Percentage Calculator

To calculate a percentage, divide the part by the whole and multiply by 100. For example, if you want to know what percentage 30 is of 150, divide 30 by 150 to get 0.2, then multiply by 100 to get 20%. The basic formula is: Percentage = (Part ÷ Whole) × 100. You can use the calculator above to do this instantly without any manual working.

The formula for percentage change is: ((New Value − Old Value) ÷ Old Value) × 100. If the result is positive, the value has increased. If it is negative, the value has decreased. For example, going from 80 to 100 gives ((100 − 80) ÷ 80) × 100 = 25% increase. This formula works for any two numbers you want to compare over time.

To calculate percentage increase, subtract the original value from the new value, divide by the original value, then multiply by 100. The formula is: ((New Value − Original Value) ÷ Original Value) × 100. For example, if a price goes from £40 to £50, the increase is £10. Dividing £10 by £40 gives 0.25, multiplied by 100 gives a 25% increase. Use the Percentage Change calculator above and it will tell you automatically whether the result is an increase or decrease.

To calculate percentage decrease, subtract the new value from the original value, divide by the original value, then multiply by 100. The formula is: ((Original Value − New Value) ÷ Original Value) × 100. For example, if a price drops from £50 to £40, the decrease is £10. Dividing £10 by £50 gives 0.20, multiplied by 100 gives a 20% decrease. Note that percentage increase and decrease use different denominators, so a 25% increase followed by a 25% decrease does not return to the starting value.

Percentage change measures how much a value has moved from a specific starting point — it has a clear direction (increase or decrease) and the original value is the reference point. Percentage difference, on the other hand, compares two values without implying which came first or which is the reference. It uses the average of the two values as the denominator: (|Value A − Value B| ÷ ((Value A + Value B) ÷ 2)) × 100. Use percentage change when tracking movement over time, and percentage difference when comparing two independent figures side by side.

A percentage expresses a proportion as a fraction of 100 — for example, 75% means 75 out of every 100. A percentile is a position within a ranked data set: scoring in the 90th percentile means you scored higher than 90% of people in the group. A percentage answers "how much of the whole", while a percentile answers "where does this value rank within a distribution". The two terms are frequently confused but describe entirely different things.

To find what percentage one number is of another, divide the first number by the second number and multiply by 100. For example, to find what percentage 25 is of 200: divide 25 by 200 to get 0.125, then multiply by 100 to get 12.5%. The formula is: (Part ÷ Whole) × 100. This is useful for calculating test scores, market share, proportions, and many everyday situations.

To find 10% of any number, move the decimal point one place to the left. For example, 10% of 350 is 35, and 10% of 84 is 8.4. From there, other percentages become easy: 5% is half of 10%, 20% is double 10%, and 15% is 10% plus 5%. This mental arithmetic shortcut is the fastest way to estimate tips, discounts, and tax without a calculator.

To add a percentage to a number, multiply the number by (1 + the percentage expressed as a decimal). For example, to add 20% to 150: multiply 150 by 1.20, which gives 180. Alternatively, calculate 20% of 150 (which is 30) and add it to 150 to get 180. This is the calculation used for adding VAT, tips, service charges, and markups to a base price.

To subtract a percentage (such as a discount) from a number, multiply the number by (1 − the percentage as a decimal). For example, a 20% discount on £150 means multiplying 150 by 0.80, which gives £120. Alternatively, calculate 20% of 150 (which is 30) and subtract it from 150. You can also use the 'Subtract a Percentage' calculator above to work this out instantly. This applies to sale prices, commission deductions, and any reduction from a base figure.

A reverse percentage works backwards from a known result to find the original value. If you know that a number is a certain percentage of an unknown whole, you divide the known number by the percentage (expressed as a decimal) to find the original. For example, if 150 is 75% of some number, divide 150 by 0.75 to get 200. This is useful when a price shown already includes a percentage added or removed and you want to find the original figure before that change.

To add VAT or sales tax to a price, use the 'Add a Percentage' calculator and enter the tax rate as the percentage. For example, to add 20% UK VAT to a price of £100, enter 100 as the number and 20 as the percentage — the result is £120. To find the pre-VAT price from a VAT-inclusive price, use the 'Reverse Percentage' calculator: if £120 is the VAT-inclusive price at 20% VAT, then the original price is £120 ÷ 1.20 = £100. The same approach works for any sales tax rate.

A 25% increase followed by a 25% decrease does not return to the original value because each percentage is applied to a different base number. Starting from 100: a 25% increase gives 125. A 25% decrease applied to 125 gives 93.75 — not 100. The increase uses 100 as its base, while the decrease uses the larger number 125 as its base. This asymmetry means that equal percentage increases and decreases never perfectly cancel each other out.

Percentage points measure the arithmetic difference between two percentages. Percent (%) measures a relative change. If an interest rate rises from 4% to 6%, it has increased by 2 percentage points, but it has increased by 50% relative to its original value. These are not the same — a 2 percentage point change and a 50% change describe the same move but from different perspectives. Percentage points are commonly used in economics, finance, and polling.

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 × 100 = 75%. For 1/3: 1 ÷ 3 = 0.3333 × 100 = 33.33%. If the denominator divides evenly into 100, you can scale the fraction directly — for example, 3/5 = 60/100 = 60%. The formula (numerator ÷ denominator) × 100 works for any fraction.

A basis point (abbreviated bp or bps) equals one hundredth of one percentage point, or 0.01%. There are 100 basis points in one percentage point and 10,000 basis points in 1 (100%). Basis points are used in finance to describe small changes in interest rates, bond yields, and fees with greater precision. For example, a central bank raising rates by 25 basis points means an increase of 0.25 percentage points — from 5.00% to 5.25%.

15% of 200 is 30. To calculate this, multiply 200 by 0.15 (which is 15 ÷ 100). The formula is: 200 × 0.15 = 30. You can verify this by finding 10% of 200 (which is 20) and then adding half of that (10% ÷ 2 = 10): 20 + 10 = 30.

20% of 150 is 30. To calculate this, multiply 150 by 0.20. The formula is: 150 × 0.20 = 30. You can also find 10% of 150 (which is 15) and double it: 15 × 2 = 30. This is a common calculation for tips, discounts, and markups.

To calculate a tip, multiply the bill amount by the tip percentage expressed as a decimal. For a 15% tip on a £60 bill: 60 × 0.15 = £9. For a 20% tip on a £60 bill: 60 × 0.20 = £12. A quick mental shortcut: find 10% by moving the decimal left, then adjust. 10% of £60 = £6, so a 20% tip is £12 and a 15% tip is £9. Use the "Add a Percentage" calculator above to work this out for any amount.

To find what percentage something is of your total budget, divide the item cost by the total budget and multiply by 100. For example, if you spend £300 on food from a £1,500 monthly budget: (300 ÷ 1,500) × 100 = 20%. That means food represents 20% of your budget. Use the "X is what percent of Y?" calculator above to work this out instantly.

In Excel or Google Sheets, percentage calculations use the same formulas as manual calculation but written as cell references. To find what percentage A2 is of B2, use the formula =A2/B2 and format the cell as a percentage. To find X% of a number, use =A2*0.15 (for 15%). For percentage change, use =(B2-A2)/A2 and format as percentage. Excel and Sheets apply the multiplied-by-100 step automatically when you format a cell as a percentage, so you only need to divide — not multiply by 100.

Yes. PercentageHQ uses standard mathematical formulas for all eight calculator types: the core percentage formula (Part ÷ Whole × 100), the standard percentage change formula ((New − Old) ÷ Old × 100), and the recognised percentage difference formula using the average of two values as the denominator. All calculations run entirely in your browser using JavaScript floating-point arithmetic, with results rounded to 8 significant figures to avoid rounding artefacts. There are no external API calls, no server-side processing, and no opportunity for a network error to affect results.