Percentage Calculator: How to Work Out Discounts, Increases and Percent Change Without Mistakes

You stand in front of a sign that says "35% off" and wonder what you will actually pay. Or you read that a company's sales rose from 80 to 92 and want the percentage. Or you need the tax on an invoice. These are all percentage questions, all solved with simple formulas, yet mistakes are common because people mix up the base a percentage is taken from with the result. Sahel's percentage calculator answers the three most frequent questions and shows the formula, so you understand what happened rather than just copying a number.

What a percentage means

"Per cent" means "out of a hundred". So 25% is 25 out of every 100, a quarter. A percentage is simply a fraction written differently: 50% is a half, 10% is a tenth, and 100% is the whole. A percentage above 100% means more than the original, so 150% is one and a half times.

The most important thing to remember is that a percentage means nothing without a base. "A 10% increase" says nothing until you know an increase on what. Most percentage errors come from taking the percentage of the wrong base.

Question one: what is X% of Y?

This is the best-known question. The formula is: result = number × percentage ÷ 100.

• 15% of 200 is 200 × 15 ÷ 100 = 30.
• 35% of 80 is 80 × 35 ÷ 100 = 28.
• 5% of 1,250 is 1,250 × 5 ÷ 100 = 62.5.

There are useful mental shortcuts. Ten per cent is moving the decimal point one place, so 10% of 340 is 34. Five per cent is half of that, 17. And 15% is the two added together, 51. That is how you estimate a tip or a tax in seconds.

Question two: what percent is X of Y?

Here you know the part and the whole and want the percentage. The formula: percentage = part ÷ whole × 100.

• You scored 42 out of 60 on a test: 42 ÷ 60 × 100 = 70%.
• You finished 18 tasks of 24: 18 ÷ 24 × 100 = 75%.

The common error is swapping the two numbers. The whole always goes underneath, as the base you are measuring against.

Question three: how much did the value change?

This is the increase-and-decrease question. The formula: percent change = (new value − old value) ÷ old value × 100.

• A price rose from 80 to 92: (92 − 80) ÷ 80 × 100 = a 15% increase.
• It fell from 200 to 150: (150 − 200) ÷ 200 × 100 = −25%, a 25% decrease.

A negative sign means a decrease. And the base is always the old value here, not the new one.

The base is the starting point. For an increase or decrease it is the old value, for a discount it is the original price, for a share it is the whole.

The classic trap: a discount after an increase

If a shop raises a price by 20% and then cuts it by 20%, does the price return to where it was? No. Start with 100: after the increase it is 120, and 20% off 120 is 24, leaving 96. The reason is that the discount was taken from a bigger base. It is also why a share that falls 50% and then rises 50% does not get back to its start: 100 became 50, then 75.

The practical rule: two percentages cannot be added or subtracted unless they share a base. To undo a 20% decrease you need a 25% increase, not 20%.

Percentage points or percent?

If unemployment rises from 5% to 6%, it rose by one percentage point, yet by 20% relative to its previous value. News writing mixes the two constantly, so when you read a headline ask: is this a difference between two percentages or a relative change? The two answers are very different.

Everyday cases

• Discounts: price after discount = price × (1 − discount ÷ 100). 35% off 80 gives 80 × 0.65 = 52.
• Tax: price with tax = price × (1 + rate ÷ 100). If you know the price including tax and want the price before it, divide by (1 + rate ÷ 100) rather than subtracting the rate.
• Grades: a student's mark out of the maximum is question two above.
• Interest: an annual rate is multiplied by the principal and scaled to the period it covers.

How to use it

1. Choose the kind of question: a percentage of a number, what percent one number is of another, or percent change.
2. Enter the two numbers needed.
3. Read the result, which appears at once together with the formula used.
4. Change either number to see its effect on the answer straight away.

A realistic scenario

You see a jacket priced at 240 with 35% off. You choose "percentage of a number" and find the discount is 84, so the price after it is 156. Another shop has the same jacket at 170 with no discount. Using "percent change" between 170 and 156 shows the first is about 8.2% cheaper. You are comparing with numbers, not impressions.

Frequently asked questions

How do I find a percentage of a number?

Multiply the number by the percentage and divide by 100. For example, 15% of 200 is 30.

What is the difference between a 50% increase and an increase of two percentage points?

The first is a relative change from the previous value; the second is a direct difference between two percentages. Going from 4% to 6% is a rise of two points, but a relative increase of 50%.

What happens when the base is zero?

Percent change from zero cannot be calculated because division by zero is undefined. The tool says so plainly rather than showing a misleading number.

Why does 20% off after a 20% rise not bring me back to the first price?

Because each percentage is taken from a different base. After the rise the base is larger, so the discount is a bigger amount than the increase was.

Are my numbers sent to a server?

No. All the calculation runs in your browser.