How to Calculate Percentage Error with Sample Problems
The concept of percentage error plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Whether you’re in school, preparing for JEE or NEET, or doing science experiments, understanding percentage error helps you judge how accurate your results are.
What Is Percentage Error?
A percentage error is defined as the measure of how far an estimated (measured) value is from an exact (true) value, shown as a percentage of the true value. You’ll find this concept applied in areas such as experimental errors in physics, chemistry practicals, and data accuracy in maths and statistics. Calculating percentage error helps students check if their measurement or answer is close enough to what's expected.
Key Formula for Percentage Error
Here’s the standard formula: \( \text{Percentage Error} = \left| \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right| \times 100\% \)
In this formula, always use the absolute value (ignore the sign) to make sure the error is positive. This formula is used in all school boards (CBSE, ICSE), competitive exams like JEE, NEET, as well as in science experiments and assignments.
Cross-Disciplinary Usage
Percentage error is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. For example, in physics, it shows how close your experimental calculations are to the standard value (like gravity or the speed of sound). In chemistry, it is used to compare actual and theoretical chemical yields. Students preparing for JEE, NEET, NTSE, or Olympiads will see its relevance in various questions.
Step-by-Step Illustration
Let’s solve a typical percentage error example:
Question: If you estimate the length of a table as 90 cm, but the actual (true) length is 100 cm, what is the percentage error?
1. Write the values:Measured Value = 90 cm, True Value = 100 cm
2. Subtract to find the difference:
Difference = 90 − 100 = -10 cm (ignore negative sign)
3. Use the absolute value:
|Measured Value − True Value| = 10 cm
4. Divide by True Value:
Relative Error = 10 / 100 = 0.1
5. Multiply by 100 to get the answer in %:
Percentage Error = 0.1 × 100 = 10%
So, the percentage error in this measurement is 10%.
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for finding percentage error fast in multiple-choice exams:
- Subtract the measured value from the true value, ignore the minus sign.
- Mentally divide the difference by the true value.
- Multiply by 100 for %.
Example Trick: If the true value is 80 and measured is 72: Difference = 8, Divide: 8/80 = 0.1, % Error = 0.1 × 100 = 10%.
This saves time in competitive exams! Vedantu coaches share such tips & tricks online to help you revise smarter.
Try These Yourself
- If the actual temperature is 40°C and you record it as 38°C, what is the percentage error?
- Your chemistry experiment expects 50g yield, but you get 47g. Find the percentage error.
- True value = 120m, measured value = 126m. What is the percentage error?
Frequent Errors and Misunderstandings
- Forgetting to use the modulus (absolute value) for the difference. Percentage error must be positive except in rare chemistry/sign-specific cases.
- Confusing “measured” and “true” value – denominator should always be the true value.
- Dividing by the measured value (it should be divided by true value in most school applications).
- Reporting negative percentage error when not required.
Relation to Other Concepts
The idea of percentage error connects closely with topics such as absolute values in mathematics, error calculation formula, and even standard deviation when talking about data spread. Mastering this helps you learn more about data analysis and scientific experiments.
Classroom Tip
A quick way to remember the percentage error formula: “Difference over True, make it positive, times 100.” You can even remember the mnemonic: “MDT100” (Measured-True, Divide by True, ×100). Many Vedantu teachers use posters or board diagrams during live sessions for easy recall.
We explored percentage error—from definition, formula, examples, mistakes, and connections to other subjects. With ongoing revision and practice at Vedantu, you’ll be able to instantly calculate error in experiments and answer all related school and competitive exam questions confidently.
Related and Useful Links
FAQs on Percentage Error: Definition, Formula, Calculation & Solved Examples
1. What is the percentage of error?
The percentage of error measures how far an experimental or measured value is from the true or accepted value. It is calculated using the formula \(\text{Percent Error} = \frac{|\text{Experimental Value} - \text{True Value}|}{|\text{True Value}|} \times 100\%.
2. What is a good percentage error?
A good percentage error depends on the context, but in most cases, an error under 5% is considered excellent. Lower values mean your measurement is close to the true value, improving your results’ accuracy and the reliability of your percentage error calculation.
3. Do you want your percent error closer to 100 or 0?
You want your percent error as close to 0% as possible. A lower percentage error means your measurement is accurate. A percent error approaching 100% shows a large difference between measured and true values, which signals poor accuracy in your percentage error results.
4. How to calculate percent error with multiple values?
To find percent error with multiple values, calculate the average of your measured values, then use the percent error formula:
- Find the difference from the accepted value
- Divide by accepted value
- Multiply by 100%
5. Why is percentage error important in experiments?
The percentage error is important because it shows how accurate your experimental results are compared to a known or expected value. It helps scientists and students evaluate the quality and reliability of measurements taken during an experiment.
6. What factors can affect percentage error?
Several factors can affect percentage error, including:
- Instrument accuracy
- Human error
- Environmental conditions
- Calculation mistakes
7. Is percentage error always positive?
Yes, percentage error is always a positive value because it uses the absolute difference between the measured and actual values. The formula uses \(|\text{Measured} - \text{True}|\), which ensures negative signs are removed in the calculation.
8. How do you interpret a high percentage error?
A high percentage error means your measurement is far from the accepted value, suggesting significant inaccuracies in your experiment or process. It signals that you may need to review your method or recalculate to reduce the percentage error.
9. Can percentage error be used in real-life examples?
Yes, percentage error is commonly used in real life. For example, you might compare the expected and actual fuel consumption in a car or check the difference between measured weights and labeled package weights, calculating the percentage error in every case.
10. What is the difference between percentage error and absolute error?
The percentage error shows the error as a percent of the accepted value, while the absolute error is the actual difference between measured and true values. Percentage error makes it easier to compare errors across different measurements.
