What's the difference between percent change and percent error?

Percent error compares a measured value to the true value and always uses absolute value, while percent change compares a new value to an old value and can be positive or negative. Use percent change when tracking how something changed over time, and percent error when you're checking how accurate a measurement is.

Can percent change be more than 100%?

Yes. If something increases from 10 to 50, that's a 400% increase. Percent change can also be much larger if the old value is very small. The only restriction is that the old value cannot be zero, because you cannot divide by zero.

Why is my percent change negative?

A negative percent change means the quantity decreased from the old value to the new value. For example, if a price drops from 100 to 75, the percent change is \frac{75 - 100}{100} \times 100\% = \frac{-25}{100} \times 100\% = -25\%, indicating a 25% decrease.

What if the old value is negative?

The formula works the same way. For example, if temperature went from -10°C to 5°C, then old = -10, new = 5, and percent change = \frac{5 - (-10)}{-10} \times 100\% = \frac{15}{-10} \times 100\% = -150\%. This means the final temperature is 150% different from and much lower than where it started.

Percent Change

Percent change calculates how much a quantity has increased or decreased, expressed as a percentage of its original value.

\%\,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%

Solve a problem with Percent Change

Type the problem. The solver will use Percent Change where Percent Change is the right tool, and tell you when it is not.

What each symbol means

Symbol	Meaning

When to use it

Use percent change when you need to compare how much something changed relative to where it started.

Level

Usually taught in: Pre-Algebra · Appears on: SAT, ACT

Worked examples

1. Stock price increase with whole numbers

Problem

A stock increased from

50

65

. What is the percent change?

$\text{new} = 65, \quad \text{old} = 50$
Identify the new and old values from the problem.
$65 - 50 = 15$
Subtract to find the change from old to new.
$\frac{15}{50} = \frac{3}{10} = 0.3$
Divide the change by the old value to find what fraction of the old value the change represents.
$0.3 \times 100\% = 30\%$
Multiply by 100% to convert the decimal to a percentage.

Answer: $30\%$

Since the stock price went up from its starting value, we subtract to find the change, divide by the original price to see how large that change is relative to the start, and multiply by 100% to express it as a percentage. The answer is positive, indicating an increase.

2. Temperature drop with negative values

Problem

A temperature fell from

12°C

-8°C

. What is the percent change?

$\text{new} = -8, \quad \text{old} = 12$
Identify the new and old values; note that new is negative.
$-8 - 12 = -20$
Subtract carefully: when subtracting a positive from a negative, the result becomes more negative.
$\frac{-20}{12} = -\frac{5}{3}$
Divide by old and simplify the fraction.
$-\frac{5}{3} \approx -1.667$
Convert the fraction to a decimal for easier multiplication by 100%.
$-1.667 \times 100\% \approx -166.7\%$
Multiply by 100% to get the percent change; the negative sign indicates a decrease.

Answer: $-166.7\% \text{ (or equivalently, about } -166\tfrac{2}{3}\%\text{)}$

A negative change means the temperature dropped. Even though both the starting and ending temperatures span zero, the formula works the same way. The large negative percentage means the final temperature is far below the starting temperature relative to where it started.

3. Garden plot expansion with word problem

Problem

A rectangular garden plot measured

3 \text{ m}

4 \text{ m}

. The gardener expanded it to

5 \text{ m}

7 \text{ m}

. What is the percent change in the perimeter?

$\text{Old perimeter} = 2(3 + 4) = 2(7) = 14$
Calculate the original perimeter using the formula $2(\text{length} + \text{width})$ .
$\text{New perimeter} = 2(5 + 7) = 2(12) = 24$
Calculate the new perimeter with the expanded dimensions.
$24 - 14 = 10$
Subtract to find the change in perimeter.
$\frac{10}{14} = \frac{5}{7}$
Divide by the old perimeter and simplify the fraction.
$\frac{5}{7} \approx 0.714$
Convert the fraction to a decimal.
$0.714 \times 100\% \approx 71.4\%$
Multiply by 100% to express as a percentage.

Answer: $71.4\% \text{ (or equivalently, about } 71\tfrac{3}{7}\%\text{)}$

This word problem requires you to first calculate what each perimeter is before using the percent change formula. The positive result tells us the new perimeter is about 71% larger than the old one, which makes sense because the garden expanded in both dimensions.

Common mistakes

Where Percent Change usually goes wrong

The mistake	Why it is wrong	The fix
A stock went from $50$ to $65$ , so the percent change is $(65 - 50) \times 100\% = 1500\%$ .	Without dividing by the old value, you're not accounting for scale; the raw difference of 15 doesn't tell you what percentage it represents.	Always divide by old: % change $= \frac{65 - 50}{50} \times 100\% = \frac{15}{50} \times 100\% = 30\%$ .
A stock went from $50$ to $65$ , so the percent change is $\frac{65 - 50}{65} \times 100\% \approx 23.1\%$ .	This compares the change to the final value, not the starting value, so it measures what fraction of the new amount was added rather than how much the original grew.	Divide by old: % change $= \frac{65 - 50}{50} \times 100\% = \frac{15}{50} \times 100\% = 30\%$ .
A stock went from $50$ to $65$ , so the percent change is $\frac{65 - 50}{50} = 0.3$ and that's the answer.	The result $0.3$ is in decimal form, not percentage form; the answer is incomplete without converting to a percentage.	Multiply by 100%: $0.3 \times 100\% = 30\%$ .

Tips and when to use something else

Positive percent change means an increase; negative means a decrease—the sign tells you the direction of change.
If the old value is negative, the formula still works, but watch your signs carefully when subtracting.
Percent Error uses a similar approach but compares to the true value and takes the absolute value; use it instead when checking measurement accuracy.
A percent change over 100% means the new value exceeds the old by more than the old's amount (e.g., going from $10$ to $30$ is a 200% increase).

Related formulas

Percent of a NumberPercent of a Number finds how much you get when taking a percentage of a quantity—essential for tips, discounts, grades, and everyday calculations.Percent ErrorPercent Error measures how far off a measurement is from the true value, as a percentage — use it to check accuracy of lab work or approximations.Discount and Sale PriceCalculate the sale price after subtracting a discount percentage from the original list price of the item you're buying.

Frequently asked questions

What's the difference between percent change and percent error?: Percent error compares a measured value to the true value and always uses absolute value, while percent change compares a new value to an old value and can be positive or negative. Use percent change when tracking how something changed over time, and percent error when you're checking how accurate a measurement is.
Can percent change be more than 100%?: Yes. If something increases from $10$ to $50$ , that's a 400% increase. Percent change can also be much larger if the old value is very small. The only restriction is that the old value cannot be zero, because you cannot divide by zero.
Why is my percent change negative?: A negative percent change means the quantity decreased from the old value to the new value. For example, if a price drops from $100$ to $75$ , the percent change is $\frac{75 - 100}{100} \times 100\% = \frac{-25}{100} \times 100\% = -25\%$ , indicating a 25% decrease.
What if the old value is negative?: The formula works the same way. For example, if temperature went from $-10°C$ to $5°C$ , then old $= -10$ , new $= 5$ , and percent change $= \frac{5 - (-10)}{-10} \times 100\% = \frac{15}{-10} \times 100\% = -150\%$ . This means the final temperature is 150% different from and much lower than where it started.

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Reviewed 2026-09-18