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Percentage Calculator

Calculate percentages instantly: find X% of a number, what percentage one number is of another, or the percentage change between two values.

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Percentage calculator. Find X% of a number, ratios, and percentage changes.
A percentage calculator solves three operations: what X% of a number is, what percentage one number is of another, and the percentage change between two values. It divides, multiplies, or compares values against a base of 100 so you get exact results without manual arithmetic.

What Is a Percentage?

A percentage is a number expressed as a fraction of 100, represented by the symbol %. For example, 45% means 45 out of every 100. Percentages are one of the most widely used mathematical concepts in daily life, appearing in discounts, tax rates, exam scores, tipping, nutritional labels, and financial reports.
This percentage calculator handles the three most common percentage operations: finding what X% of a number is, determining what percentage one number is of another, and calculating the percentage change between two values. Whether you are a student checking a test grade, a shopper calculating a sale price, or an employee figuring out how much a raise adds to your paycheck, this tool gives you the answer instantly.

How to Calculate Percentages: 3 Methods

There are three fundamental percentage calculations, each answering a different question:
1. What is X% of Y? Multiply Y by X and divide by 100. For example, what is 15% of $200? Multiply 200 by 15, then divide by 100 to get $30.
2. X is what percent of Y? Divide X by Y and multiply by 100. For example, you scored 42 out of 50 on a test. Divide 42 by 50 to get 0.84, then multiply by 100 to find that your score is 84%.
3. What is the percentage change from X to Y? Subtract the old value from the new value, divide by the old value, and multiply by 100. For example, your rent went from $1,200 to $1,350. The difference is $150, divided by $1,200, times 100 equals a 12.5% increase.
A useful mental math shortcut: percentages are reversible thanks to the commutative property of multiplication. 8% of 50 is the same as 50% of 8, which is simply 4. Whenever one side of the calculation is easier, swap them and get the same result.

Percentage Formulas

Result=X100×Y\text{Result} = \frac{X}{100} \times Y
  • XX = The percentage value (e.g., 20 for 20%)
  • YY = The base number you are taking a percentage of
The formula above answers "What is X% of Y?" The other two modes use related formulas:
To find what percentage X is of Y:
P=XY×100P = \frac{X}{Y} \times 100
To find the percentage change from an old value to a new value:
Δ%=Vnew−VoldVold×100\Delta\% = \frac{V_{\text{new}} - V_{\text{old}}}{V_{\text{old}}} \times 100
A positive result means an increase, and a negative result means a decrease. All three formulas are variations of the same core idea: a percentage relates a part to a whole, scaled to 100.

Percentage Calculation Examples

Calculating a Restaurant Tip: 18% of a $74 Bill

You want to leave an 18% tip on a $74 dinner tab. Using the formula: $74 times 18 divided by 100 equals $13.32. Your total bill including the tip would be $87.32. Quick mental math shortcut: 10% of $74 is $7.40, and 20% is $14.80, so 18% is just under $14.80 which confirms $13.32.

Finding Your Test Score: 37 Correct Out of 45 Questions

You got 37 questions right on a 45-question exam and need to know your percentage score. Divide 37 by 45 to get 0.8222, then multiply by 100 to find your score is 82.2%. In most US grading systems, that is a solid B. If you needed a 90% to get an A, you would have needed at least 41 correct answers (40.5 rounded up).

Salary Increase: From $52,000 to $56,160

Your annual salary went from $52,000 to $56,160 after a raise. To find the percentage increase: $56,160 minus $52,000 equals $4,160. Divide $4,160 by $52,000 to get 0.08, then multiply by 100. Your raise was exactly 8%. For context, the average US salary increase in 2025 was around 3.5-4%, so an 8% raise is well above the national average.

Tips for Working With Percentages

  • Use the reversibility trick for mental math. If 7% of 200 feels hard, flip it: 200% of 7 is 14, so 7% of 200 is also 14. This works because X% of Y always equals Y% of X.
  • Break complex percentages into easy chunks. To find 35% of a number, calculate 10% three times (30%) and then add half of 10% (5%). For example, 35% of $240: 10% is $24, so 30% is $72, plus 5% ($12) gives you $84.
  • Do not confuse percentage change with percentage point change. If interest rates go from 3% to 5%, that is a 2 percentage point increase but a 66.7% relative increase. The distinction matters in finance and news reporting.
  • When comparing discounts, convert everything to the same base. A 25% discount followed by an additional 10% off is not 35% off total. It is actually 32.5% off because the second discount applies to the already-reduced price.
  • For quick estimates of sales tax, memorize your local rate as a simple fraction. A 6% sales tax is roughly 1/16 of the price, and an 8% tax is roughly 1/12. On a $50 purchase, 8% tax is about $4.
  • Percentages greater than 100% are perfectly valid and common. A 150% increase means the new value is 2.5 times the original. A 200% increase means the value tripled.

Frequently Asked Questions About Percentages

Is 20% of 50 the same as 50% of 20?

Yes, they are always equal. Both give you 10. This works because of the commutative property of multiplication: 20/100 times 50 equals 50/100 times 20. You can use this trick to simplify any percentage calculation by flipping the numbers to whichever direction is easier to compute mentally.

What is the difference between percent and percentage points?

Percent measures relative change, while percentage points measure absolute change between two percentages. If a tax rate rises from 5% to 8%, it increased by 3 percentage points but by 60% in relative terms (3 divided by 5 times 100). Confusing the two is one of the most common errors in media and finance.

How do I calculate what percent one number is of another?

Divide the part by the whole and multiply by 100. For example, if 15 students out of 60 chose pizza for lunch, divide 15 by 60 to get 0.25, then multiply by 100. The answer is 25%. The formula is: Percentage = (Part / Whole) times 100.

Can a percentage be more than 100%?

Yes. A percentage over 100% means the value exceeds the reference amount. If a stock was worth $40 and is now $100, the increase is 150% because $60 divided by $40 times 100 equals 150%. The new value is 250% of the original (2.5 times as much).

How do I find the original price before a discount?

Divide the sale price by (1 minus the discount rate as a decimal). If you paid $68 after a 15% discount, the original price was $68 divided by 0.85, which equals $80. This reverses the discount formula to recover the starting price.

What is a percentage of a percentage?

Multiply the two percentages together and divide by 100. For example, 30% of 50% equals 30 times 50 divided by 100, which is 15%. This comes up when calculating stacked discounts: a 30% discount followed by a 50% discount on the reduced price results in a total discount of 65%, not 80%.

How do I convert between fractions, decimals, and percentages?

To go from a percentage to a decimal, divide by 100 (25% becomes 0.25). To go from a decimal to a percentage, multiply by 100 (0.75 becomes 75%). To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100 (3/8 equals 0.375 which is 37.5%).

Why does a 50% loss require a 100% gain to recover?

Because the gain is calculated from the smaller, post-loss value. If you have $1,000 and lose 50%, you are left with $500. To get back to $1,000, you need to gain $500, which is 100% of $500. This asymmetry is why investment losses hurt more than equivalent gains help, and it is a key concept in financial risk management.

Key Terms

Percentage

A number or ratio expressed as a fraction of 100, written with the % symbol. For example, 45% means 45 per hundred.

Percentage Point

The arithmetic difference between two percentages. A change from 10% to 15% is a 5 percentage point increase, distinct from a 50% relative increase.

Percentage Change

The relative difference between an old value and a new value, expressed as a percentage of the old value. A positive result indicates an increase, a negative result indicates a decrease.

Basis Point

One hundredth of a percentage point (0.01%). Used in finance to describe small changes in interest rates. A move from 4.50% to 4.75% is 25 basis points.

Per Mille

A rate expressed per thousand, written with the symbol ‰. One per mille equals 0.1%. It is commonly used in real estate tax rates and blood alcohol content measurements.

Base Value

The reference number that a percentage is calculated from. In the statement '20% of 150,' the number 150 is the base value.

Relative Change

The size of a change expressed as a proportion of the starting value, as opposed to the absolute (raw number) change. A $10 increase on a $50 item is a 20% relative change.