Key takeaway
Percent increase = ((new − old) ÷ old) × 100 when the value goes up. A rise from 40 to 50 is ((50 − 40) ÷ 40) × 100 = 25%. The base is the old value — dividing by the new value understates the increase. For several rises, compound them; do not add the percents.
Scope and assumptions
General arithmetic. Multi-period growth should use the net/compound method. This site is informational and not official.
Short answer: Percent increase = ((new − old) ÷ old) × 100 when the value goes up. A rise from 40 to 50 is ((50 − 40) ÷ 40) × 100 = 25%. The base is the old value — dividing by the new value understates the increase. For several rises, compound them; do not add the percents. This page covers increases only; the combined up-and-down treatment is in Percentage Increase and Decrease, and drops are in Calculate Percent Decrease.
Quick navigation
- Increase & decrease → percentage-increase-and-decrease
- Percent decrease → calculate-percent-decrease
- Net change → net-percentage-change
- The calculator → Percentage Calculator
1. The formula
% increase = ((new − old) ÷ old) × 100
Use it only when new > old; otherwise you have a decrease.
2. Worked example
Followers 40 → 50.
((50 − 40) ÷ 40) × 100 = (10 ÷ 40) × 100 = 25%
3. A multi-step rise
A price moves 100 → 120 → 150.
- Step 1: (120−100)/100 = +20%
- Step 2: (150−120)/120 = +25%
- Total from 100: (150−100)/100 = +50%
Note +20% and +25% do not "add" to 45%; the two-step rise from the original is +50% because each step compounds on a new base.
4. Annual growth
Value $1,000 → $1,210 over two years.
Yearly factor = √(1210/1000) ≈ 1.10 → +10% per year
Compound growth is the province of net-percentage-change.
5. Table
| Old | New | ((new−old)÷old)×100 | Read |
|---|---|---|---|
| 40 | 50 | +25% | increase |
| 80 | 100 | +25% | increase |
| 100 | 150 | +50% | increase |
| 200 | 220 | +10% | increase |
6. Common mistakes
- Base = new value — (10÷50) = 20% understates the true 25%.
- Adding step percents — +20% then +25% is +50% total, not 45%.
- Using the wrong old — for a rise from 120, the base is 120, not 100.
- Forgetting the sign check — if new < old, report a decrease instead.
7. Increase in the real world
Percent increase shows up as growth: subscribers, sales, scores, populations. A test score of 40 rising to 50 is a 25% improvement; a salary of $50,000 to $55,000 is 10%. The formula is identical — only the labels change. When you report the increase, pair it with the before-and-after numbers so the reader can see the base you divided by, because the same 25% looks very different on 40 versus 40,000.
8. Growth compounds, do not add
When a value rises in steps, the steps compound on a moving base, so they do not add to the total rise. A climb from 100 to 120 (+20%) then to 150 (+25%) is a total +50%, not +45%, because the second step acts on 120, not on 100. The same is true in reverse for falls. If you need the overall change, go straight to (new − old) ÷ old on the endpoints and skip summing the middle percents, which quietly double-counts the shifting base and misstates the true growth across the whole period.
9. Endpoints give the whole answer
For a rise, name the two endpoints and the base is the first one; everything else follows. 40 to 50 is +25% because the base is 40, and stating 40 first is what keeps you from dividing by 50 and landing at 20%. The endpoint order is the formula, so writing "from 40 to 50" is not decoration — it is the calculation laid out in words. Do that and the percent increase is forced to be correct, because the base was chosen before any arithmetic happened and cannot be quietly swapped later.
FAQ
Q: What is the percent increase formula? ((new − old) ÷ old) × 100, used when new > old.
Q: 40 to 50 is what percent increase? ((50 − 40) ÷ 40) × 100 = 25%.
Q: Can I add two increases? No — compound them by multiplying factors; adding overstates the total rise.
Q: What if it actually fell? Then it is a percent decrease (negative). See calculate-percent-decrease.
Q: Why use old as the base? Percent change measures relative to where you started; the new value is the result, not the base.
Sources: Investopedia — Percentage Change; Khan Academy percentages.
Disclaimer: General arithmetic. Multi-period growth should use the net/compound method. This site is informational and not official.
Sources and references
- Investopedia — Percentage Changehttps://www.investopedia.com/terms/p/percentage-change.asp
- Khan Academy percentageshttps://www.khanacademy.org/math/pre-algebra/x31947de81e3f6453:percentages