Percentage Calculator: Find Percentages, Increases & Decreases

How to Use Our Percentage Calculator

Our calculator is structured to solve the three most common types of percentage problems. Simply choose the calculator that matches the question you’re trying to answer.

1. What is X% of Y?

Use this calculator when you know the percentage and the total amount, and you need to find the part.

• Example Question: What is 15% of 200?

• How to Use:

  • In the first field, enter the percentage (e.g., 15).

  • In the second field, enter the total amount (e.g., 200).

  • Click “Calculate”.

2. X is what percent of Y?

Use this calculator when you know the part and the total amount, and you need to find the percentage.

• Example Question: 30 is what percent of 200?

• How to Use:

  • In the first field, enter the “part” number (e.g., 30).

  • In the second field, enter the “total” amount (e.g., 200).

  • Click “Calculate”.

3. What is the percentage change from X to Y?

Use this calculator to find the percentage increase or decrease when a value changes.

• Example Question: What is the percentage increase from 50 to 75?

• How to Use:

  • In the first field, enter the starting value (e.g., 50).

  • In the second field, enter the final value (e.g., 75).

  • Click “Calculate”. The result will show if it’s an increase or decrease.

Understanding Your Results

A percentage is simply a part of a whole expressed as a fraction of 100. The word “percent” comes from the Latin per centum, meaning “by the hundred.” Understanding the simple formulas behind these calculations can help you feel more confident with math in your daily life.

The Math Behind “What is X% of Y?”

This calculation finds a specific portion of a whole number.

• Formula: Part = (Percentage / 100) * Whole

• Step 1: Convert the percentage to a decimal. You do this by dividing it by 100. For example, 15% becomes 15 / 100 = 0.15.

• Step 2: Multiply the decimal by the whole number.

• Example: To find 15% of 200:

  • 0.15 * 200 = 30

  • So, 15% of 200 is 30.

The Math Behind “X is what percent of Y?”

This calculation expresses one number as a percentage of another.

• Formula: Percentage = (Part / Whole) * 100

• Step 1: Divide the “part” by the “whole”. This gives you a decimal value representing the proportion.

• Step 2: Convert the decimal to a percentage. You do this by multiplying it by 100.

• Example: To find what percent 30 is of 200:

  • 30 / 200 = 0.15

  • 0.15 * 100 = 15%

  • So, 30 is 15% of 200.

The Math Behind “Percentage Change”

This calculation measures the relative change between two numbers. It’s one of the most common calculations in finance, statistics, and science.

• Formula: Percentage Change = ((Final Value - Starting Value) / Starting Value) * 100

• Step 1: Calculate the change. Subtract the starting value from the final value.

• Step 2: Divide the change by the original starting value. This determines the change relative to the starting point.

• Step 3: Multiply by 100 to express the result as a percentage.

• Example: To find the percentage change from 50 to 75:

  • Change: 75 - 50 = 25

  • Divide by original value: 25 / 50 = 0.5

  • Multiply by 100: 0.5 * 100 = 50%

  • The result is a 50% increase. If the final value were smaller than the starting value, the result would be negative, indicating a decrease.

Frequently Asked Questions

How do you calculate a tip for a restaurant bill?

This is a classic “What is X% of Y?” problem. Let’s say your bill is $60 and you want to leave a 20% tip.

1. Use the first calculator: “What is 20% of 60?”

2. Calculation: (20 / 100) * 60 = 0.20 * 60 = $12.

3. Total Bill: $60 (bill) + $12 (tip) = $72.

How do you calculate a discount on a sale item?

This is another “What is X% of Y?” problem. Imagine a jacket that costs $150 is on sale for 30% off.

1. Use the first calculator to find the discount amount: “What is 30% of 150?”

2. Discount Amount: (30 / 100) * 150 = 0.30 * 150 = $45.

3. Final Price: $150 (original price) - $45 (discount) = $105.

How do I add or subtract a percentage from a number?

You can do this in two steps. Let’s say you want to increase 80 by 25%.

1. Find the percentage amount: Calculate “What is 25% of 80?”. The answer is 20.

2. Add it to the original number: 80 + 20 = 100.

A faster way is to convert the percentage to a decimal and add or subtract it from 1.

• To increase by 25%: 1 + 0.25 = 1.25. Then 80 * 1.25 = 100.

• To decrease by 25%: 1 - 0.25 = 0.75. Then 80 * 0.75 = 60.

What is the difference between a 10% increase and a 10% decrease?

The key is the starting point. The percentage change is always calculated based on the original number.

• Increase: If you increase 100 by 10%, you add 10. The new number is 110.

• Decrease: If you then decrease 110 by 10%, you are now calculating 10% of 110 (which is 11). 110 - 11 = 99. You don’t end up back at 100 because the starting point for the decrease was a larger number.

What is the difference between “percent” and “percentage points”?

This is an important distinction, especially in finance and news reporting.

• Percent measures a relative change. If your investment grows from $100 to $150, it’s a 50% increase.

• Percentage Points measure an absolute change between two percentages. If an interest rate goes from 4% to 5%, it has increased by one percentage point. It has not increased by 1%. The actual percentage increase is ((5-4)/4) * 100 = 25%.

How do you calculate a reverse percentage?

This is when you know the final price after a discount and want to find the original price. Let’s say you paid $80 for a coat after a 20% discount.

1. If there was a 20% discount, you paid 80% of the original price (100% - 20% = 80%).

2. So, $80 is 80% of the original price. We can set this up as: Original Price * 0.80 = $80.

3. To find the original price, divide the final price by the decimal: Original Price = $80 / 0.80 = $100.

How can I calculate a percentage from a fraction?

To convert a fraction to a percentage, you first convert the fraction to a decimal, then multiply by 100.

• Example: For the fraction $frac35$:

  1. Divide the numerator by the denominator: 3 / 5 = 0.6.

  2. Multiply the decimal by 100: 0.6 * 100 = 60%.

How do I calculate percentages for a pie chart?

To create a pie chart, each segment’s percentage must add up to 100%.

1. Find the total: Add up all the values for each category. (e.g., 20 apples, 30 oranges, 50 bananas. Total = 100 fruits).

2. Calculate the percentage for each category: Use the “X is what percent of Y?” calculator.

   • Apples: (20 / 100) * 100 = 20%

   • Oranges: (30 / 100) * 100 = 30%

   • Bananas: (50 / 100) * 100 = 50%

Concrete Example: Calculating a Final Price with Sales Tax

Let’s combine two percentage calculations. You buy a shirt for $40 that’s on sale for 25% off. The local sales tax is 6%. What is your final price?

1. Step 1: Calculate the discount.

   • Use “What is 25% of 40?”.

   • (25 / 100) * 40 = $10. The discount is $10.

2. Step 2: Find the sale price.

   • $40 (original) - $10 (discount) = $30.

3. Step 3: Calculate the sales tax on the new price.

   • Use “What is 6% of $30?”.

   • (6 / 100) * 30 = $1.80. The sales tax is $1.80.

4. Step 4: Find the final price.

   • $30 (sale price) + $1.80 (tax) = $31.80.

How is compound interest related to percentages?

Compound interest is essentially a percentage increase that is calculated repeatedly on the new, larger total. If you have $1,000 in a savings account with 5% annual compound interest:

• Year 1: You earn 5% of $1,000, which is $50. Your new total is $1,050.

• Year 2: You earn 5% of the new total ($1,050), which is $52.50. Your new total is $1,102.50. The growth accelerates because you earn interest on your interest.

Now that you’ve mastered percentages, you might find other math tools useful. If you need to work with parts of a whole in a different format, try our Fraction Calculator. For quick calculations on the go, our Basic Calculator is always available.