How to Calculate Percentages: Increase, Decrease, and Difference

What Is a Percentage?

A percentage is a fraction of 100. The word comes from the Latin per centum, meaning “per hundred.” So 25% simply means 25 out of every 100 — the same value as the fraction 1/4 or the decimal 0.25.

That last conversion is the key to everything else: to use a percentage in a calculation, turn it into a decimal by dividing by 100. 8% becomes 0.08, 150% becomes 1.5, and 0.5% becomes 0.005.

The Three Percentage Formulas

Every percentage question is one of these three in disguise. “What is 15% of 80?” is formula 1. “48 out of 60 — what percentage is that?” is formula 2. “My rent went from 900 to 990 — what’s the increase?” is formula 3.

How to Calculate a Percentage Step by Step

To find a percentage of a number (the most common task):

1. Convert the percentage to a decimal. Divide it by 100: 15% → 0.15.
2. Multiply by the whole amount. 0.15 × 80 = 12.
3. Attach the units. 15% of 80 dollars is 12 dollars.

To find what percentage one number is of another:

1. Divide the part by the whole. 48 ÷ 60 = 0.8.
2. Multiply by 100. 0.8 × 100 = 80%.

Percentage Increase and Decrease

Percentage change always measures the change relative to the starting value:

• Price rises from 900 to 990: (990 − 900) ÷ 900 × 100 = 10% increase
• Price falls from 990 to 900: (900 − 990) ÷ 990 × 100 = −9.09% (a 9.09% decrease)

Notice the asymmetry: a 10% rise followed by a 10% fall does not return you to the start, because the second percentage is taken from a bigger base. This is one of the most misunderstood facts in everyday math — and it matters for sales, salaries, and investments alike. The same relative-change logic drives compound interest, where each year’s percentage builds on the last.

Reverse Percentages

Sometimes you know the final amount and need the original. If a jacket costs 68 after a 15% discount, the price paid represents 85% (100% − 15%) of the original:

The mistake to avoid: adding 15% back onto 68 gives 78.20 — wrong, because the 15% was taken from the original 80, not from 68. Reverse percentages power everything from un-discounting prices to working out pre-tax amounts, and our discount calculator handles the store-sale version of this automatically.

Worked Examples

Example 1: Exam score

You scored 42 out of 56. Percentage = (42 ÷ 56) × 100 = 0.75 × 100 = 75%.

Example 2: Restaurant bill

A 12% service charge on a 4,500-rupee bill: 0.12 × 4,500 = 540 rupees. (The tip calculator also splits it between friends.)

Example 3: Salary raise

Salary goes from 52,000 to 55,640. Change = (55,640 − 52,000) ÷ 52,000 × 100 = 3,640 ÷ 52,000 × 100 = 7% raise.

Example 4: Reverse percentage

A phone costs 25,300 including 10% sales tax. Pre-tax price = 25,300 ÷ 1.10 = 23,000.

Mental-Math Shortcuts

• 10% trick: move the decimal one place left. 10% of 340 = 34. From there, 5% is half (17), 20% is double (68), and 15% is 34 + 17 = 51.
• 1% trick: move the decimal two places. 1% of 340 = 3.4, so 3% = 10.2.
• Flip trick: X% of Y always equals Y% of X. 8% of 50 feels hard; 50% of 8 = 4 is instant.
• Quarters: 25% = divide by 4; 75% = three quarters; 50% = half.

Common Percentage Mistakes

1. Dividing by the wrong base. Percentage change divides by the old value, never the new one.
2. Adding percentages of different bases. A 20% discount plus a further 10% off is 28% total, not 30% — the second discount applies to an already-reduced price.
3. Confusing percentage points with percent. Interest moving from 4% to 6% is a rise of 2 percentage points, but a 50% relative increase.
4. Reverse-percentage errors. To undo a 15% discount, divide by 0.85 — don’t multiply by 1.15.
5. Forgetting that percentages over 100 are valid. 250% of 40 is simply 2.5 × 40 = 100.

Frequently Asked Questions

How do I calculate a percentage of a number?

Divide the percentage by 100 to get a decimal, then multiply by the number. For 18% of 250: 0.18 × 250 = 45. This one operation handles tips, taxes, discounts, and interest alike.

How do I work out what percentage one number is of another?

Divide the part by the whole and multiply by 100. Scoring 34 out of 40 gives (34 ÷ 40) × 100 = 85%. Always ask “out of what?” — that answer is your denominator.

How do I calculate percentage increase between two numbers?

Subtract the old value from the new one, divide the result by the old value, and multiply by 100. From 80 to 92: (92 − 80) ÷ 80 × 100 = 15% increase.

What is the difference between percentage and percentile?

A percentage measures a share of 100. A percentile ranks you within a group: scoring in the 90th percentile means you did better than 90% of participants — regardless of your actual percentage score.

Why do two consecutive discounts not simply add up?

Because each discount applies to a new, smaller base. 20% off then 10% off leaves 0.8 × 0.9 = 0.72 of the original price — a 28% total discount, not 30%.

Can a percentage be negative?

Yes — a negative percentage change means a decrease. If sales fall from 200 to 170, the change is (170 − 200) ÷ 200 × 100 = −15%, read as “down 15 percent.”

How do I convert a fraction to a percentage?

Divide the top by the bottom and multiply by 100. 5/8 = 0.625 → 62.5%. Going the other way, write the percentage over 100 and simplify: 40% = 40/100 = 2/5.

Conclusion

Learning how to calculate percentages comes down to three formulas: decimal × whole for a percentage of a number, part ÷ whole × 100 to express one number as a percentage of another, and change ÷ original × 100 for increases and decreases. Add the 10% mental trick and the flip trick, and you can handle most everyday cases without a pen. For everything else — or to check your work — the free percentage calculator on CalcRange gives the answer instantly, and it pairs naturally with our GPA calculator when exam season arrives.