Percentage increase and decrease: the formula, the base and five common mistakes.

Start with the original number

The percentage-change formula is (new value − original value) ÷ original value × 100. The word original matters. If a product costs LKR 800 and later costs LKR 920, the difference is LKR 120. Divide 120 by 800, not by 920: the increase is 15%.

For a decrease, the same formula produces a negative result. A price moving from LKR 920 down to LKR 800 changes by −120 ÷ 920 × 100, approximately −13.04%. Those two percentages differ because the starting amounts differ. The change in currency is the same; the reference value is not.

Five worked cases you can check

1. Finding a part: 18% of 250 is 0.18 × 250 = 45. 2. Finding the share: if 45 out of 250 responses are positive, 45 ÷ 250 × 100 = 18%. 3. Finding growth: orders rise from 120 to 150, so (150 − 120) ÷ 120 × 100 = 25%.

4. Finding a decrease: a file shrinks from 8 MB to 5 MB, so (5 − 8) ÷ 8 × 100 = −37.5%, a size reduction of 37.5%. 5. Finding the amount before a discount: a LKR 1,600 item after a 20% discount represents 80% of its original price. The original was 1,600 ÷ 0.8 = LKR 2,000.

You can check cases 1–4 using the free Percentage Calculator. The fifth uses reverse reasoning: divide the final value by the remaining decimal share (0.8) rather than subtracting another 20%.

Why increases and decreases do not reverse each other

Start with LKR 1,000. A 20% increase makes it LKR 1,200. A 20% decrease of 1,200 is 240, leaving LKR 960. The second percentage applied to a larger base. A 20% rise therefore needs a 16.67% fall, approximately, to return to the original value.

If a store claims a '20% off, then 20% back' promotion, calculate the amounts in sequence. Percentage operations multiply the starting value by factors such as 1.2 or 0.8; they are not automatically reversible by changing the sign.

Percentage points are different

When an email click-through rate goes from 2% to 3%, the difference is one percentage point. Relative to the original 2%, that is a 50% increase. If you write 'increased by 1%' without specifying points, readers may misunderstand the result.

This matters in survey results, finance, analytics and public statistics. Use percentage points when comparing rates as rates. Use relative percentage change when explaining how much a measured value grew relative to its starting level.

When a percentage is not a helpful answer

If the original number is zero, the standard percentage-change formula has a zero denominator, so the result is undefined. A change from zero customers to ten customers is ten additional customers, not a mathematically meaningful 'infinite percent growth' to publish as a routine metric.

Negative values can also make a naive growth percentage misleading. A shift from −10 to +10 has a difference of 20, but describing it as ordinary 200% growth without context obscures that the sign changed. Report the original and new values and explain the convention.

For high-stakes financial calculations, keep more precision during intermediate steps and round only the final answer. If you are calculating tax, interest or regulated fees, check which base and rounding rules the relevant authority requires.