Question 1

How do I calculate a percentage?

Accepted Answer

Divide the part by the whole, then multiply by 100. For example, if 30 out of 120 students passed a test, the pass rate is (30 / 120) × 100 = 25%. The result tells you how many there are 'per hundred' of the whole.

Question 2

How do I find a percentage of a number?

Accepted Answer

Divide the percentage by 100 to get a decimal, then multiply that decimal by the number. For example, to find 15% of 200: 15 / 100 = 0.15, then 0.15 × 200 = 30. So 15% of 200 is 30.

Question 3

What is the difference between percentage change and percentage difference?

Accepted Answer

Percentage change compares a new value against a clearly defined original or starting value. The formula is ((new − original) / |original|) × 100. Percentage difference, on the other hand, compares two values when neither is the obvious starting point — it uses their average as the reference. Use percentage change when one value is the clear 'before' and the other is 'after'. Use percentage difference when comparing two peer measurements where there is no natural baseline.

Question 4

How do I calculate percentage increase?

Accepted Answer

Subtract the original value from the new value to find the amount of increase, divide that by the original value, and multiply by 100. Example: a rise from 80 to 100 is ((100 − 80) / 80) × 100 = (20 / 80) × 100 = 25%. The original value (80, where you started) is always the denominator.

Question 5

How do I calculate percentage decrease?

Accepted Answer

Subtract the new value from the original value to find the reduction, divide by the original value, and multiply by 100. Example: a fall from 60 to 45 is ((60 − 45) / 60) × 100 = (15 / 60) × 100 = 25%. The result is expressed as a positive number representing the size of the reduction.

Question 6

What is a reverse percentage calculation?

Accepted Answer

A reverse percentage finds the original value before a percentage change was applied, given only the final value and the percentage. The key is to divide by the multiplier, not subtract the percentage directly. For an increase of 25%, the multiplier is 1.25. For a decrease of 25%, it is 0.75. Example: if a price after a 20% increase is £120, the original is £120 / 1.20 = £100. If a price after a 10% discount is £90, the original is £90 / 0.90 = £100.

Question 7

How do I calculate a discount percentage?

Accepted Answer

To find the discounted price: multiply the original price by the discount rate divided by 100 to get the saving, then subtract that from the original price. Example: 25% off £80 → saving = £80 × 0.25 = £20; final price = £80 − £20 = £60. Alternatively, multiply the original price by (1 − discount rate / 100): £80 × 0.75 = £60.

Question 8

How do I add VAT to a price?

Accepted Answer

Multiply the net (pre-VAT) price by (1 + VAT rate / 100). For a 20% VAT rate, multiply by 1.20. Example: a net price of £250 with 20% VAT gives £250 × 1.20 = £300 gross. To remove VAT from a gross price, divide by the same multiplier: £300 / 1.20 = £250 net.

Question 9

Can a percentage be greater than 100%?

Accepted Answer

Yes. A percentage is greater than 100% whenever the part is larger than the whole. For example, if a company had revenue of £100,000 last year and £180,000 this year, the increase is 80%, but this year's revenue is 180% of last year's. Percentages above 100% are perfectly valid — they simply mean the value has more than doubled relative to the reference.

Question 10

Why can't I calculate percentage change from zero?

Accepted Answer

The standard percentage change formula divides by the original value. When the original value is zero, division by zero is mathematically undefined, so no finite percentage can be calculated. This situation arises when measuring growth from a zero baseline, such as the first month of sales when there were previously none. In these cases, alternative metrics such as absolute change or ratios are more useful.

Question 11

How do percentages work with decimal and negative values?

Accepted Answer

The formulas work with decimals and negatives in exactly the same way. For example, 2.5% of 80 = (2.5 / 100) × 80 = 2. For a change from −20 to −15, the percentage change is ((−15 − (−20)) / |−20|) × 100 = (5 / 20) × 100 = 25% increase. Using the absolute value of the original (|original|) ensures the sign of the result reflects the direction of change, not the sign of the original value.

Question 12

How should I handle rounding in percentage calculations?

Accepted Answer

Rounding introduces small errors that compound when you use a rounded result in further calculations. The safest approach is to carry full precision through all intermediate steps and round only the final result. How many decimal places to show depends on context: financial amounts typically round to two decimal places, while percentages expressing rates are often shown to one decimal place. The calculators on this site show up to a practical number of decimal places and let you copy the result before rounding.

Question 13

Which calculator should I use for my question?

Accepted Answer

Use the core calculator at the homepage for general questions about percentages of numbers, ratios, or changes. Use the percentage increase or decrease calculator when you have a clear before-and-after value and want to measure the change. Use the percentage difference calculator when comparing two peer values with no natural baseline. Use the reverse percentage calculator when you know the result of a percentage change and want to find the original. Use the discount calculator for retail pricing, the VAT calculator for VAT-inclusive or VAT-exclusive prices, and the sales tax calculator for adding or checking sales tax.

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