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Percentage Error Calculator
Calculate, understand, and apply percentage error accurately for science, mathematics, engineering, statistics, and laboratory measurements.
Percentage error calculator
Enter the true (actual/theoretical) value and measured (experimental) value. Get percentage error, absolute error, and difference instantly.
Percentage error
Absolute error
Difference (measured - true)
Example calculations
Chemistry lab
True: 0.100 M · Measured: 0.103 M
3% percentage error
Physics motion
True: 2.00 m · Measured: 1.94 m
3% percentage error
Engineering part
True: 50.0 mm · Measured: 50.4 mm
0.8% percentage error
What is percentage error?
Percentage error measures how far an experimental or measured value is from an accepted true, theoretical, or actual value.
Definition and meaning
Percentage error expresses the size of a measurement mistake as a percent of the reference value. It answers: how far off was my result, relative to what was expected?
In science and math, the measured value (also called the experimental value) is what you record. The true value (also called the actual or theoretical value) is the accepted standard you compare against.
A small percentage error usually means your method and equipment were close to the reference. A large percentage error signals a bigger gap that may need investigation.
Use the Percentage Error Calculator on this page whenever you need a fast, accurate result.
Why percentage error matters
Percentage error helps you report lab results clearly, compare trials, and judge whether equipment or technique needs improvement.
It is used in physics labs, chemistry titrations, engineering tolerances, quality checks, and introductory statistics when one value is the clear reference.
Because the result is a percentage, you can compare accuracy across different units and scales more easily than with raw difference alone.
Read more in our guide on what is percentage error.
Percentage error formula
The standard formula compares absolute difference to the true value, then scales to a percent.
Basic percentage error formula
Percentage error = ( |Measured - True| / |True| ) × 100
Here, True is the accepted reference value and Measured is your experimental reading. The absolute value bars mean direction (high or low) does not change the percent error.
Absolute error = |Measured - True|. It is the size of the gap without a percent scale.
See the full walkthrough in percentage error formula.
Relative error and formula steps
Relative error is often written as absolute error divided by the true value, without multiplying by 100. Percentage error is relative error expressed as a percent.
Step 1: Subtract true from measured.
Step 2: Take the absolute value.
Step 3: Divide by |true|.
Step 4: Multiply by 100.
Example: True = 40.0 mL, Measured = 42.0 mL. Absolute error = 2.0 mL. Percentage error = (2.0 / 40.0) × 100 = 5%.
How to calculate percentage error
You can calculate percent error by hand, with a spreadsheet, or with our online tool.
Manual and calculator methods
Write down the true value and measured value with the same units. Compute the difference, apply the absolute value, divide by the true value, then multiply by 100.
The fastest method is the Percentage Error Calculator: enter both values and read percentage error, absolute error, and signed difference instantly.
For repeated homework sets, a spreadsheet works well. Put true values in one column and measured values in another, then use a formula for absolute difference and percent error.
Our article on how to calculate percentage error covers manual steps, calculator use, and shortcuts.
Quick methods compared
Online tool
Best for speed, labs, and checking many trials.
Spreadsheet
Best for data tables and repeated calculations.
Percentage error examples
Worked examples help you see how the formula behaves in real measurements.
Science and lab examples
Chemistry: Accepted concentration = 0.100 M, measured = 0.103 M. Absolute error = 0.003 M. Percentage error = 3%.
Physics: Expected distance = 2.00 m, measured = 1.94 m. Absolute error = 0.06 m. Percentage error = 3%.
Engineering: Target length = 50.0 mm, measured = 50.4 mm. Percentage error = 0.8%.
More worked problems are in percentage error examples.
Statistical and reporting note
When you report percentage error in a lab write-up, state the true and measured values, show absolute error, then give percent error with sensible significant figures.
If percent error is very large, mention possible sources such as technique, calibration, or environmental conditions rather than only reporting the number.
Absolute error vs percentage error
Both describe a gap between values, but they answer slightly different questions.
Key differences
Absolute error keeps the original units (grams, meters, seconds). Percentage error scales that gap relative to the true value, which makes comparisons easier across different sizes.
Use absolute error when the raw gap matters for safety or specs. Use percentage error when you need a proportional view of accuracy.
A 2 mm error is tiny on a 2 m part but large on a 10 mm part. Percentage error captures that context.
Compare both ideas in absolute error vs percentage error.
Relative error vs percentage error
Relative error and percentage error are closely related scaling methods.
Formula comparison
Relative error = |Measured - True| / |True|. Percentage error = relative error × 100.
In statistics and data analysis, relative error helps interpret deviation without tying results to specific units. Percentage error is the same idea in percent form.
Do not confuse percentage error with percent difference, which compares two values when neither is a fixed reference.
Learn more in relative error vs percentage error.
Percentage error in science
Laboratory work relies on percent error for accuracy, precision, and honest reporting.
Labs, precision, and validation
In science classes and research labs, percentage error supports measurement precision checks, instrument validation, and comparison between methods.
Low percent error does not automatically mean high precision if your true value itself is uncertain. Always note what reference you used.
Repeat trials and average results when appropriate, then calculate percent error for each trial or for the average compared to the standard.
Explore applications in percentage error in science.
Mean percentage error
When you have several trials, mean-based error metrics can summarize performance.
Mean percentage error and MAPE
Mean percentage error can describe the average percent deviation across multiple measurements. In forecasting and data analysis, a related idea is mean absolute percentage error (MAPE).
MAPE is used when you compare many predicted and actual values. It is not the same as a single lab percent error, but both focus on percentage-scale deviation.
For introductory science work, start with one true value and one measured value. Move to mean-based metrics only when your assignment or dataset requires it.
Read mean percentage error for definitions and when each metric fits.
Percentage error calculator
Use the tool above to compute percent error, absolute error, and difference instantly.
How to use this calculator
Enter the true (actual/theoretical) value and the measured (experimental) value in the Percentage Error Calculator section on this page, then select Calculate.
The result shows percentage error, absolute error, and the signed difference (measured minus true) so you can see direction and magnitude.
Try the sample values in the examples under the calculator, or read how to use the percentage error calculator.
Go to calculatorCommon percentage error mistakes
Avoid these errors when calculating or reporting percent error.
Mistakes to avoid
Dividing by measured
The denominator should be the true value, not the experimental value, unless your instructor specifies otherwise.
Skipping absolute value
Most definitions use |measured - true| so high and low readings give the same percent error.
Mixing units
Convert to the same unit before subtracting.
True value of zero
Percent error is undefined when true = 0 because you cannot divide by zero.
Accuracy vs precision
Percent error relates to accuracy. Precision describes repeatability.
How they work together
Accuracy is how close you are to the correct value. Precision is how close repeated measurements are to each other.
You can be precise but inaccurate (tight cluster around the wrong value) or accurate but imprecise (scattered around the correct value).
Percentage error mainly describes accuracy against a reference. Use repeated trials and spread (such as range or standard deviation) to discuss precision.
FAQs about percentage error
Quick answers to common questions about percent error, formulas, and reporting.
It is the size of the gap between measured and true values, expressed as a percent of the true value.
Percentage error = ( |measured - true| / |true| ) × 100.
Most courses use absolute value in the formula, so percent error is reported as a positive value. The sign of the error appears in the measured - true difference.
It depends on the field. Many school labs treat single-digit percent error as reasonable, but always follow your rubric or industry standard.
No. Percent error needs a clear true value. Percent difference compares two values without a fixed reference.
It helps interpret relative deviation. Related summary metrics include mean absolute percentage error for many data points.
Yes. Use ABS(measured-true)/ABS(true)*100. See our percentage error in Excel guide.