How to use the Percentage Change Calculator
- Enter the old value, which is the starting point.
- Enter the new value.
- Read the percentage change. A positive number is an increase and a negative number is a decrease.
Formula used
Percentage change = ((New − Old) ÷ |Old|) × 100. A positive result is an increase and a negative result is a decrease.
Worked example
Here is the Percentage Change Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Old value | 80 |
| New value | 100 |
| Result | |
| Percentage change | 25% |
| Difference | 20 |
| Direction | Increase |
The percentage change formula
Percentage change = (new value − old value) ÷ |old value| × 100. If a salary rises from ₹50,000 to ₹55,000, the difference is ₹5,000, and 5,000 ÷ 50,000 × 100 gives a 10% increase. If a price falls from 200 to 150, the change is −50 ÷ 200 × 100 = −25%, a 25% decrease.
The calculator divides by the old value, because the change is always measured against where you started.
Why increase and decrease are not symmetric
Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is a 20% decrease. The two percentages differ because each one uses a different starting value. This is why a share price that falls 50% needs to rise 100% to get back to where it began.
Percentage points versus percent
If an interest rate moves from 6% to 7%, it rises by 1 percentage point, but the relative change is 1 ÷ 6 × 100, which is about 16.7%. News and reports often mix these up, so look at which one is being used.
The old value cannot be zero, because a change from zero cannot be expressed as a percentage. In that case, describe the change as the plain difference instead.
Why up 50% and down 50% do not cancel out
Percentage changes are not symmetrical. If a price rises 50% from 100 to 150, and then falls 50%, it goes to 75, not back to 100: a net fall of 25%. After a 20% fall, you need a 25% rise to get back to the start. This is why losses are harder to recover from than they seem.
Be careful when the starting value is zero, because the percentage change is undefined. Also be clear about percentage points versus percent: a rate moving from 10% to 12% is up 2 percentage points but up 20% in relative terms. Always state the starting value when you quote a percentage change.
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 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.
How do I calculate percentage decrease?
Use the same formula. From 200 to 150, (150 − 200) ÷ 200 × 100 = −25%, so the decrease is 25%.
Why is the change from 100 to 80 not −25%?
Because the starting value is different. From 100 down to 80 is a 20% decrease, while 80 up to 100 is a 25% increase.
What is the difference between percentage change and percentage points?
Percentage points are the plain difference between two percentages. Percentage change compares the new percentage with the old one. A move from 6% to 7% is 1 percentage point and about a 16.7% relative increase.
What happens if the old value is zero?
The percentage change is undefined because you cannot divide by zero. Report the actual difference instead.
Can I use this for a salary hike?
Yes. Enter your old salary and your new salary to see the hike percentage. A rise from ₹50,000 to ₹55,000 is a 10% hike.
If something rises 20% and then falls 20%, is it back to where it started?
No. 100 rises to 120 and then falls to 96, a net fall of 4%.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.