Percentage Calculator
Three tools in one: find a percentage of a number, figure out what percent one number is of another, or calculate percent change between two values.
What is X% of Y?
X is what percent of Y?
Percent change from X to Y
The three percentage formulas
Most percentage questions are one of three problems:
Example 1: What is 15% of $200? Answer: 200 × 0.15 = $30. Example 2: $30 is what percent of $200? Answer: (30 ÷ 200) × 100 = 15%. Example 3: A price goes from $150 to $180 — what’s the percent increase? Answer: (180 − 150) ÷ 150 × 100 = 20%.
Why percent change is asymmetric
A 20% increase followed by a 20% decrease does not get you back to where you started. If you go up 20% from 100 you reach 120. Down 20% from 120 brings you to 96, not 100. This asymmetry matters for investment returns, pricing, and any scenario where you apply sequential percentage changes. The way to reverse a percentage increase is to divide by (1 + the rate), not subtract the same percentage.
Percentage points vs. percentages
When an interest rate rises from 4% to 5%, that’s an increase of 1 percentage point. It’s also a 25% increase in the rate itself (because 1 is 25% of 4). Confusing these two is one of the most common errors in financial reporting. Percentage points describe absolute differences between two percentages; percentage change describes relative change.
Compound discounts don’t add up
A 20% discount followed by an additional 10% off does not equal 30% off. The second discount applies to the already-reduced price. The combined discount is: 1 − (0.80 × 0.90) = 1 − 0.72 = 28% off total, not 30%. Retailers know this — now you do too.
What is 20% of 350?
350 × 0.20 = 70. Use the first calculator above for any “what is X% of Y” problem.
How do I calculate a tip?
Multiply the bill by the tip percentage as a decimal. A 20% tip on a $45 bill: 45 × 0.20 = $9. Or use the tip calculator to split it automatically.
What’s the difference between percent and percentage points?
Percent describes a ratio; percentage points describe the absolute difference between two percentages. If your score goes from 60% to 75%, that’s 15 percentage points, but a 25% increase in your score.
How do I find the original price after a discount?
Divide the sale price by (1 − discount rate). A $80 item after a 20% discount means the original was 80 ÷ 0.80 = $100.
How percentage calculations actually work
A percentage is a ratio expressed as a fraction of 100. Every percentage problem reduces to one of three fundamental questions: What is X% of Y? What percentage is X of Y? And if X is N% of some number, what is that original number? These three operations cover virtually every real-world percentage calculation you will encounter.
The reason percentages trip people up is that English uses the word "percent" for all three very different operations. "15% tip on $80" (operation 1), "you scored 43 out of 52, what percentage?" (operation 2), and "you saved $15 which was 20% off, what was the original price?" (operation 3) all involve percentages but require completely different math.
The three operations with formulas
Operation 1: What is X% of Y?
Formula: Result = (X ÷ 100) × Y
Example: What is 18% of $340? (18 ÷ 100) × 340 = 0.18 × 340 = $61.20. This covers tips, discounts, sales tax, commissions, and investment returns.
Operation 2: X is what percentage of Y?
Formula: Percentage = (X ÷ Y) × 100
Example: You scored 43 out of 52. (43 ÷ 52) × 100 = 82.7%. This covers test scores, market share, and performance metrics.
Operation 3: X is N% of what number?
Formula: Original = X ÷ (N ÷ 100)
Example: You saved $45 and the discount was 30%. What was the original price? 45 ÷ 0.30 = $150. Essential for understanding sale prices and reverse-engineering totals.
Percentage change — the most commonly misunderstood calculation
Percentage change: Change% = ((New − Old) ÷ Old) × 100. A home worth $350,000 now worth $420,000: ((420,000 − 350,000) ÷ 350,000) × 100 = 20% appreciation.
The most common mistake: dividing by the new value instead of the old. A stock going from $100 to $150 is a 50% gain (50 ÷ 100). Falling from $150 back to $100 is a 33.3% loss (50 ÷ 150) — not 50%. A 50% gain followed by a 33% loss gets you back to zero. This asymmetry explains why investment math feels counterintuitive.
Real-world scenarios with actual numbers
Scenario 1 — Restaurant tip in Las Vegas: Bill is $187. 20% tip: (20 ÷ 100) × 187 = $37.40. Total: $224.40. Quick mental math: 10% = $18.70, double it for 20% = $37.40.
Scenario 2 — Sales tax in Clark County, Nevada: The rate is 8.375%. On a $2,400 TV: (8.375 ÷ 100) × 2,400 = $201 in tax. Total: $2,601. Nevada has no state income tax, but the sales tax rate is among the higher in the US.
Scenario 3 — Home appreciation in Henderson, NV: A home bought for $320,000 in 2020 sold for $485,000 in 2024. Increase: ((485,000 − 320,000) ÷ 320,000) × 100 = 51.6% over 4 years — roughly 11% annually compounded. Use the Mortgage Calculator to model what those values mean for buying today.
Scenario 4 — Real estate commission: A 2.5% commission on a $495,000 sale: (2.5 ÷ 100) × 495,000 = $12,375. Understanding percentages directly affects your net proceeds on a home sale.
Percentage points vs. percentages — a critical distinction
If a mortgage rate rises from 4% to 6%, it rose by 2 percentage points. As a percentage change: ((6 − 4) ÷ 4) × 100 = 50%. Both accurate, completely different meanings. Politicians and marketers frequently confuse the two deliberately. "Crime fell by 10 percentage points" (from 40% to 30%) sounds very different from "crime fell 25%" — yet can describe the same data.
Mental math shortcuts for common percentages
- 10%: Move the decimal left one place. 10% of $340 = $34.
- 5%: Half of 10%. 5% of $340 = $17.
- 20%: Double the 10%. 20% of $340 = $68.
- 25%: Divide by 4. 25% of $340 = $85.
- 15%: 10% + half of 10%. 15% of $340 = $34 + $17 = $51.
- 1%: Move the decimal left two places, then multiply.
Frequently asked questions
What is 15% of 200?
15% of 200 = (15 ÷ 100) × 200 = 30. Mental shortcut: 10% of 200 is 20, add half of that (5% = 10), total is 30.
How do I calculate a percentage increase?
Percentage increase = ((New Value − Original Value) ÷ Original Value) × 100. Example: price goes from $80 to $96. Increase = ((96 − 80) ÷ 80) × 100 = 20%.
How do I find the original price after a discount?
Original = Sale Price ÷ (1 − Discount%). Paid $60 after a 25% discount: $60 ÷ 0.75 = $80 original price.
What is the difference between 50% more and 50% of?
"50% more than $100" = $150. "50% of $100" = $50. These are completely different numbers. "More than" adds to the original; "of" takes a fraction of it.
How do I calculate tip percentage quickly?
Move the decimal left to get 10%, then scale. On a $64 bill: 10% = $6.40, 20% = $12.80, 15% = $6.40 + $3.20 = $9.60.
What is compound percentage growth?
When a percentage increase applies to a growing base rather than the original value, it compounds. A 10% return on $10,000 yields $1,000 in year 1, but $1,100 in year 2 (on a $11,000 base). See the Compound Interest Calculator to model it over time.
How does Nevada sales tax work with percentages?
Clark County sales tax is 8.375%. Apply it as: Tax = Price × 0.08375. Total = Price × 1.08375. To find the pre-tax price from a tax-included total: Pre-tax = Total ÷ 1.08375.
Disclaimer: This calculator provides general mathematical information only. Results are based on the inputs you provide. Not financial or professional advice.