Percentage Calculator

A percentage is a number expressed as a share of 100. The word comes from the Latin per centum— “by the hundred” — and the % sign is a compressed way of writing /100.

So 25% = 25 out of 100. The same quantity can be written three ways, and they are interchangeable:

• As a percentage: 25%
• As a fraction: 25/100, or a quarter
• As a decimal: 0.25

Expressing shares out of 100 is what makes them comparable. Scoring 17 out of 20 and 42 out of 50 are hard to rank in your head; 85% and 84% are not. That is the entire purpose of the notation — putting everything on a common denominator so it can be compared at a glance.

The basic formula divides the part by the total and multiplies by 100:

If 30 people out of 150 chose an option, that is (30 ÷ 150) × 100 = 20%. If 45 out of 60 seats are taken, that is 75%.

Two things go wrong most often. The first is putting the numbers the wrong way round — the total belongs on the bottom, and swapping them answers a different question. The second is forgetting the × 100, which leaves you with a decimal rather than a percentage: 0.2 and 20% are the same quantity, but only one of them is written as a percentage.

This is the question behind most everyday percentage arithmetic:

20% of 150 is (20 ÷ 100) × 150 = 30. 15% of 200 is 30. 12.5% of 80 is 10.

A useful property: percentages are reversible. 8% of 50 is awkward to do in your head, but 50% of 8 is obviously 4 — and they are the same answer, because both are (8 × 50) ÷ 100. When one arrangement is difficult, try the other.

A percentage above 100 is perfectly valid and gives a result larger than the number you started with: 150% of 40 is 60.

Percentage increase measures growth against where it started. The original value is the reference point, and it always goes on the bottom:

Going from 100 to 125: ((125 − 100) ÷ 100) × 100 = 25%. The absolute increase is 25, and the percentage increase is 25% — two different figures describing the same movement.

Dividing by the new value instead of the original is the most common error in percentage change. It gives 20% for the example above, which is a real number answering no useful question.

An original value of zero has no percentage increase. Any growth from nothing is infinite however small the new value, so the calculator says so rather than showing a number.

The same calculation with the subtraction the other way round:

Going from 100 to 75: ((100 − 75) ÷ 100) × 100 = 25%, with an absolute decrease of 25. A price falling from ₹1,000 to ₹850 is a 15% decrease.

The original value is the denominator here too. The same ₹150 reduction is a 15% cut on a ₹1,000 item and a 30% cut on a ₹500 one — which is why the amount saved never tells you how good a discount is on its own.

If the new value is higher than the original, the result is negative, and that means the value rose. This calculator shows the negative figure and says plainly that it is an increase, rather than presenting it as a decrease of the same size.

Percentage difference is for comparing two values where neither is a baseline — two quotes, two measurements, two branches. It divides the gap between them by their midpoint:

For 100 and 120: the gap is 20, the midpoint is 110, and 20 ÷ 110 × 100 = 18.18%.

Using the midpoint is what makes the measure symmetric: you get the same answer whichever value you enter first, which is exactly what you want when neither has priority. It is also always positive, because the gap is taken in absolute terms — there is no direction to report when there is no starting point.

Two values that average to zero — 100 and −100, or two zeros — have no percentage difference, because there is no midpoint to measure against.

These are answers to different questions, and the numbers do not match. The deciding question is whether one of your two values is a starting point.

• Percentage changehas a baseline and a direction. Revenue went from last year’s figure to this year’s; last year is the reference. 100 to 120 is a 20% increase.
• Percentage differencehas neither. Two suppliers quoted 100 and 120; neither is the “original”. The difference between them is 18.18%.

Both figures are correct. They differ because change divides by 100 and difference divides by the midpoint of 110.

There is a practical tell for percentage change: it is not symmetric. Going from 100 to 120 is a 20% increase, but going from 120 back to 100 is a 16.67% decrease — the same journey in reverse, a different percentage, because the base changed. Percentage difference gives 18.18% in both directions.

Two questions come up, and they use different modes of the calculator.

How much do I save? Take the percentage of the price. A 20% discount on ₹2,000 is 400 off, leaving 1,600 to pay. Note that the percentage calculation gives you the discount amount, not the final price — you still have to subtract it.

What discount was I given? Use percentage decrease on the two prices. An item marked ₹2,000 selling at ₹1,600 has been reduced by 20%.

Two cautions worth carrying into a shop. Stacked discounts do not add: 20% off then a further 10% off is not 30% off, it is 28% off — ₹100 becomes 80 and then 72 — because the second reduction is taken of the already-reduced price. And the amount you actually pay may still include taxes, delivery or other charges that the marked price does not reflect, so a discount percentage is not the same as money saved overall. A GST calculator handles the tax part.

Marks obtained divided by total marks, multiplied by 100:

Scoring 450 out of 500 is (450 ÷ 500) × 100 = 90%. Scoring 80 out of 100 is 80%.

Across several subjects, add all the marks obtained and divide by the sum of all the totals. Averaging the individual subject percentages gives a different answer unless every subject is out of the same total — a 90% in a 500-mark paper and a 60% in a 100-mark paper average to 75%, but the real combined figure is 85%, because the larger paper carries more weight.

Percentage increase, with the old salary as the original value. A rise from ₹50,000 to ₹55,000 is ((55,000 − 50,000) ÷ 50,000) × 100 = 10%.

Compare like with like. Two gross figures or two take-home figures will give a meaningful answer; one of each will not, and the error is hard to spot because the result still looks plausible.

To work the other way — you have been offered a percentage and want the new figure — multiply: a 12% rise on ₹50,000 gives 56,000. And if you know only the new salary and the percentage, divide to recover the old one: 56,000 after a 12% rise came from 50,000.

A reverse percentage recovers the original amount from a figure that already includes an increase or a discount. The rule is divide, do not subtract.

• Increase a number by 20% — multiply by 1.20. 100 becomes 120.
• Reduce a number by 20% — multiply by 0.80. 100 becomes 80.
• ₹120 is after a 20% increase — divide by 1.20. The original was 100.
• ₹80 is after a 20% decrease — divide by 0.80. The original was 100.

Subtracting instead is the trap. Taking 20% off ₹120 gives 96, not ₹100, because the 20% that was added was 20% of 100 while the 20% being removed is 20% of 120. The two percentages are taken of different bases and do not cancel.

The same asymmetry explains a fact that surprises people: adding 20% and then removing 20% leaves you at 96, not back where you started.

This distinction matters whenever the quantity being compared is itself a percentage — interest rates, tax rates, market share, vote share.

Suppose an interest rate moves from 5% to 7%:

• The increase is 2 percentage points — the arithmetic gap between the two figures.
• The relative increase is 40%, because 2 is 40% of 5.

Both describe the same event, and they differ by a factor of twenty. Saying “rates rose 2%” when they rose 2 percentage points understates the change enormously; saying they rose 40% when they rose 2 points overstates it just as badly to anyone who reads it as points.

The convention worth keeping: use percentage points for the gap between two percentages, and percent for a relative change. When a headline is ambiguous, work out both — the difference is usually large enough to tell you which one was meant.

Worked through with the calculator’s own arithmetic. The rupee amounts are illustrations for the maths, not prices, offers or financial advice.

All five, in one place.