CalcKitPercentage change is the single number behind salary hikes, price rises, discounts, exam scores and falling bills — yet it is also one of the most miscalculated figures in everyday maths. The good news is that increases and decreases both use exactly the same formula, and once you know it, every version of the question becomes a thirty-second calculation.
The percentage change formula
You need just two numbers: the old (starting) value and the new value. The formula is:
Percentage change = ((New value − Old value) ÷ Old value) × 100
Work it in three steps. First, find the difference: new minus old. Second, divide that difference by the old value — always the old value, because the change is measured relative to where you started. Third, multiply by 100 to turn the result into a percentage. A positive answer means an increase; a negative answer means a decrease, and you simply read it as a positive decrease (so −25% becomes "a 25% decrease").
Worked example: a percentage increase
Say your monthly rent rises from 1,200 to 1,380. Step one: 1,380 − 1,200 = 180. Step two: 180 ÷ 1,200 = 0.15. Step three: 0.15 × 100 = 15. Your rent has gone up by 15%. The same steps work for a salary: a rise from 3,000 to 3,450 is (450 ÷ 3,000) × 100 = 15% as well. Notice how the same percentage can hide very different amounts of money — 15% of a small rent and 15% of a large salary are not the same cash figure, which is why percentages alone never tell the whole story.
Worked example: a percentage decrease
Now take a jacket marked down from 80 to 60. Step one: 60 − 80 = −20. Step two: −20 ÷ 80 = −0.25. Step three: −0.25 × 100 = −25. The price has fallen by 25% — this is exactly how a "25% off" discount is calculated. The same logic applies to a bill that drops from 200 to 170: (170 − 200) ÷ 200 × 100 = −15%, a 15% decrease. Try your own numbers in our free Percentage Calculator — its percent-change mode runs this formula instantly and shows the working.
Percentage points are not the same as percent
Here is where even careful people slip up. If an interest rate rises from 20% to 25%, that is a 5 percentage-point increase — the plain gap between the two percentages. But the relative percentage increase is 5 ÷ 20 × 100 = 25%. Headlines sometimes blur the two, so when you read that something "rose by 5%", check whether the writer means 5 percentage points or a 5% relative rise: on a 20% base, those are very different claims.
Reversing a percentage change
Sometimes you know the new price and the change, but not the original. To undo an increase, divide by (1 + rate): a price of 120 after a 20% increase started at 120 ÷ 1.20 = 100. To undo a decrease, divide by (1 − rate): a price of 60 after a 25% discount started at 60 ÷ 0.75 = 80. This is the trick behind "was 100, now 80" sale labels, and it is worth checking — a shop that claims a 50% discount on an inflated "original" price is not really halving anything.
Common mistakes to avoid
Three errors account for nearly every wrong answer. First, dividing by the new value instead of the old one: from 80 to 100, the increase is 20 ÷ 80 = 25%, not 20 ÷ 100 = 20%. Second, adding successive percentages: a 10% rise followed by a 10% fall does not return you to the start — 100 becomes 110, then loses 11 to land on 99. Third, confusing percentage points with percent change, as above. Avoid those three, and the formula will serve you for salaries, prices, discounts and investments alike.