Percentage Change Calculator — Increase & Decrease
Three calculators in one: find the percentage change from an old value to a new one, calculate what a value becomes after a given percentage increase or decrease, or work backwards to find the original value before a percentage change was applied. Results are color-coded green for increases and red for decreases.
Enter values to calculate the percentage change.
How it works
The percentage change formula and what it means
Percentage change measures how much a quantity has grown or shrunk relative to its starting point: Percentage Change = ((New − Old) / |Old|) × 100%. A positive result is an increase; a negative result is a decrease. The absolute value in the denominator handles the case where the old value is negative — for example, a loss that became a smaller loss should still show as an improvement.
The formula always divides by the original (old) value, not the new one. This is what makes a 50% gain followed by a 50% loss leave you at 75% of where you started — the first 50% is taken relative to 100, but the second 50% is taken relative to 150. Percentage changes do not simply add or subtract; they compound. If you need a net change over multiple steps, multiply the growth factors: (1.50) × (0.50) = 0.75, a 25% net loss.
Percentage increase vs percentage decrease — worked examples
Percentage increase example: a product costs $80 in January and $100 in March. Change = (100 − 80) / 80 × 100 = 25%. The price rose by 25%. Reverse check: $80 × 1.25 = $100. To find the reverse — what was the original price before a 25% increase produced $100? — use Original = New / 1.25 = $80.
Percentage decrease example: a stock falls from $250 to $175. Change = (175 − 250) / 250 × 100 = −30%. The stock declined 30%. Reverse check: $250 × 0.70 = $175. A common mistake is to calculate the percentage needed to recover: a 30% loss requires a 42.9% gain to recover (100 / 70 − 1 ≈ 0.429), not 30%, because the base has changed.
Common mistakes: flipping old and new, and percentage points vs percentages
Swapping old and new values is the most frequent error. If a salary rises from $50,000 to $60,000, the change is (60,000 − 50,000) / 50,000 = 20%, not (50,000 − 60,000) / 60,000 = −16.7%. The denominator must always be the starting value. A useful check: the percentage increase from A to B is never the same magnitude as the percentage decrease from B back to A.
Percentage points and percentages describe different things. If an interest rate rises from 3% to 4%, that is a 1 percentage-point increase but a 33.3% relative increase (1/3 × 100). Financial media often say 'rates rose 1%' when they mean 1 percentage point — a very different claim. This calculator reports relative percentage change. If you need the absolute-point difference, subtract the two values directly.
Frequently asked questions
›What is the percentage change formula?
Percentage Change = ((New Value − Old Value) / |Old Value|) × 100%. The absolute value in the denominator ensures correct signs when the old value is negative. A positive result means an increase; negative means a decrease.
›How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. Example: from 40 to 55 — (55 − 40) / 40 × 100 = 37.5% increase. You can also use the '% Change' tab above: enter 40 as the old value and 55 as the new.
›How do I calculate a percentage decrease?
The same formula applies — a negative result simply means the value went down. From 200 to 150: (150 − 200) / 200 × 100 = −25%. The value decreased by 25%.
›What if the old value is zero?
The formula requires dividing by the old value, so when the old value is zero, the percentage change is mathematically undefined. You cannot express 'going from nothing to something' as a percentage change — report the absolute change instead.
›How do I find the original value before a percentage change?
Use the formula: Original = New Value / (1 + Percentage Change / 100). For example, if a price of $120 already includes a 20% increase, the original price was $120 / 1.20 = $100. The 'Original Value' tab automates this calculation.
›Is a 50% loss recovered by a 50% gain?
No. A 50% loss on $100 leaves $50. A 50% gain on $50 returns only $75 — not $100. To recover from an X% loss, you need a gain of X / (100 − X) × 100 percent. A 50% loss requires a 100% gain to break even.
›What is the difference between percentage change and percentage points?
Percentage points measure the arithmetic difference between two percentages. If unemployment goes from 5% to 7%, that is a 2 percentage-point increase. Percentage change measures the relative shift: (7 − 5) / 5 × 100 = 40% relative increase. These are very different — always clarify which one is being reported.
›Can I use this for financial calculations like stock returns?
Yes. Enter the purchase price as the old value and the current price as the new value to get the return percentage. For multi-period returns, note that you need to compound: a 10% gain in year 1 and a 20% gain in year 2 produces a net return of (1.10 × 1.20 − 1) × 100 = 32%, not 30%.
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