Key takeaway: Percent error is the size of the difference between an estimated or measured value and the true value, written as a percent of the true value.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Percent Error
Percent error tells how far off a guess or measurement is, compared with the true, accepted value. A small percent error means the estimate was close; a large one means it missed by a lot.
The difference between the two values is taken without a sign, since only the size of the miss matters. That size is then divided by the true value, so the answer reads as a part of the real amount.
Science labs, surveyors and cooks who check a scale all rely on it. It lets you compare a 2-inch slip on a 100-inch board with a 2-inch slip on a 20-inch board fairly.
Formula and notation
Use absolute value bars to ignore which value was bigger:
\[\text{percent error} = \frac{|\text{estimate} – \text{actual}|}{\text{actual}} \times 100\%\]
The result is never negative. Write it with a percent sign, such as \(4\%\).
Key facts
- The divisor is the true (actual) value, not the estimate or measurement.
- Absolute value makes the result positive whether you guessed high or low.
- A percent error of 0% means the estimate matched the actual value exactly.
- Scientists use it to judge how reliable a measurement is.
Percent Error example
A tree in a park is known to be 150 feet tall. Using a homemade clinometer, Ben estimates 138 feet. What is his percent error?
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Difference without a sign: \(|138 – 150| = 12\).
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Divide by the actual height: \(\frac{12}{150} = 0.08\).
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Convert: \(0.08 \times 100\% = 8\%\).
Ben’s estimate has a percent error of 8%.
Common mistake
Watch out
Ben divides by his own estimate: \(\frac{12}{138} \approx 0.087\), and reports about 8.7%.
Why it is wrong
The miss is measured against the real value, not against the guess. Dividing by 150 gives exactly 8%. Using the estimate as the divisor changes the answer and breaks the definition. A good habit is to circle the word “actual” or “accepted” in the problem and use that number underneath the fraction bar every time.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents