This explorer compares two fictional values and shows how the choice of base changes the percentage. It helps students in Mathematics, Additional Mathematics and Economics who want to check a percentage change, an index number or a rate question.
Free tool · Mathematics
Percentage base and index explorer
You get a percentage question wrong because you divided by the wrong base.
Everything you enter stays on this device.
How do I use it?
- Choose whether the values are amounts (like prices) or rates in per cent.
- Type value 1 and value 2, and change the labels to the periods they belong to.
- Pick which value is the base, the 100%.
- Optionally add value 3 to see a second change, then press “Compare”.
How does it work?
The difference is the later value minus the base. The percentage change is that difference divided by the base, times 100, and the index sets the base to 100.
The table also shows the change in both directions, each with its own base. That makes it easy to see why the same gap gives different percentages.
For rates, the change in percentage points is a simple subtraction. The relative change divides the gap by the starting rate, and the tool shows both.
A short worked example
Take 80 and 100. Going from 80 to 100 is a rise of 20, and 20 ÷ 80 × 100 = +25%. Going back from 100 to 80 is a fall of 20, and 20 ÷ 100 × 100 = -20%.
Now add a third value of 80. A rise of 25% and then a fall of 20% gives a net change of 0%, because 80 to 80 is no change. Adding +25% and -20% to get +5% is wrong, since the second change uses the new base.
For rates, 4% to 5% is +1 percentage point, and relative to 4% it is a 25% increase.
What are its limits?
The tool works with fictional values up to 1 000 000 000 000 and uses no real prices. Zero bases and negative values are rejected with a message. Inflation, investment, tax and admissions questions are outside its scope, and your course may use a specific formula or wording that you should follow.
Where does it connect to the lessons?
Use it with recovering an original price after successive percentage changes and distinguishing percentage points from a percentage change. For index numbers, read interpreting a composite index without confusing base years. Economics students can continue with comparing nominal and real changes.
If choosing the base is where marks slip, SPM Mathematics tuition gives you a teacher to practise with. The one-hour trial class (from RM50) is the first step.
Common questions
Why is 80 to 100 a 25% rise but 100 to 80 a 20% fall?
The difference is 20 both ways, but the base changes. 20 is 25% of 80 and 20% of 100. Percentage change always divides by the starting value, so a different start gives a different percentage.
What is the difference between percentage points and percent?
A rate moving from 4% to 5% has risen by 1 percentage point. Relative to the starting rate of 4%, that is a 25% increase. Both are true, so say which one you mean.
What does an index with base 100 mean?
The base period is set to 100, and other values are scaled to match. A value of 125 means 25% above the base. Changing the base period changes every index number.
Why does the tool refuse a base of zero?
Percentage change divides by the base, and division by zero is undefined. The tool says so instead of giving a number. Negative values are also refused, since this tool models quantities that cannot be negative.
A teacher can go through your own percentage and index mistakes in a one-to-one lesson and practise naming the base first, until choosing it becomes automatic.
- Online one-to-one lessons for your child with an experienced teacher.
- Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
- Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.