Percentage Calculator

What is P% of X?

To find a percentage of a number: multiply the number by the percentage and divide by 100. y = (X × P) ÷ 100. Example: 20% of 150 = (150 × 20) ÷ 100 = 30. This is used for calculating discounts (20% off £50 = £50 × 0.20 = £10 off), tips (15% of £45 restaurant bill = £6.75), tax (20% VAT on £100 net = £20 tax), and interest charges. A quick mental shortcut: 10% is always the number divided by 10; 5% is half of 10%; 1% is the number divided by 100. For percentage calculations in gambling, prize pools, and betting payouts, <a href="https://payoutmath.com" rel="noopener">PayoutMath</a> specialises in odds and payout maths.

X is what % of Y?

To find what percentage one number is of another: divide the first number by the second and multiply by 100. P = (X ÷ Y) × 100. Example: 30 is what percentage of 150? Answer = (30 ÷ 150) × 100 = 20%. Used for calculating exam scores (26 correct out of 40 total = 65%), sale comparisons (product A costs £18, product B costs £24 — A is 75% of the price of B), and efficiency measurements (actual output 340 units vs target 400 = 85% of target achieved).

X is P% of what?

Y = (X × 100) ÷ P. Example: 30 is 20% of what = (30 × 100) ÷ 20 = 150. Useful when you know the result and the percentage, but not the original number.

What should I know about Increase / Decrease by P%?

Increase: Y = X × (1 + P/100). Decrease: Y = X × (1 − P/100). Example: 150 increased by 20% = 150 × 1.20 = 180. Used for price rises, salary increases, and VAT calculations.

What's the key thing to understand about Common Percentage Mistakes to Avoid?

One of the most frequent errors is adding or subtracting percentages directly when the base values differ — for example, assuming a 10% pay cut followed by a 10% pay rise returns you to your original salary. It doesn't: a $1,000 cut of 10% leaves $900, and a 10% rise on that new $900 base is only $90, bringing the total to $990, not back to $1,000. Another common mix-up is confusing 'X% of Y' with 'X% more than Y' — '20% of 50' is 10, while '20% more than 50' is 60 (50 plus 20% of 50). A third mistake is treating percentages as if they could exceed their logical bounds without checking the context: a 150% increase is entirely valid (meaning the value more than doubled), but a '150% of a whole pie' makes no physical sense if the pie itself defines 100%. Reading percentage statements carefully — identifying exactly what the percentage is 'of' — avoids the vast majority of these errors.

What do I need to know about Converting Between Fractions, Decimals, and Percentages?

Fractions, decimals, and percentages are three ways of expressing the same underlying value, and converting between them only requires moving a decimal point or dividing. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100 — for example, 3/4 = 0.75 = 75%. To convert a decimal to a percentage, simply multiply by 100 (shift the decimal point two places right): 0.6 becomes 60%. To go the other way, from a percentage back to a decimal, divide by 100 (shift the decimal point two places left): 45% becomes 0.45, which can then be expressed as the fraction 45/100, simplified to 9/20. These conversions matter in practice because percentages are easiest to compare intuitively, decimals are what calculators and spreadsheets use internally for computation, and fractions are often the clearest way to express an exact value (like 1/3 = 33.33...%, which a decimal or percentage can only approximate).

What do I need to know about Percentage of a Percentage (Successive Percentages)?

Applying two percentages one after another does not simply add them — it compounds them. A 20% increase followed by a 20% decrease does not return you to the original value: starting from 100, a 20% increase gives 120, and a 20% decrease on 120 gives 96, not 100. The correct way to combine successive percentage changes is to multiply the scaling factors: an increase of a% followed by a change of b% gives a final multiplier of (1 + a/100)(1 + b/100). This matters for real decisions like stacked discounts (a 10% off coupon applied after a 20% store sale is not a 30% total discount — it's 1 - (0.9 × 0.8) = 28%) and for understanding why a stock that falls 50% needs a 100% gain, not a 50% gain, to get back to its starting price.

What should I know about Percentage Points vs Percentages?

Percentage points and percentages are frequently confused in news reporting and everyday statistics, but they describe different kinds of change and mixing them up leads to genuinely misleading comparisons. A percentage point refers to simple arithmetic difference between two percentages, while a percentage change describes the relative, proportional change between them. If a bank's interest rate rises from 5% to 7%, that is a change of 2 percentage points (7 − 5 = 2), but it is a 40% increase in relative terms, since the rate increased by 2 out of an original 5, and (2/5) × 100 = 40%. Both descriptions are accurate, but they tell a very different story: '2 percentage points' sounds modest, while '40% increase' sounds dramatic, even though they describe the exact same change. This distinction matters enormously in contexts like unemployment rates, exam pass rates, election poll results, and interest rates, where headlines sometimes blur the two intentionally or accidentally to make a change sound larger or smaller than it really is. The safest practice when reporting or reading about changes between two percentages is to state explicitly whether the figure given is a percentage-point difference or a percentage (relative) change, since the two numbers can differ dramatically, especially when the starting percentage is small.

Worked Example: Combining Three Percentage Operations

A $250 item is marked up 40% by a retailer, then later discounted 25% in a sale, and finally has 8% sales tax applied at checkout. Step 1 (markup): $250 × 1.40 = $350. Step 2 (discount): $350 × (1 − 0.25) = $350 × 0.75 = $262.50. Step 3 (tax): $262.50 × 1.08 = $283.50. The final price is $283.50 — notice it's higher than the original $250 despite the 25% discount, because the discount was applied to the already-marked-up price, and the 40% increase was never fully undone by the 25% decrease (1.40 × 0.75 = 1.05, a net 5% increase before tax). Chaining percentage operations always means multiplying the successive decimal factors together, never adding or subtracting the percentages themselves.

Worked Example: Calculating a Restaurant Tip Using Mental Benchmarks

Percentages are easiest to do in your head by building from 10% and 1% benchmarks rather than multiplying the full rate directly. For an $64.50 bill with an 18% tip: 10% of $64.50 = $6.45 (just move the decimal point one place). Half of that gives 5%: $3.225. Adding 10% + 5% = 15%: $6.45 + $3.225 = $9.675. The remaining 3% is three times 1% ($0.645): 3 × $0.645 = $1.935. Total 18% tip: $9.675 + $1.935 = $11.61. Final bill with tip: $64.50 + $11.61 = $76.11.

Percentage Error: A Different Use of the Same Arithmetic

Percentage error measures how far a measured or estimated value is from a known true value, and is common in science and engineering rather than finance: percentage error = |measured − true| / true × 100. If a recipe calls for exactly 200g of flour and a kitchen scale reads 206g, the percentage error is |206 − 200| / 200 × 100 = 6/200 × 100 = 3%. The formula looks almost identical to ordinary percentage change, but the framing is different: percentage change describes a real shift from one value to another over time, while percentage error describes how far an estimate or measurement deviates from a value that's treated as objectively correct — a measuring instrument, an estimate on a test, or a forecast compared against what actually happened.