Question 1

How do you calculate percentage increase?

Accepted Answer

Subtract the original value from the new one, divide by the original, then multiply by 100. Going from 120 to 150 gives (150 − 120) ÷ 120 × 100 = 25%, so a 25% increase. The original value is always the number you divide by — that is what makes it the baseline.

Question 2

How do you calculate percentage decrease?

Accepted Answer

It is the same formula, and the result simply comes out negative. From 150 down to 120 you get (120 − 150) ÷ 150 × 100 = −20%, a 20% decrease. Notice it is 20% and not 25%: the baseline has changed, so a rise and the fall that undoes it are never the same percentage.

Question 3

What's the difference between percentage change and percentage difference?

Accepted Answer

Percentage change measures a move from a starting value to a new one and depends on which came first: 50 to 75 is a 50% increase, but 75 to 50 is a 33% decrease. Percentage difference compares two values with no direction, dividing by their average, and gives the same answer either way round — 40% in this example.

Question 4

How do I compare two percentages?

Accepted Answer

Decide whether you mean the gap or the relative change. If a rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase in the rate itself. Percentage points describe the gap between two percentages; percent describes the relative size of the move. State which one you are quoting.

Question 5

How do I calculate the percentage increase between two prices?

Accepted Answer

Put the old price in Original value and the new price in New value. A £40 item rising to £46 is (46 − 40) ÷ 40 × 100 = 15%. For a discount, do the same in reverse: £46 down to £40 is a 13% reduction, which is why the discount percentage never matches the increase percentage.

Question 6

What is the formula for percentage difference?

Accepted Answer

Percentage difference = |value A − value B| ÷ ((A + B) ÷ 2) × 100. Dividing by the average of the two numbers is what removes the direction, so neither value is treated as the starting point and swapping them changes nothing.

Question 7

Which one should I use?

Accepted Answer

Use percentage change whenever there is a clear before and after: last month's sales, an old price, a previous weigh-in. Use percentage difference when the two numbers are simply alternatives being compared, such as two quotes, two measurements or two suppliers, where neither is the baseline.

Question 8

Why can't I calculate a percentage change from zero?

Accepted Answer

Because you would be dividing by zero. Going from 0 to 20 sales is an infinite increase mathematically, which is meaningless in practice. Report the absolute change instead — 'up 20 sales from none' — which is clearer and honest.

Question 9

Why don't a 50% rise and a 50% fall cancel out?

Accepted Answer

Because each percentage applies to a different base. £100 rising 50% is £150; £150 falling 50% is £75, not £100. To return to the original after a 50% rise you need a 33.3% fall. This asymmetry is why investment losses hurt more than equivalent-sounding gains.

Question 10

How do I reverse a percentage increase?

Accepted Answer

Divide rather than subtract. To strip a 20% uplift from £120, divide by 1.20 to get £100 — subtracting 20% would give £96 and be wrong. The same logic removes VAT from a gross price, which is why VAT calculations divide by 1.2 rather than multiplying by 0.8.

Question 11

How do I apply two percentage changes in a row?

Accepted Answer

Multiply the factors rather than adding the percentages. A 10% rise followed by a 5% rise is 1.10 × 1.05 = 1.155, so 15.5% overall, not 15%. This compounding effect is small over one or two steps and substantial over a decade.

Question 12

Is a big percentage always significant?

Accepted Answer

No — always check the underlying numbers. A 200% increase from one order to three is real but trivial; a 2% fall in a million-pound revenue line is £20,000. Percentages describe relative movement, and small bases produce dramatic-looking figures that mean very little.

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