Percentage increase and decrease -
the formula most people use wrong.
Salary raises, price rises, exam improvement, investment returns - all of these live in percentage change language. One formula handles every situation. Here it is, explained properly for the first time.
The two formulas - and how they connect
There's really only one formula. Whether something goes up or down, you're always asking the same question: how big is the change, as a percentage of where you started?
That's it. If the result is a positive number, the value went up by that percentage. If it's negative, it went down. The formula doesn't change - only the direction of the result does.
The most important word in that formula is Old. The old value - your starting point - goes on the bottom. This is where most people go wrong. They subtract correctly but then divide by the wrong number, usually the average of the two or the new value. Always divide by where you started.
Six real situations, one formula
((54,000 − 50,000) ÷ 50,000) × 100 = 8% increase
((3.80 − 3.20) ÷ 3.20) × 100 = 18.75% increase
((78 − 64) ÷ 64) × 100 = 21.9% increase
((9,600 − 12,000) ÷ 12,000) × 100 = −20% decrease
((1.62 − 1.85) ÷ 1.85) × 100 = −12.4% decrease
((480,000 − 400,000) ÷ 400,000) × 100 = 20% increase
Plug it straight into the formula: ((47,700 − 45,000) ÷ 45,000) × 100.
The difference is $2,700. Divide that by $45,000 = 0.06. Multiply by 100 = 6% - correct.
Now here's the more useful follow-up question: is 6% a real raise? In 2024, US average salary increases ran at around 4.8% (ADP data). Inflation was roughly 3%. So 6% means your purchasing power genuinely improved by about 3% - around $1,350 in real terms. That context matters more than the headline percentage.
The asymmetry trap - why you can't just reverse a percentage
This is the mistake that trips up financial journalists, investors, and anyone reading a "recovery" story. People assume that if something fell by X%, it needs to rise by X% to return to its original value. It doesn't - it needs a bigger percentage gain.
The reason: the percentage gain is calculated on the new, lower number. The loss was calculated on the higher original. Different bases produce different percentage results for the same dollar movement.
After a 25% fall: $200 × (1 − 0.25) = $150
To return to $200 from $150: ((200 − 150) ÷ 150) × 100 = 33.3% rise needed
Not 25%. A 25% rise on $150 only gives you $187.50 - still $12.50 short.
The pattern:
10% loss → needs 11.1% gain to recover
20% loss → needs 25% gain
33% loss → needs 50% gain
50% loss → needs 100% gain
75% loss → needs 300% gain
Discount percentage: ((90 − 120) ÷ 120) × 100 = −25%. It dropped by 25%.
Increase needed to restore: ((120 − 90) ÷ 90) × 100 = 33.3%. The price would need to rise by a third of its sale price to get back to $120.
This is exactly what happens at the end of sales seasons - retailers mark items back up. A "25% off" sale followed by prices reverting looks like a 33% rise from the sale price, which can feel dramatic even though it's just returning to the original.
Finding the new value when you know the percentage
Sometimes you already know the percentage change and just want to find the resulting number. This is the forward direction - useful for calculating future salaries, projected prices, or expected investment values.
$55,000 × (1 + 8 ÷ 100) = $55,000 × 1.08 = $59,400
Your electricity bill drops 12%:
Current bill: $180/month
$180 × (1 − 12 ÷ 100) = $180 × 0.88 = $158.40
This is the reverse version - you know the new value and the percentage, and want the original. Rearrange the formula:
Original = New ÷ (1 + Change% ÷ 100)
$62,000 ÷ (1 + 15 ÷ 100) = $62,000 ÷ 1.15 = $53,913.
This is also useful when a recruiter tells you a salary is "20% above market rate" - work backwards to find what they consider "market rate" and decide if you agree.
What percentage changes look like in the real world right now
The average salary increase in the US in 2024 was 4.8% (ADP data), down from the 5.5–6% peaks of 2022-2023. In the UK, average wage growth sits around 5.6% as of early 2026 (ONS). In the UAE private sector, salary increases typically range from 5–10% for performers. If you received a 3% raise while inflation was 3%, your real purchasing power didn't change - you broke even, not gained.
Food and energy prices rose dramatically in 2022–2023 and have moderated but not reversed. A product that was $10 in 2020, rose 15% to $11.50 in 2022, then fell 5% in 2024 is now at $10.93 - not $10. This is because the 5% decrease applied to the higher $11.50 base, not the original. Understanding this asymmetry explains why "inflation is down" doesn't feel like prices are down - because they aren't.
Investment percentage changes dominate financial news. When a stock market index is described as "up 18% year-to-date," that's a percentage increase on the value at the start of the year - not a guarantee of future performance. If the same index was down 25% the previous year, the 18% recovery leaves you still below where you started: 100 → 75 → 88.5. The numbers tell both stories simultaneously, and you need both to understand where you actually stand.