — if 12% equals $60, the total is 60 ÷ 0.12 = $500.
The classic mistake: discounts don't add up. Stacking 20% off and then 10% off is not 30% off. It's 1 − (0.80 × 0.90) = 28% off. And the reverse trap — going up 10% and then down 10% does not return you to the start. $100 rises to $110, then a 10% cut ($11) leaves $99 — a 1% loss — because the base changes between the two steps.
One more thing that confuses people: a raise and a cut are not symmetric. To undo a 25% increase you don't take 25% off — you take 20% off (1 − 1/1.25). That's why a "back to normal" sale after a price hike is always smaller than the hike itself.
This calculator handles the common cases in one place: X% of Y, percent off, percent increase, percent change between two numbers, the difference between two numbers as a percentage, and the reverse "X% = Y, what's the total?" lookup. Use it to check a sale, size up a raise, read a price swing, or just get your everyday math right.
📖 See also: How to Calculate a Tip (and Split the Bill)
Calculator
Fill in the fields and click "Calculate" for instant results.
📰 Formula
• X% of Y = (X / 100) × Y • Percent off: final = original × (1 − X/100) • Percent increase: final = original × (1 + X/100) • Percent change: ((new − old) / old) × 100 • Reverse: if X% = Y, then total = Y ÷ (X/100)
📰 Formula
• X% of Y = (X / 100) × Y • Percent off: final = original × (1 − X/100) • Percent increase: final = original × (1 + X/100) • Percent change: ((new − old) / old) × 100 • Reverse: if X% = Y, then total = Y ÷ (X/100)
🧪 Worked examples
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Example 2
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Example 3
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Example 4
⚠️ Common mistakes
- Confusing an increase with a discount (the sign and the formula differ).
- Measuring percent change against the new value instead of the original.
- Adding stacked discounts (20% + 10% is 28% off, not 30%).
- Forgetting to divide by 100 before multiplying.
💡 Tips
- Percent change always uses the older/starting value as the base.
- For stacked discounts, apply them one after another — never add the percentages.
- To find the whole from a part, use the reverse mode: total = part ÷ (percent/100).
Embed this calculator on your site
Copy the code below and paste it into the HTML of your site or blog.
<iframe src="https://www.calcnimbus.com/embed/percentage-calculator" width="100%" height="500" frameborder="0" style="border:1px solid #eee;border-radius:12px"></iframe>
❓ Frequently asked questions
How do I calculate X percent of a number?
Multiply the number by X divided by 100. Example: 10% of 200 = 200 × 0.10 = 20.
How do I calculate a percent discount?
Sale price = original price × (1 − discount/100). A $50 item at 20% off = 50 × 0.80 = $40.
How do I calculate a percent increase?
New value = original × (1 + increase/100). $1,000 with a 5% increase = 1,000 × 1.05 = $1,050.
How do I find the percent change between two numbers?
Percent change = (new − old) ÷ old × 100. From 200 to 250 = (250 − 200) ÷ 200 × 100 = +25%.
How do I find the original price before a discount?
Original = discounted price ÷ (1 − discount/100). $80 after 20% off = 80 ÷ 0.80 = $100.
Do two stacked discounts add together?
No. Apply them in sequence. 20% off then 10% off = 1 − (0.80 × 0.90) = 28% off, not 30%.
Why doesn't a 10% increase then a 10% decrease return the original value?
Because the base changes. $100 → +10% = $110 → −10% = $99. You end up 1% lower than you started.
How do I calculate a percentage for a grade or test score?
Score percentage = points earned ÷ total points × 100. 45 out of 50 = 45 ÷ 50 × 100 = 90%.
How do I work out a tip as a percentage?
Tip = bill × (tip percent / 100). A 18% tip on a $60 bill = 60 × 0.18 = $10.80.