Key takeaways
- Percentage Change = ((newValue − oldValue) ÷ oldValue) × 100.
- Always divide by the OLD value, never the new one.
- A positive result means an increase; a negative result means a decrease.
- A 100% increase means the value has exactly doubled.
In this guide
What is percentage change?
Percentage change measures the size of an increase or decrease as a percentage of the original (old) value. A positive result means the value went up; a negative result means it went down.
Why does percentage change matter?
Prices, salaries, and populations are almost always compared using percentage change rather than a raw dollar or unit amount, because it shows how big the change is relative to where things started.
A $50 increase means something very different on a $50 item (a 100% jump) than on a $5,000 item (only 1%). Percentage change captures that difference; a raw dollar amount can't.
The formula
| Symbol | What it means | Example |
|---|---|---|
| Percentage Change | The result, positive for a rise, negative for a fall | 30% |
| oldValue | The starting amount, before the change | 50 |
| newValue | The amount after the change | 65 |
How to find percentage change step by step
- 1Subtract the old value from the new value to find the raw change:
65 − 50 = 15. - 2Divide that change by the old value:
15 ÷ 50 = 0.3. - 3Multiply the result by 100 to turn it into a percentage:
0.3 × 100 = 30. - 4Check the sign. Positive means an increase, negative means a decrease.
Try your own old and new values in the calculator below to see every step.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Ignoring the negative sign. A result of −15% means a 15% decrease, not an increase.
- Using this formula for a part-to-whole comparison. If you just want to know what percentage one number is of another (not a change over time), use the percentage calculator instead.
- Rounding too early, which can shift a small percentage change enough to be misleading.
Tips and tricks
- Working backward? If you know the new value and the percentage change, you can find the old value by dividing the new value by (1 + the percentage as a decimal).
- For business results, percentage change is exactly how profit or loss is tracked year over year.
- Investment growth over time is usually measured with CAGR, which is percentage change spread across several years.
Where you'll use it in real life
- Shopping: comparing a price before and after a sale.
- Work: tracking a salary raise from one year to the next.
- Investing: measuring how much an investment gained or lost, alongside the ROI calculator.
- Fitness: tracking a change in weight, distance run, or personal best over time.
Quick summary
To find a percentage change, subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is an increase, a negative result is a decrease. Try the calculator above with your own before-and-after numbers.
Worked example
A pair of shoes cost $50 last month and now costs $65. By what percentage did the price increase?
- 01Change = (65 - 50) ÷ 50
- 02Change = 15 ÷ 50
- 03Change = 0.3
- 04Percentage = 0.3 × 100 = 30%
- 05This is a increase of 30%
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate a percentage decrease?
Use the same formula: ((new value − old value) ÷ old value) × 100. If the new value is smaller, the result comes out negative, showing a decrease.
Why do I divide by the old value and not the new value?
Percentage change measures the size of the change relative to where you started, so the old value is always the base of comparison.
What does a 100% increase mean?
It means the value has doubled. For example, going from $50 to $100 is a 100% increase, because the change ($50) equals the entire old value.
If a price goes up 20% and then down 20%, does it return to normal?
No. The 20% increase and decrease are each based on a different starting value, so the final price ends up slightly lower than the original.
