Percentage Calculator

What is a percentage?

A percentage is simply a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "per hundred", and the symbol % stands for "out of 100". So 25% means 25 out of every 100, or one quarter. Percentages make it easy to compare proportions on a common scale, which is why they appear everywhere — discounts, taxes, interest rates, exam scores, statistics and tips all use them.

This Percentage Calculator handles the four most common percentage questions in one place. Pick a mode, type your numbers, and the answer appears instantly — there is no button to press, and everything is calculated in your browser, so your figures stay private.

The four calculation modes

Each mode answers a different everyday question:

• What is X% of Y — find a percentage of a number. For example, what is 15% of 200? This is the calculation behind discounts, tips and tax.
• X is what percent of Y — express one number as a percentage of another. For example, 30 is what percent of 200? This is how you turn a score or a part-of-a-whole into a percentage.
• Percentage increase — increase a value by a given percentage. For example, increase 200 by 15%. This is used for markups, raises, inflation and growth.
• Percentage decrease — reduce a value by a given percentage. For example, decrease 200 by 15%. This is used for discounts, depreciation and reductions.

How to calculate percentages

Behind each mode is a simple formula you can also do by hand.

What is X% of Y? Multiply the value by the percentage divided by 100:

Result = Y × (X ÷ 100)

So 15% of 200 = 200 × 0.15 = 30. The same method works for tips (18% of a 50 bill is 9) and tax (5% of 1,000 is 50).

X is what percent of Y? Divide the part by the whole and multiply by 100:

Result = (X ÷ Y) × 100

So 30 is (30 ÷ 200) × 100 = 15% of 200. This is exactly how you convert an exam score of 30 out of 200 into a percentage.

Percentage increase. To increase a value by a percentage, add that percentage of the value back to it:

New value = Y × (1 + X ÷ 100)

So 200 increased by 15% is 200 × 1.15 = 230, an increase of 30. Percentage decrease works the same way but subtracts:

New value = Y × (1 − X ÷ 100)

So 200 decreased by 15% is 200 × 0.85 = 170, a decrease of 30.

Percentage change between two numbers

A closely related question is the percentage change from one number to another — for example, how much a price rose from 200 to 250. The formula subtracts the old value from the new, divides by the old value, and multiplies by 100:

Percentage change = ((New − Old) ÷ Old) × 100

From 200 to 250 that is ((250 − 200) ÷ 200) × 100 = 25% increase. A negative result means a decrease. A key point that catches people out: a percentage increase and the percentage decrease that undoes it are not the same. If a 100 item rises 50% to 150, it must then fall by 33.3% — not 50% — to return to 100, because the decrease is measured against the larger number.

Everyday uses for percentages

Percentages are one of the most practical pieces of maths in daily life:

• Shopping discounts. Work out the sale price of a "30% off" item, or how much you save.
• Tax and tips. Add sales tax or GST to a price, or calculate a restaurant tip.
• Exam and test scores. Convert marks out of a total into a percentage grade.
• Salary and raises. Calculate a pay rise, a bonus, or a deduction.
• Finance. Understand interest rates, investment returns and inflation.
• Statistics and data. Express proportions, growth rates and changes clearly.

Because each of these is just one of the four modes above, this single calculator covers the vast majority of percentage problems you will ever meet.

Percentage points vs percent — a key distinction

One of the most misunderstood ideas in percentages is the difference between a percentage point and a percent. They are not the same, and confusing them leads to real errors — especially in finance and statistics. A percentage point is the simple arithmetic difference between two percentages, while a percent change is relative. Suppose an interest rate rises from 4% to 6%. That is an increase of 2 percentage points, but it is a 50% increase in the rate itself (because 2 is half of 4). Headlines often blur the two, making a change sound larger or smaller than it is. Whenever you read that something "rose by 5%", check whether that means five percentage points or a five-percent relative change — the two can describe very different realities. When you need the relative figure, the "X is what percent of Y" and percentage-change calculations above give it precisely.

Common percentage mistakes to avoid

A few errors crop up again and again. The first, covered earlier, is assuming a percentage increase is cancelled by the same percentage decrease — it never is, because each is measured against a different base. The second is applying successive percentages by adding them: two consecutive 10% increases do not make 20%, they make 21%, because the second 10% applies to the already-increased amount. The third is taking a percentage of an inclusive figure, the same trap that affects tax calculations — to remove a percentage that is already baked into a total, you must divide, not multiply. A fourth is mixing up the part and the whole in the "what percent of" calculation, which flips the answer. And finally, rounding intermediate steps can introduce small errors, so it is best to round only the final result. Because this calculator applies the correct formula for each mode automatically, it removes the guesswork and protects you from every one of these slips.

Tips for working with percentages

A few mental shortcuts make percentages easier. To find 10% of any number, just move the decimal point one place left (10% of 250 is 25). From there, 5% is half of that, 20% is double, and 1% is moving the decimal two places. To find a tip of 15%, add 10% and half of 10% together. Remember that "of" almost always means multiply, and that to convert a percentage to a decimal you divide by 100 (and multiply by 100 to go the other way). When you need an exact answer rather than an estimate, though, this calculator gives it instantly — choose your mode, enter the numbers, and read the result, with nothing sent to a server and no sign-up required.