Percentage Calculator

What does this Percentage Calculator do?

A percentage is just a way of expressing a number as a fraction of 100 — the word literally comes from the Latin "per centum," meaning "by the hundred." This calculator handles the three questions people actually type into a search bar when they need percentage math: finding what a percentage of a number is, working out how much something has increased or decreased in percentage terms, and figuring out what percentage one number represents of another.

The formulas

Each of the three modes uses a different rearrangement of the same basic relationship:

• X% of Y: result = (X ÷ 100) × Y
• Percentage change from X to Y: result = ((Y − X) ÷ X) × 100
• X is what percent of Y: result = (X ÷ Y) × 100

Step-by-step example

Say a jacket normally costs ₹1,500 and is on sale for 20% off. To find the discount amount, you're solving "20% of 1,500": (20 ÷ 100) × 1,500 = 0.2 × 1,500 = ₹300 off, so the sale price is ₹1,200.

Now say you want to check how much the price actually dropped in percentage terms, going from ₹1,500 to ₹1,200: ((1,200 − 1,500) ÷ 1,500) × 100 = (−300 ÷ 1,500) × 100 = −20%. The negative sign confirms it's a decrease — a 20% decrease, matching the discount.

Tips & common mistakes

• When calculating percentage change, always divide by the original (starting) value, not the new one — dividing by the wrong number is the single most common error.
• A percentage increase followed by the same percentage decrease does not bring you back to the original number. A 20% increase from 100 gives 120, but a 20% decrease from 120 gives 96, not 100.
• "200% of a number" simply means double it plus the original again (i.e., multiply by 2) — percentages over 100% are completely valid and common in growth calculations.
• Don't confuse "percentage points" with "percent" when comparing two percentages — a change from 10% to 15% is a 5 percentage-point increase, but a 50% relative increase.

Common ways people use percentages

Percentages show up constantly in daily life beyond simple math homework: figuring out a discount at checkout, calculating a tip, understanding interest rates, reading a school grade report, or interpreting a raise in salary terms. Retailers use "X% off" pricing because it's more intuitive than a flat rupee discount across different price points, and lenders express interest rates as percentages so borrowers can compare loans of different sizes on equal footing.

Percentage change specifically is the metric behind headlines like "stock prices rose 3%" or "unemployment fell 0.5 percentage points" — and understanding the difference between a percentage change and a percentage-point change is genuinely useful for reading financial and economic news accurately, not just for passing a math test.

A second worked example: percentage increase

Suppose your monthly rent went from ₹15,000 to ₹16,500. To find the percentage increase: ((16,500 − 15,000) ÷ 15,000) × 100 = (1,500 ÷ 15,000) × 100 = 10%. Your rent increased by exactly 10%. If you wanted to reverse-engineer what a 10% increase on any base rent would be, you'd multiply the base by 1.10.

Reverse percentage problems

A less obvious but common real-world question is the reverse: "the discounted price is ₹1,200 after a 20% discount — what was the original price?" Here you can't just add back 20% of 1,200, because the 20% was originally taken off a larger number. Instead: original = discounted price ÷ (1 − discount rate) = 1,200 ÷ 0.80 = ₹1,500. This "reverse percentage" pattern trips up a lot of people because the intuitive-seeming shortcut (adding the percentage back) gives a slightly wrong answer.

Percentages compounding over multiple steps

When a value changes by a percentage more than once in sequence — like a stock that rises 10% one year and falls 10% the next — the two changes don't cancel out, because the second percentage applies to a different base value than the first. Starting at 100: a 10% rise takes it to 110, then a 10% fall takes it to 99, not back to 100. This is the same principle behind why compound interest and sequential percentage changes require multiplying growth factors together rather than simply adding percentages.

Percentages in statistics and reporting

News and research reports often express findings as percentages because they normalize different sample sizes for easy comparison — "35% of respondents" is meaningful regardless of whether 350 or 3,500 people were surveyed, whereas raw counts alone aren't directly comparable across studies of different sizes.

Frequently asked questions