Percent Change
Percent change compares the change to the original value.
About this topic
Percent change measures how much a quantity has grown or shrunk relative to where it started. The formula is (new − old) ÷ old × 100. A rise from 50 to 60 is a 20% increase, because the change of 10 is 20% of the original 50.
Always divide by the original value, not the new one. This is why a 20% rise followed by a 20% fall does not return you to the start. Starting at 100, a 20% rise gives 120, but a 20% fall from 120 takes off 24, leaving 96. A positive answer means an increase, and a negative answer means a decrease.
Imagine a town whose population goes from 8,000 to 7,200. The change is −800, and −800 ÷ 8,000 × 100 = −10%, so the population fell by 10%. In shopping, a coat marked down from 120 to 90 dollars is discounted by 25%. Growth over several periods, like compound interest, multiplies by a factor each time: a 5% rise each year means multiplying by 1.05.
Percent change appears in prices, populations, discounts, tax and investment returns. A common mistake is dividing by the new value, which gives the wrong percent. Another is adding successive percent changes instead of multiplying the factors, so two 10% rises make 21%, not 20%. Always identify the starting value first.
Key ideas
- Change = (new − old) ÷ old
- Positive is an increase, negative a decrease
- Use the original as the base
Quick check
Use cases: where Percent Change helps
- Homework: review the key idea behind Percent Change before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Percent Change without notes.
- Visual learning: play with the interactive lab to see how Percent Change changes when you adjust its inputs.
- Teaching a friend: explain Percent Change in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Percent Change?
Percent change compares the change to the original value.
What will I learn in Percent Change?
Change = (new − old) ÷ old. Positive is an increase, negative a decrease. Use the original as the base.
Is Percent Change part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Percent Change lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Percent Change?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.