how do we calculate percentage

What does percentage mean?

A percentage is simply a way to express a number as parts of 100. The word comes from Latin: per centum, meaning “out of one hundred.” So when we say 35%, we mean 35 out of 100.

Percentages are useful because they make comparisons easy. Whether you are looking at exam scores, discounts, taxes, interest rates, or growth in income, percentages let you compare values on the same scale.

The core formula behind all percentage calculations

Almost every percentage question can be solved using one relationship:

Part = Percentage × Whole

To use it correctly, convert the percentage to a decimal first:

• 50% = 0.50
• 12% = 0.12
• 7.5% = 0.075

You convert by dividing by 100 (move decimal two places left).

How do we calculate percentage in common situations?

1) Finding a percentage of a number

Question type: “What is 20% of 150?”

Steps:

• Convert 20% to decimal: 0.20
• Multiply: 0.20 × 150 = 30

Answer: 20% of 150 is 30.

2) Finding what percent one number is of another

Question type: “45 is what percent of 60?”

Steps:

• Divide part by whole: 45 ÷ 60 = 0.75
• Convert to percent: 0.75 × 100 = 75%

Answer: 45 is 75% of 60.

3) Finding the original number from a percentage

Question type: “30 is 25% of what number?”

Steps:

• Convert 25% to decimal: 0.25
• Use whole = part ÷ percentage: 30 ÷ 0.25 = 120

Answer: The original number is 120.

4) Calculating percentage increase

Question type: “Price rises from 80 to 100. What is the percentage increase?”

• Change = 100 − 80 = 20
• Divide by old value: 20 ÷ 80 = 0.25
• Convert to percent: 0.25 × 100 = 25%

Answer: 25% increase.

5) Calculating percentage decrease

Question type: “Sales drop from 200 to 150. What is the percentage decrease?”

• Change = 200 − 150 = 50
• Divide by original: 50 ÷ 200 = 0.25
• Convert to percent: 25%

Answer: 25% decrease.

Quick mental shortcuts

• 10% of a number = move decimal one place left (10% of 450 = 45)
• 1% = move decimal two places left (1% of 450 = 4.5)
• 5% = half of 10%
• 15% = 10% + 5%
• 25% = one quarter
• 50% = half

Common mistakes to avoid

• Forgetting to divide by 100 when converting percent to decimal.
• Using the wrong base number in increase/decrease problems (always use the original value).
• Mixing up “of” and “is” in word problems.
• Dividing by zero (if the whole value is 0, percentage is undefined).

Where percentages are used in real life

Percentages are everywhere:

• Shopping: discounts, sales tax, tips
• Finance: savings interest, loan rates, returns
• Education: test scores and grade averages
• Business: profit margin, growth rate, conversion rate
• Health: nutrition labels and body statistics

Practice questions

Try these:

• What is 18% of 250?
• 72 is what percent of 90?
• A salary goes from 40,000 to 46,000. What is the percentage increase?

Answers:

• 18% of 250 = 45
• 72 is 80% of 90
• Increase = 15%

Final takeaway

If you remember just three formulas, you can solve almost any percentage question:

• Percentage of a number: (P ÷ 100) × N
• What percent: (Part ÷ Whole) × 100
• Percent change: ((New − Old) ÷ Old) × 100

Use the calculator above to check your work, then practice a few examples until the steps feel natural. Once you understand percentages, many everyday math problems become much easier.