Percent Guide

Percent Change Guide: Increase, Decrease, and Difference

Learn how to compare an old value and a new value as a percentage change. This guide keeps the math practical, so you can understand what to enter, why it works, and how to spot an answer that does not make sense.

Quick Answer

Percent change compares the change to the original value. The original value is the denominator.

Plain-language ruleSubtract old value from new value.

When to Use This

This topic is useful when a problem looks familiar, but you are not sure which button, formula, or order of steps to use. Start by naming the goal in normal words, then translate it into the calculator setup.

discounts, tips, tax, and grade scores
before-and-after price comparisons
quick checks for growth or decline

Step-by-Step Method

Subtract old value from new value.
Divide by the old value.
Multiply by 100.
Use a positive sign for increase and a negative sign for decrease.

After you get the answer, do one quick reasonableness check. Ask whether the answer should be bigger or smaller than the starting number, whether the unit is correct, and whether a rounded answer is acceptable.

Calculator Tips

Use the original value as the comparison base.
Convert the percent to a decimal before multiplying.
A quick estimate catches most decimal-place errors.

Worked Example

Price changes from 80 to 100

The change is 20. Divide 20 by the original 80, then multiply by 100. The increase is 25%.

Common Mistakes

Dividing by the new value instead of the original value.

Pause and check this before trusting the final answer. A small setup mistake can make the calculator look wrong even when it only followed the input.

Writing 4% as 0.4 instead of 0.04.

Pause and check this before trusting the final answer. A small setup mistake can make the calculator look wrong even when it only followed the input.

FAQ

Can I use a calculator for this?

Yes. A calculator helps with arithmetic, but the important part is choosing the right formula and entering the values in the right places.

How should I check my answer?

Estimate first, then substitute the answer back into the problem or reverse the operation. If the result is wildly larger or smaller than expected, recheck the setup.