Percentage calculator:
the four questions it answers

What a percentage calculator does

Percent means per hundred. Almost every percentage question has three parts: the whole, the part and the rate. You are always solving for whichever one is missing.

A calculator saves arithmetic, but it cannot tell you which number is the whole. That judgement is yours, and it is where most wrong answers come from: 20% of what, exactly?

In daily life this covers a surprising range: a 15% tip, the share of a salary that goes on rent, marks in an exam, a discount in a sale, a year of interest, or the share of a bill that comes from one item. All of them reduce to the same three numbers.

Before you press any button, write the question in words: "what is X percent of Y" or "X is what percent of Y". The wording tells you which number is the whole. In "X is what percent of Y", the whole is the number that comes after "of".

It also helps to know what a percentage cannot do by itself. It says nothing about the size of the whole: 50% of 10 and 50% of 10,000 are the same share but very different amounts. Quote the amount alongside the percentage whenever it matters.

Percentage formula: part, whole and rate

Because percent means per hundred, 15% is 15 out of every 100, or 0.15 as a decimal, or 3/20 as a fraction. All three forms are the same number, and converting between them is the quickest way to unblock a stuck problem.

The note under the formula lists the three arrangements, and they answer the first three questions in the table. The fourth question adds or removes a percentage in one step.

Note the multiplier idea in the last row. A percentage written as a decimal, 12% = 0.12, lets you add it in one step: 1 + 0.12 = 1.12. For a reduction use 1 − 0.12 = 0.88. Once you are comfortable with that, you rarely need to calculate the percentage amount separately.

Worked example: 15% of 240

Running the check in both directions takes seconds and catches most slips. If the part comes out larger than the whole for a rate under 100%, a figure has been swapped.

The same method works for other sizes. 35% of 450 is 157.5. And 63 is 14% of 450, because 63 ÷ 450 × 100 = 14.

Percentages of 10% and 1% are useful anchors for mental maths. Ten percent of any number moves the decimal point one place left, so 10% of 240 is 24. Half of that is 5%, which is 12, and 15% is 24 + 12 = 36, matching the answer.

Here is a slightly different problem. A shop takes ₹360 off a ₹1,800 item. The part is ₹360 and the whole is ₹1,800, so the discount rate is 360 ÷ 1,800 × 100 = 20%.

Adding or removing a percentage

To add a percentage, multiply by 1 plus the rate as a decimal. To take one off, multiply by 1 minus the rate. Adding 12% to ₹2,500 means × 1.12, which gives ₹2,800.

The rule is to divide by the same multiplier you used going forward. That is how you strip a percentage back out of a final price.

This matters most when a percentage is added by a seller, such as a service charge, and you want to know the price before it. If a bill totals ₹2,800 after a 12% addition, ₹2,500 is the base and ₹300 is the addition.

Use the same multiplier to project a figure forward: a salary of ₹40,000 with a 6% increase becomes 40,000 × 1.06 = ₹42,400.

Two quick cases show the pattern. Adding 18% to ₹1,000 gives ₹1,180 (× 1.18), and removing 25% from ₹1,000 gives ₹750 (× 0.75). Each works in a single multiplication, with no separate percentage amount to add or subtract.

Two discounts in a row

Take the discount amount first, subtract it, and only then apply the next one. Two discounts of 20% and 10% do not add up to 30% off, because the second is taken from the reduced price.

The same logic applies when a percentage is added twice, for example a fee on top of a price that already includes a mark-up. Apply the steps in order and write down each intermediate price.

Customers often meet this in stacked offers: a seasonal discount followed by a coupon. Because each discount works on a smaller price, the order does not change the final price, but the combined percentage is always less than the simple sum.

To find a single equivalent discount for any pair, multiply the two remaining shares and subtract from 1: 0.80 × 0.90 = 0.72, so the discount is 1 − 0.72 = 28%.

Percentage mistakes to avoid

• Using the wrong whole: 20% of the original price is not 20% of the sale price.
• Reading "20% more" and "20% of" as the same thing: one adds, the other only finds a share.
• Treating two successive percentages as if they simply add.
• Mixing up percent and percentage points when comparing two rates.
• Rounding too early, which can move a final rupee figure by a few paise.

Three habits prevent most of these errors. State the whole in words, estimate the answer before calculating so you can spot an absurd result, and check by running the calculation backwards.

An estimate helps here. If you know that 10% of 240 is 24, then 15% must be between 24 and 48, and 36 fits. A calculator that returns 3.6 or 360 has been fed the wrong number, and you notice immediately.

For a rise or fall between an old and a new value, the percentage change guide goes further, and the percentage decrease guide focuses on price drops.