Percentage Calculator

Three Ways to Calculate a Percentage

Percentage questions usually come in one of three shapes, and each needs a slightly different formula, though people often mix them up because a "percentage" always feels like it should be one simple thing.

X% of Y answers "what is 20% of 500?" Multiply Y by X, then divide by 100. So 20% of 500 is (20 × 500) ÷ 100 = 100.

X is what % of Y answers "80 out of 200 is what percent?" Divide X by Y, then multiply by 100. So 80 out of 200 is (80 ÷ 200) × 100 = 40%.

Percentage increase or decrease answers "a price went from 80 to 100, what's the percentage change?" Subtract the old value from the new one, divide by the old value, then multiply by 100. So going from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25%.

Notice that the first two questions only need two numbers and don't care about a before-and-after relationship, while the third specifically compares an old value to a new one. Mixing these up, treating a percentage-of question like a percentage-change question, is one of the most common sources of wrong answers in everyday percentage math.

A Worked Example

If a shirt's price rose from ₹800 to ₹960, the increase is (960 − 800) ÷ 800 × 100 = 20%. If it had instead dropped to ₹640, that would be (640 − 800) ÷ 800 × 100 = −20%, shown as a 20% decrease.

Notice something important here: a 20% increase followed by a 20% decrease does not bring you back to the starting price. ₹800 increased by 20% is ₹960. But ₹960 decreased by 20% is ₹768 (960 × 0.8), not ₹800. This happens because the 20% decrease is calculated on the new, larger base of ₹960, not the original ₹800. This asymmetry trips up a lot of people and is worth remembering whenever a percentage increase is followed by an equal-looking percentage decrease.

Percentage Points vs Percent Change

One of the most common sources of confusion in news headlines and financial reports is the difference between a percentage point and a percent change. If an interest rate moves from 5% to 7%, that's an increase of 2 percentage points, a simple subtraction of 7 minus 5. But expressed as a percent change, it's actually a 40% increase, since (7 − 5) ÷ 5 × 100 = 40%.

Both descriptions are technically correct, but they sound very different, and mixing them up can badly misrepresent the size of a change. Always check whether a reported figure is a percentage-point difference or a percent change, especially for numbers already expressed as percentages, like interest rates, tax rates, or survey results.

Reverse Percentage: Finding the Original Value

Sometimes you know the result of a percentage change and need to work backward to the original number. If a discounted price of ₹850 reflects a 15% discount, the original price isn't simply 850 plus 15% of 850, since the 15% discount was taken off the original price, not the discounted one.

Instead, the discounted price represents 85% of the original, since 100% minus the 15% discount leaves 85%. So the original price is 850 ÷ 0.85 = ₹1,000. This reverse calculation, dividing by one minus the decrease as a decimal, or by one plus the increase as a decimal for an increase, is genuinely useful for checking whether an advertised discount matches the actual math, or for reconstructing a pre-tax price from a tax-inclusive total.

Percentages Over Multiple Periods (Compounding)

When a value changes by the same percentage repeatedly, like a population growing 5% every year, the changes compound rather than simply adding up. A value growing 5% a year for 3 years doesn't grow 15% total; it grows by a factor of 1.05 × 1.05 × 1.05, or 1.157625, about 15.76%. The gap between simple addition and the compounded result is small over a few periods but grows substantially over many, which is the same underlying idea behind compound interest.

This matters whenever you see a series of percentage changes described as happening over time, such as year-over-year sales growth, population growth, or inflation across several years. Multiplying the growth factors together, rather than adding the percentages, gives the accurate combined result.

Percentage Error

Percentage error measures how far an estimated or measured value is from the true or expected value, expressed as a percentage of the true value. The formula is the absolute difference between the estimated and true value, divided by the true value, multiplied by 100.

If a recipe calls for 250 grams of flour and you accidentally measure 260 grams, the percentage error is |260 − 250| ÷ 250 × 100, which is 4%. This concept shows up often in science experiments, budgeting versus actual spending, and forecasting versus actual results, anywhere an estimate is being checked against reality. A smaller percentage error generally means a more accurate estimate, though what counts as "acceptable" error varies a lot by context, a 4% error might be trivial in a cooking recipe but significant in a financial forecast or an engineering measurement.

Percentages in Grades and Test Scores

Academic scores are one of the most common everyday uses of percentages. Scoring 42 out of 50 on a test converts to a percentage using the same X-is-what-percent-of-Y formula: (42 ÷ 50) × 100 = 84%. When averaging percentage scores across multiple tests with different total marks, it's more accurate to average the raw scores and totals first, or weight by the number of questions, rather than simply averaging the percentages themselves, since a percentage from a 10-mark test and one from a 100-mark test don't carry equal weight in a true overall average.

Common Real-World Uses of Percentages

Discounts and sales. A "30% off" sale on a ₹2,000 item takes off ₹600, leaving a sale price of ₹1,400. Stacking two discounts, like "30% off, plus an extra 10%," does not add up to 40% off. The second discount applies to the already-reduced price, so the combined discount is actually 37% off the original, since 0.7 × 0.9 = 0.63, meaning you pay 63% of the original price.

Tips and service charges. A 10% tip on a ₹1,500 bill is ₹150, a straightforward X% of Y calculation. Many restaurants in India also add a service charge before GST is calculated, so it's worth checking whether a printed "10% service charge" is calculated on the subtotal or a different base before assuming what the final total will be.

Markup vs margin. These two are often confused in business contexts. Markup is the percentage added to cost to set a selling price. Margin is the percentage of the selling price that ends up as profit. A product that costs ₹100 and sells for ₹150 has a 50% markup, but only a 33.3% margin, since the ₹50 profit is 33.3% of the ₹150 selling price, not 50%. Businesses that set prices using a target markup percentage but report profitability using margin percentage should keep this distinction in mind when comparing the two figures.

Converting Between Percentages, Fractions, and Decimals

A percentage is just a fraction with a denominator of 100, expressed differently. To convert a percentage to a decimal, divide by 100, so 25% becomes 0.25. To convert a decimal to a percentage, multiply by 100, so 0.6 becomes 60%. To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100, so 3/4 becomes 75%.

These conversions matter because most calculators, spreadsheets, and programming formulas work with decimals internally, even when the number is described as a percentage on screen. If you're building a spreadsheet formula or double-checking a calculator's math by hand, remembering to convert a percentage to its decimal form before multiplying is one of the most common places people go wrong.

Percentages in Tax and Pricing

Sales tax, GST, and similar consumption taxes are almost always expressed as a percentage of the pre-tax price, added on top. A ₹500 item with 18% GST costs ₹590 at checkout, since 500 plus 18% of 500 is 590. Working backward from a tax-inclusive price to find the pre-tax amount uses the same reverse-percentage method covered earlier: divide the final price by 1 plus the tax rate as a decimal, so ₹590 ÷ 1.18 gives back the original ₹500. If you regularly work with GST specifically, our dedicated GST Calculator handles the add and remove directions automatically, including the CGST/SGST split.

Common Mistakes with Percentages

Adding percentages that apply to different bases. A 10% increase followed by a 10% decrease doesn't cancel out, and neither does the reverse order. Each percentage change applies to whatever the current value is at that moment, not to the original starting value.

Confusing "of" and "off." "20% of 500" (100) and "20% off 500" (400, since you subtract the 20%) are very different answers to questions that sound almost identical. Reading percentage questions carefully to spot which one is actually being asked, before reaching for a formula, avoids a lot of otherwise avoidable mistakes.

Forgetting that percentages can exceed 100%. A value can grow by more than 100%, meaning it more than doubled. Going from 50 to 150 is a 200% increase, not 100%, since the change of 100 divided by the original 50 works out to 2, or 200%.

Ignoring the absolute numbers behind a percentage. A 50% increase sounds dramatic, but if it means going from 2 units sold to 3 units sold, the actual change is trivial in real terms. It's worth glancing at the underlying absolute numbers behind any percentage figure, not just the percentage itself, especially when the sample size or base value is small or unfamiliar.

Quick Reference: Percentage Formulas

Bookmark this section if you regularly need to switch between these five variations. Each one starts from the same underlying relationship between a part, a whole, and a rate, just rearranged to solve for whichever piece is missing.

• Find X% of Y: (X ÷ 100) × Y
• Find what % X is of Y: (X ÷ Y) × 100
• Find percent change from X to Y: ((Y − X) ÷ X) × 100
• Find the original value after a known % increase to a result R: R ÷ (1 + percent ÷ 100)
• Find the original value after a known % decrease to a result R: R ÷ (1 − percent ÷ 100)

Frequently Asked Questions

Can the numbers be negative or decimals?

Yes, all three calculators accept negative numbers and decimals, useful for things like calculating a loss, a discount, or a change involving fractional values.

Why does the increase/decrease result show a negative sign?

A negative result means the value decreased, for example, going from 100 to 80 shows as −20%, indicating a 20% decrease rather than an increase.

What's the difference between a percentage point and a percent change?

A percentage point is a simple subtraction between two percentages, like going from 5% to 7% being a 2 percentage point increase. A percent change expresses that same move relative to the starting value, which in this example works out to a 40% increase.

Does a 20% increase followed by a 20% decrease bring a value back to where it started?

No. The decrease is calculated on the new, larger value, not the original one, so you end up slightly below where you started. 100 increased by 20% is 120, but 120 decreased by 20% is 96, not 100.

How do I find the original price before a discount was applied?

Divide the discounted price by 1 minus the discount as a decimal. For a 15% discount resulting in a price of ₹850, the original price is 850 ÷ 0.85, which is ₹1,000.

Is markup the same as margin?

No, they're commonly confused but calculated differently. Markup is profit as a percentage of cost, while margin is profit as a percentage of the selling price. The two numbers are always different unless there's no profit at all.