Stock market foundationsModule 1, lesson 3 of 29
Percentages, percentage change and percentage points
How to calculate a percentage change, why a 50% fall needs a 100% rise to recover, and the difference between percent and percentage points.
In this lesson
- Calculate a percentage of an amount and a percentage change between two numbers.
- Explain why gains and losses of the same percentage do not cancel out.
- Combine several percentage changes in a row correctly.
- Tell a change in percent from a change in percentage points.
- Read a ratio as "so much per ₹100" and use it to compare companies of different sizes.
On this page
In simple terms
"Per cent" means "per hundred". Saying a share rose 8% means it rose ₹8 for every ₹100 it was worth before. Percentages let you compare changes in things of very different sizes: a ₹50 share and a ₹5,000 share, or a small company and a giant.
Almost every number in this course is a percentage of something, so the few rules in this lesson are worth getting completely comfortable with.
Percentage of an amount, and percentage change
To find a percentage of an amount, multiply by the percentage written as a decimal: 12% of ₹2,500 is 0.12 × 2,500 = ₹300.
Percentage change = (new value − old value) ÷ old value × 100
A positive answer is a rise and a negative answer is a fall. Always divide by the starting value.
Worked example: A share price that rises
You buy a share at ₹250 and it rises to ₹290.
| Change in price: 290 − 250 | ₹40 |
|---|---|
| Percentage change: 40 ÷ 250 × 100 | 16% |
Gains and losses do not cancel out
A fall and a rise of the same percentage leave you worse off, because the rise is measured from a smaller starting point.
Worked example: Down 50%, then up 50%
| Start | ₹1,000 |
|---|---|
| After a 50% fall: 1,000 × 0.5 | ₹500 |
| After a 50% rise: 500 × 1.5 | ₹750 |
| Overall change: (750 − 1,000) ÷ 1,000 × 100 | −25% |
To get back to ₹1,000 from ₹500, the share needs to double: a 100% gain. A 20% fall needs a 25% gain, and a 30% fall needs about 43%. The loss recovery calculator works this out for any fall.
Changes in a row multiply
When one percentage change follows another, you cannot simply add them. Convert each change into a multiplier (a 10% rise is × 1.10, a 20% fall is × 0.80) and multiply.
| Two rises of 10%: 1.10 × 1.10 = 1.21 | +21% |
|---|---|
| A 20% rise, then a 20% fall: 1.20 × 0.80 = 0.96 | −4% |
| A 5% rise, then a 5% fall: 1.05 × 0.95 = 0.9975 | −0.25% |
This is the idea behind compounding, the subject of the next lesson.
Working backwards
If a price is ₹600 after a 20% rise, the old price was not ₹600 less 20%. Divide by the multiplier instead: 600 ÷ 1.20 = ₹500. Taking 20% off ₹600 gives ₹480, which is wrong, because the 20% was a percentage of the old price, not the new one.
Percent and percentage points
When the thing that changes is itself a percentage, such as an interest rate or a profit margin, there are two ways to describe the change, and they are easy to mix up.
Worked example: An interest rate from 6% to 7%
| Change in percentage points: 7 − 6 | 1 percentage point |
|---|---|
| Percentage change in the rate: (7 − 6) ÷ 6 × 100 | 16.7% |
Both are correct descriptions, but they say different things. News reports usually mean percentage points when they say an interest rate "rose by 0.25%"; the precise wording is "rose by 0.25 percentage points", sometimes written as 25 basis points, where one basis point is a hundredth of a percentage point.
Ratios: so much per ₹100
A ratio compares two numbers by dividing one by the other. A company with ₹30 crore of profit on ₹200 crore of sales has a profit margin of 30 ÷ 200 = 0.15, or ₹15 of profit per ₹100 of sales. Writing ratios as percentages, or as "per ₹100", makes it possible to compare a small company with a large one. Later lessons use ratios constantly, from market capitalisation to profit margins and valuation measures.
Small bases make big percentages
A percentage change says nothing about size. If one company's profit rises from ₹2 crore to ₹3 crore, that is a 50% rise, but only ₹1 crore more. Another company whose profit rises from ₹100 crore to ₹110 crore has grown only 10%, but it earned ₹10 crore more. Headlines like "profit jumps 300%" often come from a tiny or unusually low starting point, called a base effect. Always look at the amounts as well as the percentage.
Why it matters
Percentages are how markets talk. Returns, interest rates, inflation, index moves, profit growth and margins are all percentages, and many misleading claims rely on percentage tricks: quoting a big percentage on a small base, adding returns instead of multiplying them, or hiding that "down 50%, up 50%" is still a loss. Getting these rules right protects you from most of them.
Limitations
- A percentage hides the amount. Pair it with the rupee figure when the size matters.
- Percentage changes from a starting value of zero or below are meaningless. A company going from a loss to a profit has no sensible "percentage growth".
- Rounding in news reports can hide meaningful differences, especially in percentage points.
Common mistakes
- Dividing by the wrong number. Percentage change is measured from the starting value, not the ending value.
- Adding changes in a row. Multiply the multipliers instead.
- Assuming a gain undoes an equal loss. It needs a bigger gain to recover.
- Mixing up percent and percentage points. A rate going from 2% to 3% is a 1 point rise but a 50% increase.
- Being impressed by big percentages on small bases. Check the amounts.
Try it yourself
- Pick any listed share. Note its price today and its price on the same date a year ago, and calculate the percentage change.
- Using the same share, imagine it falls 15% next year and then rises 15% the year after. Where does it end up compared with today?
- Find a news report about an interest rate change. Is the change described in percentage points or percent? Calculate the other one.
- Check your answers with the share return calculator.
Key takeaways
- Percentage change = (new value − old value) ÷ old value × 100. Always divide by the starting value.
- Gains and losses do not cancel. A 50% fall followed by a 50% rise leaves you 25% down.
- Changes in a row multiply rather than add. Two 10% gains make 21%, not 20%.
- A move from 6% to 7% is a rise of 1 percentage point, which is a 16.7% increase in the rate.
- A big percentage change from a small base can be a small change in rupees. Look at both.
Check your understanding
Try the numbers yourself
- Share return calculatorHow much did I really make or lose on a share?
- Loss recovery calculatorWhat gain do I need to recover from a loss?
- CAGR and percentage change calculatorHow fast did something grow each year, on average?
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Terms used in this lesson
- Percentage point
- The unit for the difference between two percentages. A rate rising from 6% to 7% has gone up one percentage point, which is a 16.7% increase.
- Base effect
- A large percentage change caused mainly by an unusually small or unusual starting value, rather than by a large change in amount.
- Total return
- The complete gain or loss on an investment, combining the change in price with any dividends or interest received.
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This lesson is general education, not investment advice. Examples use made-up or clearly dated figures to explain ideas; they are not recommendations. Read the disclaimer.