Percent Change Calculator
Find the percent increase or decrease from an old value to a new one, the symmetric percentage difference, or add or take X% off a number, with every step.
Percent Change Calculator: with the default inputs, result is 25.
The value you are measuring from.
Not used when increasing or decreasing by a percentage.
Used only in the increase / decrease mode.
A percentage in the first two modes; the new number when applying a percentage.
- In words
- 80 to 100 is a 25% increase
- Increase or decrease
- Increase
- Change (new − old)
- 20
- Multiplier (new ÷ old)
- 1.25
Assumptions
- Percent change is measured against the absolute value of the old value, so a rise is always positive even for negative numbers.
- Percentage difference uses the mean of the two absolute values as the reference.
| Percent | Increased by it | Decreased by it | |
|---|---|---|---|
| 5% | 84 | 76 | |
| 10% | 88 | 72 | |
| 15% | 92 | 68 | |
| 20% | 96 | 64 | |
| 25% | 100 | 60 | ◀ your change |
| 30% | 104 | 56 | |
| 50% | 120 | 40 | |
| 75% | 140 | 20 | |
| 100% | 160 | 0 |
A rise and an equal fall do not cancel: 100 up 50% is 150, and 150 down 50% is 75. To undo an increase of p%, decrease by p ÷ (100 + p).
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Free Percent Change Calculator from CalculateItNow
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How this is worked out
The formula
Percent change = (new − old) ÷ |old| × 100 (positive = increase, negative = decrease) Percentage difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100 Increase by p%: new = old × (1 + p/100) Decrease by p%: new = old × (1 − p/100)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- What do you want to find?
- Choose one of 3 options.Percent change from the old value to the new value · Percentage difference between two values · Increase or decrease a number by X%
- Old value (starting number)
- The value you are measuring from.defaults to 80
- New value
- Not used when increasing or decreasing by a percentage.defaults to 100
- Percentage
- Used only in the increase / decrease mode.a percentage · 0 or more · defaults to 15
- Direction
- Choose one of 2 options.Increase (add X%) · Decrease (take X% off)
What you get back
- Resultmain answer
- A percentage in the first two modes; the new number when applying a percentage.
- In words
- Increase or decrease
- Change (new − old)
- Multiplier (new ÷ old)
What this assumes
- Percent change is measured against the absolute value of the old value, so a rise is always positive even for negative numbers.
- Percentage difference uses the mean of the two absolute values as the reference.
About this calculator
Percent change answers "by how much did this grow or shrink, relative to where it started?" This percent change calculator works it out from an old and a new value, tells you whether it is an increase or a decrease, and shows every step. Two related questions are one menu away: the percentage difference between two values when neither is the starting point, and increasing or decreasing a number by a percentage.
How to use it
Pick the question, then type the numbers. For percent change, the old value is the one you are measuring from — last year's price, the starting weight, the original salary. The answer is signed: positive for an increase, negative for a decrease, and the "In words" line says which. To add tax, apply a raise or take a discount off, switch to "Increase or decrease a number by X%" and enter the percentage.
The percent change formula
Subtract the old value from the new, divide by the old value, and multiply by 100: (new − old) ÷ old × 100. From 80 to 100 the change is 20, and 20 ÷ 80 = 0.25, so a 25% increase. From 100 back to 80 the change is −20, and −20 ÷ 100 = −0.2, a 20% decrease. The two percentages differ because they are measured against different starting points — which is why a 20% drop followed by a 20% rise leaves you below where you began.
Percent change versus percentage difference
Percent change has a direction and a baseline. Percentage difference has neither: it divides the gap by the average of the two values, so 80 and 100 differ by 22.22% whichever you list first. Use it to compare two measurements, two shops' prices or two lab results where neither is "before". When you compare two percentages, also say whether you mean percentage points: going from 10% to 15% is 5 points but a 50% increase.
Edge cases
- Old value of zero. Percent change from zero is undefined — any growth from nothing is infinitely large — so the calculator says so instead of printing a meaningless number. Report the change as an amount, or use percentage difference.
- Negative values. The change is divided by the size of the old value, so a rise from −50 to −25 reads as a 50% increase, which is the direction it moved.
- Undoing a change. To reverse a p% increase, decrease by p ÷ (100 + p), not by p. The table of common increases and decreases shows both directions side by side.
Frequently asked questions
▸How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 50 to 65 is 15 ÷ 50 × 100 = a 30% increase.
▸How do I calculate a percent decrease?
Use the same formula: (new − old) ÷ old × 100. The result is negative, and its size is the decrease. From 200 to 150 is −50 ÷ 200 × 100 = a 25% decrease.
▸What is the difference between percent change and percentage difference?
Percent change measures from a starting value, so direction and order matter. Percentage difference divides the gap by the average of the two values, so it is the same whichever comes first and has no direction.
▸Why can't I calculate percent change from zero?
Dividing by an old value of zero has no answer: going from 0 to anything is an infinitely large relative increase. Report the absolute change instead.
▸If something rises 20% and then falls 20%, is it back where it started?
No. 100 up 20% is 120, and 120 down 20% is 96 — a 4% net loss, because the fall is taken from a bigger number.
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