Percentage Calculator

What this calculator does

Percentages come up constantly and go wrong almost as often, usually because there are six different questions hiding behind the same word and it is easy to answer the wrong one.

This calculator handles all six. What is 25 per cent of 180. What percentage of 180 is 45. What is the percentage change from 350 to 430. Increase a number by a percentage. Decrease it. And the reverse question: 7,500 is 60 per cent of what number.

Each result comes with the working shown, so you can check it, reproduce it by hand, or use it to explain the answer to somebody else. That matters more than the answer itself if you are trying to learn the operation rather than just complete one calculation.

How the calculation works

A percentage is a fraction expressed out of a hundred. Twenty five per cent is simply 25 divided by 100, which is 0.25, and multiplying by that fraction is what taking a percentage means.

Finding what percentage one number is of another reverses the operation: divide the part by the whole and multiply by a hundred. Percentage change follows the same logic but the whole is always the starting value, which is the rule people break most often.

Increases and decreases use a multiplier. Adding 20 per cent means multiplying by 1.20. Removing 20 per cent means multiplying by 0.80. Note that these do not cancel: increasing by 20 per cent and then decreasing by 20 per cent leaves you at 96 per cent of where you started, not back at the beginning.

The reverse calculation divides by the multiplier instead. If a figure is 60 per cent of an unknown number, divide it by 0.60 to recover the original.

The formula

X per cent of Y = (X ÷ 100) × Y

X as a percentage of Y = (X ÷ Y) × 100

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

Increase by X per cent = Value × (1 + X ÷ 100)

Decrease by X per cent = Value × (1 − X ÷ 100)

Reverse = Value ÷ (Percentage ÷ 100)

A worked example

A salary moves from ₦350,000 to ₦430,000. The percentage change is 430,000 minus 350,000, divided by 350,000, times 100, which is 22.86 per cent. Note the denominator is the old figure. Dividing by the new figure instead gives 18.6 per cent, which is a different and wrong answer to this question.

Now the asymmetry. If the salary went back down from ₦430,000 to ₦350,000, that is a decrease of 18.6 per cent, not 22.86. The same ₦80,000 is a different percentage because it is being measured against a larger base. A price that rises 50 per cent needs to fall only 33.3 per cent to return to where it started.

And a reverse example. A jacket is on sale for ₦7,500, which is 60 per cent of the original price. Dividing 7,500 by 0.60 gives ₦12,500 as the price before the discount, so the saving is ₦5,000.

Things worth knowing

The base matters more than the number

Percentage change is always measured against where you started. Most percentage errors are not arithmetic mistakes, they are the wrong number in the denominator, and the answer looks entirely plausible when it happens.

Increases and decreases do not cancel

Up 20 per cent then down 20 per cent leaves you at 96 per cent of the original. This shows up in discount stacking, in investment returns after a fall, and in any situation where percentages are applied in sequence.

Percentage points are different

If a rate moves from 10 per cent to 12 per cent, that is a rise of two percentage points but a 20 per cent increase. Both descriptions are correct and they mean very different things, which is why the distinction matters in reporting.

Check reasonableness

Ten per cent of a number is that number with the decimal point moved one place left. Use it as a quick sanity check before trusting any percentage result, particularly one that came from a spreadsheet formula you did not write.

Common mistakes to avoid

Dividing by the new value instead of the original when calculating percentage change.
Assuming an increase and a decrease of the same percentage cancel out.
Confusing percentage points with percentage change.
Applying two discounts by adding them, when they should be applied in sequence.
Reading a percentage of a percentage as a simple percentage.
Using a percentage of the discounted price when working backwards to the original.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. Twenty five per cent of 180 is 0.25 times 180, which is 45.

How do I work out percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100. The denominator is always the starting figure, which is where most errors occur.

What is the difference between percentage and percentage points?

A move from 10 per cent to 12 per cent is two percentage points, and also a 20 per cent increase. Percentage points describe the absolute gap between two percentages, while percentage change describes the relative movement.

How do I reverse a percentage?

Divide by the percentage expressed as a decimal. If a figure is 80 per cent of the original, divide by 0.80 to recover it. This is what you need for working back from a discounted price or a VAT inclusive amount.

Why do two 10 per cent discounts not equal 20 per cent?

Because the second discount applies to the already reduced price. Two successive 10 per cent reductions leave you at 81 per cent of the original, which is a 19 per cent total discount rather than 20.