Percentage Calculator

What is a percentage?

A percentage is a fraction expressed out of one hundred. The word comes from the Latin per centum — by the hundred — and the symbol % is a compressed way of writing /100. So 25% is 25/100, which is the decimal 0.25, which is one quarter. Four notations, one quantity.

The reason percentages exist at all is comparison. Fractions with different denominators are hard to compare at a glance: is 17/40 bigger than 22/50? Converting both to a common denominator of 100 gives 42.5% and 44%, and the answer is immediate. That is the entire job percentages do — put unlike quantities on a shared scale.

This also explains why a percentage on its own means nothing. "A 30% increase" is not information until you know 30% of what. Every percentage is a relationship between two numbers, and losing track of which number is the base is the root of nearly every percentage error.

How to calculate a percentage

Two questions look similar and have different answers, and telling them apart is most of the skill.

The first is finding a percentage of a number: you know the percentage and the whole, and you want the part. Divide the percentage by 100 and multiply. 25% of 200 is 0.25 × 200 = 50.

The second is finding what percentage one number is of another: you know the part and the whole, and you want the percentage. Divide the part by the whole and multiply by 100. 50 out of 200 is 0.25 × 100 = 25%.

Notice these are inverses. In the first you multiply by the percentage; in the second you divide to find it. A calculator that wires them the wrong way round gives an answer that looks entirely plausible — which is precisely what makes the mistake dangerous.

The percentage formula

One relationship, rearranged three ways:

• Percentage = (Part ÷ Whole) × 100 — you have both numbers and want the rate
• Part = (Percentage ÷ 100) × Whole — you have the rate and the whole
• Whole = Part ÷ (Percentage ÷ 100) — you have the rate and the part

If you can identify which of the three quantities you are missing, you already know which arrangement to use. That is why the modes on this calculator are written as questions rather than formulas: naming what you have is easier than remembering which way round the division goes.

Finding what percent one number is of another

Divide the number you are measuring by the number you are measuring against, then multiply by 100. A score of 45 out of 60 is 45 ÷ 60 × 100 = 75%.

The ordering matters and is easy to invert under pressure. The whole — the total, the maximum, the original, the thing being divided into — always goes on the bottom. A useful check: if the answer should be less than 100% and you get more, you have the numbers the wrong way round.

This is the calculation behind exam marks, completion rates, market share, attendance, pass rates and conversion rates. It is probably the single most-used percentage in ordinary life.

How to calculate percentage increase

Subtract the original from the new value, divide by the original, multiply by 100.

A salary rising from ₹50,000 to ₹57,500 is (57,500 − 50,000) ÷ 50,000 × 100 = 15%. The critical detail is the denominator: you divide by the original, because the increase is being measured relative to where it started. Dividing by the new value instead gives 13.04%, which is a different and wrong answer to a different question.

An equivalent shortcut for going the other way: to increase a number by 15%, multiply by 1.15. To increase by 8%, multiply by 1.08. Recognising percentages as multipliers makes chains of them far easier to handle.

How to calculate percentage decrease

The same formula, producing a negative result. From 100 to 75 is (75 − 100) ÷ 100 × 100 = −25%, which we read as a 25% decrease.

Increase and decrease are not two calculations — they are one calculation and a sign. This calculator reports the magnitude with a direction word and an arrow rather than leaving you to interpret a minus sign, because "−25%" and "a 25% decrease" are the same fact stated two ways and one of them is easier to misread.

As a multiplier, decreasing by 25% means multiplying by 0.75. Decreasing by 8% means multiplying by 0.92.

Percentage change versus percentage difference

These are genuinely different measurements and are constantly confused. The distinction is worth getting right because the two produce different numbers for the same pair of values.

Percentage change measures movement from a specific starting point. It has a direction and it is not symmetric. Going from 100 to 120 is a 20% increase. Going from 120 to 100 is a 16.67% decrease. Same two numbers, different answers, because the base changed.

Percentage difference compares two values that have no natural order — two measurements, two products, two branches — against their average. It has no direction and it is symmetric. The percentage difference between 100 and 120 is 20 ÷ 110 × 100 = 18.18%, whichever order you take them in.

The test is whether one value came before the other. If there is a before and an after, use percentage change. If you are simply comparing two things, use percentage difference. Reporting a difference as a change implies a direction that does not exist.

Percentage points are not percentages

If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points — and a 50% increase. Both are correct; they measure different things. The first is the arithmetic gap between two percentages. The second is the relative change from the starting rate.

This distinction is a favourite of misleading headlines, because the same movement can be described as "up 2 points" or "up 50%" depending on which sounds better. When a figure is itself a percentage, always check which of the two is being reported.

How to reverse a percentage

Reverse percentage answers "this is X% of what?" Divide the known part by the percentage expressed as a decimal. If 50 is 25% of something, that something is 50 ÷ 0.25 = 200.

The instinct to multiply instead of divide is strong and wrong. It shows up most often with discounts: if a jacket costs ₹800 after 20% off, the original was not ₹800 + 20% = ₹960. You paid 80% of the original, so the original is ₹800 ÷ 0.8 = ₹1,000. The difference between ₹960 and ₹1,000 is exactly the error this page's reverse discount mode exists to prevent.

The general rule: to undo a multiplication, divide. If a value was multiplied by 0.8, dividing by 0.8 returns it. Adding the percentage back applies it to the wrong base.

Adding and subtracting percentages

To add a percentage: multiply by (1 + rate ÷ 100). To subtract one: multiply by (1 − rate ÷ 100). Increasing 200 by 25% is 200 × 1.25 = 250; decreasing it by 25% is 200 × 0.75 = 150.

Thinking in multipliers rather than steps pays off as soon as more than one percentage is involved. It also makes an important asymmetry obvious: 1.25 × 0.75 = 0.9375, not 1. Adding 25% and then removing 25% does not return you to where you started — it leaves you 6.25% down, because the second percentage applies to a larger base than the first did.

Sequential percentages

Percentages applied one after another multiply; they do not add. A 20% discount followed by an extra 10% off is 0.8 × 0.9 = 0.72 — a 28% total discount, not 30%.

The same arithmetic explains a well-known trap in investing. A portfolio that falls 50% and then rises 50% is not back to even: 0.5 × 1.5 = 0.75, a 25% loss. To recover from a 50% fall you need a 100% gain, because the gain applies to the halved balance. More generally, recovering from a loss of L% requires a gain of L ÷ (100 − L) × 100 percent — 25% to recover from 20%, 100% to recover from 50%.

Order does not matter for a chain of pure percentages, since multiplication commutes: 20% off then 10% off gives the same figure as 10% off then 20% off. It does matter when a fixed amount is mixed in, such as a flat coupon combined with a percentage discount.

How to calculate a discount

Multiply the price by the discount rate and divide by 100 to get the saving, then subtract. Or do it in one step by multiplying by (1 − rate ÷ 100).

A 20% discount on ₹2,000 is a ₹400 saving and a ₹1,600 price. The one-step version is ₹2,000 × 0.8 = ₹1,600, which is faster and less error-prone because it avoids a subtraction.

For mental arithmetic, 10% is the anchor: move the decimal point one place left. 10% of ₹2,499 is ₹249.90, so 20% is about ₹500 and 30% about ₹750. Most shop-floor percentage estimation is built from that one move.

Finding the original price after a discount

Divide the price you paid by (1 − discount ÷ 100). ₹800 after 20% off means the original was ₹800 ÷ 0.8 = ₹1,000.

This is worth being able to do quickly, because it is how you check whether a "was ₹1,499, now ₹899" claim is arithmetically consistent with the discount percentage advertised alongside it. It is also how you work backwards from a final invoice to a list price.

The mistake to avoid, again: adding the discount percentage to the discounted price. ₹800 plus 20% is ₹960, not ₹1,000, because 20% of ₹800 is smaller than 20% of ₹1,000. The percentage has to be applied to the original base, which is exactly the number you do not yet have — hence the division.

Markup versus margin

Both describe the same profit against different bases, and mixing them up costs businesses real money.

Markup is profit as a percentage of cost: (Selling − Cost) ÷ Cost × 100. It answers "how much did I add on top of what I paid?"

Margin is profit as a percentage of the selling price: (Selling − Cost) ÷ Selling × 100. It answers "how much of each rupee I take in is profit?"

An item costing ₹1,000 and selling at ₹1,250 carries ₹250 of profit. That is a 25% markup and a 20% margin. Because the selling price is always larger than the cost when there is a profit, the margin is always the smaller figure — and the gap widens as profitability rises. A 100% markup is a 50% margin; a 300% markup is a 75% margin.

The practical failure mode: a retailer wanting a 30% margin who applies a 30% markup ends up with a 23% margin and a shortfall on every unit sold. To hit a target margin, the markup required is margin ÷ (100 − margin) × 100. This calculator shows the equivalent of each alongside whichever you asked for, precisely so the two are never confused.

Tax and percentage calculations

Adding tax is an ordinary percentage increase: multiply by (1 + rate ÷ 100). ₹1,000 plus 18% tax is ₹1,180.

Removing tax from a tax-inclusive figure is a reverse percentage, and it is where people slip. ₹1,180 including 18% tax does not contain 18% of ₹1,180 in tax. Divide instead: ₹1,180 ÷ 1.18 = ₹1,000 before tax, so the tax is ₹180. Taking 18% of the inclusive figure gives ₹212.40, overstating the tax by ₹32.40, because that figure already includes the tax you are trying to extract.

As a proportion, 18% tax works out to 15.25% of the tax-inclusive total. If you need a full breakdown of Indian GST into its CGST, SGST and IGST components, the dedicated GST calculator handles that; this page's tax modes are the general arithmetic.

Percentages above 100 and below zero

Both are perfectly legitimate and this calculator does not block either.

A percentage above 100 simply means the part is larger than the base. Something that triples has grown by 200%. A company earning ₹5 crore against a ₹2 crore target has hit 250% of target. Refusing to compute 150% of a number, as some calculators do, is a bug rather than a safeguard.

Negative percentages represent decreases and are handled consistently rather than quietly converted to positive. One case does need care: when the starting value is negative, the naive formula produces a misleading sign. Moving from −100 to −50 is an improvement, but dividing by −100 makes it read as −50%. This calculator divides by the magnitude of the original, so that move correctly reports as a 50% increase, and says so in a note when it applies.

Decimals, rounding and floating point

Percentages produce awkward decimals constantly. One third of anything is 33.333…% and no amount of arithmetic will make it terminate.

There is also a subtler problem specific to computers. Binary floating point cannot represent most decimal fractions exactly, so (8.75 ÷ 100) × 800 evaluates to 70.00000000000001 rather than 70. A calculator that prints that has failed at its only job. This one removes those artifacts before anything is displayed, and keeps full precision internally while rounding only for display — so changing the rounding setting never changes the calculation, only how much of it you see.

The rounding control here is a maximum rather than padding: at two decimals, 50 shows as 50 and 33.3333 shows as 33.33. Money is the exception and pads to its full precision, because ₹1,600.00 is how prices are written.

One practical rule: round at the end, never in the middle. Rounding intermediate values and then combining them accumulates error, which is how a column of correctly-rounded figures ends up not adding to its own total.

Worked examples

All of these are produced by the calculator above rather than typed into the page.

Percentages in your head

A few reliable moves cover most everyday cases.

• 10% is a decimal shift. 10% of 847 is 84.7. Everything else builds from this.
• 5% is half of 10%; 20% is double it. 15% is 10% plus 5%.
• 1% is two decimal shifts. Useful for tips, small rates and sanity checks.
• Percentages are reversible. 8% of 25 is awkward; 25% of 8 is 2, and they are equal, because both are 0.08 × 25. Whenever one order is easier, use it.
• Halves and quarters. 50% is half, 25% is a quarter, 75% is three quarters — usually faster than any multiplication.
• 33% is about a third, 67% about two thirds. Good enough for estimating.

Common percentage mistakes

Confusing "X% of Y" with "X is what % of Y". The first multiplies, the second divides. This is the error that produced the wrong answers on the previous version of this page.

Adding a discount back to find the original. Divide by (1 − rate), do not add the rate.

Adding sequential percentages. They multiply. 20% then 10% is 28%, not 30%.

Assuming an equal gain undoes a loss. A 50% fall needs a 100% rise to recover.

Reporting percentage points as percentages. 4% to 6% is 2 points and a 50% increase.

Confusing markup with margin. A 25% markup is a 20% margin; targeting one and applying the other loses money on every sale.

Taking a percentage of a tax-inclusive figure. Divide to extract tax; multiplying overstates it.

Using percentage difference where percentage change belongs. If there is a before and an after, the change is the right measure.

Rounding too early. Round once, at the end.

Dividing by zero. Nothing can be a percentage of zero, and percentage change from zero is undefined. A calculator that returns "Infinity%" here is telling you it has no error handling.

Privacy

Every calculation on this page runs in your browser. There is no server involved and no request is made — nothing you type leaves your device.

Nothing is stored either, unless you switch on the optional history. That saves to your own browser's local storage and only for calculations you explicitly copy; turning it off deletes the entries immediately.