How to Find Percentage Change Step by Step
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Finding percentage change becomes simple when you keep one question in mind: how large is the change compared with the original amount? You find the difference first, divide by the original value, and then multiply by 100 to express the result as a percentage.
The basic formula
The basic formula is change divided by original value, multiplied by 100. Suppose a price rises from 40 to 50. The change is 10. Divide 10 by the original value, 40, to get 0.25. Multiply by 100, and the percentage change is a 25 percent increase.
The original value is the key part of finding percentage change. If the price instead falls from 50 to 40, the change is 10 in size, but now you compare that 10 with the original 50. Ten divided by 50 is 0.2, so the decrease is 20 percent. A 25 percent increase and a 20 percent decrease can therefore reverse each other between the same two numbers.
You may also write percentage change as new value minus original value, divided by original value, multiplied by 100. This version keeps the sign. A positive result shows an increase and a negative result shows a decrease. In many school questions, you find the size first and then label it clearly as an increase or decrease.
Here is another example. A test score rises from 60 to 72. The increase is 12. Divide 12 by the original score of 60 to get 0.2, then multiply by 100. The score increased by 20 percent. Notice that the answer describes the relative change, not the 12-point difference itself.
Why the original value belongs in the denominator
A percentage is always a comparison with some reference amount. In percentage change, the reference is where you started. That is why you divide by the original value rather than the new value or the average of the two. Changing the denominator changes the question you are answering.
When finding percentage change, say the comparison aloud: the amount changed by this much, compared with what it was before. That sentence points directly to the original value. It is a useful check when the problem contains several numbers and you are tempted to divide by whichever one appears last.
Percentage change is useful because it lets you compare changes across different starting sizes. An increase of 10 units is huge if the original value was 20, but small if the original was 1,000. Converting both changes to percentages puts them on a common scale and makes the comparison more meaningful.
Use a short routine to avoid common mistakes
A steady method is more reliable than trying to remember several separate percentage rules:
- •Identify the original value and the new value.
- •Subtract to find the size of the change.
- •Divide the change by the original value.
- •Multiply by 100 to convert the decimal to a percentage.
- •Label the answer as an increase or a decrease.
Be careful when the original value is zero. The usual percentage change formula asks you to divide by the original value, and division by zero is undefined. In that case, report the absolute change or use another comparison that fits the context rather than forcing the standard formula.
The takeaway
Finding percentage change follows one consistent idea: compare the change with the original value. Subtract, divide by the starting amount, multiply by 100, and label the direction. The most common mistake is using the wrong denominator, so circle or note the original value before you start calculating.