Getting a measurement close to an accepted value is one of the main goals of an experiment, but the numerical difference alone does not always tell you how reliable the result is. A difference of 1 unit might be significant in one experiment and almost negligible in another. The size of the accepted value matters when judging the result.
Consider two students measuring the length of different metal rods:
Both students are off by exactly 1 cm. However, their results do not have the same percent error.
Student A has a 2% error, while Student B has a 0.5% error.
Although the absolute measurement error is identical, Student B’s result is closer to the accepted value in relative terms.
This is why percent error is useful in science. It puts the difference between an experimental measurement and its reference value into context, making results easier to evaluate across measurements of different sizes.
It is particularly useful in physics and chemistry experiments where students measure quantities such as mass, temperature, length, density, volume and acceleration.
Percent Error vs. Percent Difference vs. Relative Error
These three terms appear frequently in laboratory assignments, but they describe different ways of evaluating measurements. Choosing the wrong one can lead to an incorrect interpretation of experimental results.
The main distinction is whether you have an accepted reference value or are simply comparing two measurements.
Percent Error: Comparing an Experimental Result With an Accepted Value
Percent error is appropriate when you have a measured result and a known reference value against which to compare it.
For example, a student measures the boiling point of a liquid as 98°C, while the accepted reference under the specified experimental conditions is 100°C.
The absolute difference is 2°C, representing a 2% error relative to the reference value.
This calculation helps determine how far the experimental result deviates from the expected result.
Percent Difference: Comparing Two Measurements
Percent difference is used when comparing two measurements without treating either one as the accepted or correct value.
Suppose two laboratory groups measure the density of the same material:
-
Group A: 48 units
-
Group B: 52 units
Their average is 50 units, and the difference between their measurements is 4 units.
Percentage difference:
(4 ÷ 50) × 100 = 8%
The results differ by 8% relative to their average.
This calculation is useful when comparing results from two experimental methods or different laboratory groups, particularly when an established reference value is unavailable.
Relative Error: Expressing the Error as a Proportion
Relative error describes the size of the absolute error in relation to the accepted value. It is usually expressed as a decimal or ratio rather than a percentage.
For example, a student measures a metal object as 19.5 cm when its accepted length is 20 cm.
Absolute error = 0.5 cm
Relative error = 0.5 ÷ 20 = 0.025
Multiplying this result by 100 gives a percent error of 2.5%.
The three measurements serve different purposes:
| Term |
Main purpose |
| Percent error |
Evaluates an experimental result against an accepted value |
| Percent difference |
Compares two values relative to their average |
| Relative error |
Expresses the error as a proportion of the accepted value |
Understanding this distinction helps prevent confusion when working through physics, chemistry and other scientific laboratory assignments.
How Should You Interpret a High or Low Percent Error?
After calculating percent error, the next question is usually whether the result is acceptable. A lower percentage generally means the experimental measurement is closer to its accepted reference value, but there is no single percentage that determines whether every experiment has been performed successfully.
The acceptable error depends on the measurement, equipment, experimental method and level of precision required.
For example, consider two different experiments:
A student measures the length of a wooden object using a basic ruler. A small deviation may be reasonable because the instrument has limited measurement resolution.
Another student measures the concentration of a chemical solution using laboratory equipment designed for highly precise analysis. The same percentage deviation might be unacceptable for that experiment.
Here is how different results can be understood:
| Percent error |
General interpretation |
| 0% |
The experimental value matches the accepted value |
| 0.5% |
A very small relative deviation |
| 2% |
A relatively close result in many measurement situations |
| 5% |
A deviation that should be assessed against the experiment’s requirements |
| 10% |
A more noticeable difference that may need investigation |
| 25% |
A substantial deviation from the accepted value |
These are illustrative descriptions, not universal scientific acceptance limits.
Does a Smaller Percent Error Always Mean a Better Experiment?
Not necessarily. A small percent error indicates that a result is close to its reference value, but it does not prove that the experimental procedure was reliable or that repeated measurements would produce similar results.
For instance, a student might obtain one measurement very close to the accepted value by chance, even though their other readings vary considerably.
To evaluate an experiment properly, consider both accuracy and precision, along with the uncertainty of the measuring equipment.
What Causes Experimental Results to Differ From Accepted Values?
An experiment does not always produce the expected result, even when the underlying scientific principle is correct. Small differences can develop during measurement, observation, equipment handling and data recording.
Understanding the source of an error is often more valuable than simply knowing its percentage.
Incorrectly Calibrated Measuring Instruments
A measuring instrument may consistently provide readings that are slightly higher or lower than the actual value if it has not been calibrated correctly.
For example, imagine an electronic balance that displays 5.2 grams when an empty container is placed on it. If the student does not account for this initial reading, every subsequent mass measurement may be affected.
Similar problems can occur with thermometers, pressure gauges, graduated cylinders and digital measuring devices.
Checking the calibration and zero setting before beginning an experiment can help prevent this type of systematic error.
Mistakes While Reading Measurements
Some errors happen because of the way a measurement is observed or recorded rather than because the equipment is defective.
A common example occurs when measuring liquid volume with a graduated cylinder. Reading the liquid level from above or below eye level can produce an incorrect reading because of the curved liquid surface, known as the meniscus.
Other examples include:
-
Reading the wrong graduation on a measuring scale.
-
Recording 12.6 instead of 12.9.
-
Starting or stopping a stopwatch at the wrong moment.
-
Using the wrong measurement unit during calculations.
Careful observation and consistent measurement techniques can reduce these errors.
Environmental Conditions Affecting Measurements
The surrounding environment can influence experimental results, particularly when working with temperature-sensitive materials or physical quantities.
For example, temperature changes can affect the volume of liquids and the dimensions of some materials. Air pressure and temperature can also influence gas measurements.
If an experiment requires specific environmental conditions, performing it outside those conditions may produce results that differ from the accepted reference.
Recording the conditions under which measurements are taken can help explain unexpected differences.
Limited Precision of Measuring Equipment
Every measuring instrument has limitations. A ruler with markings every millimeter cannot provide the same level of detail as an instrument designed to measure smaller changes.
For example, if the actual length of an object is 12.47 cm but the available ruler only supports readings to the nearest 0.1 cm, the recorded result may be 12.5 cm.
This does not necessarily mean the student made a mistake. The instrument itself limits the resolution of the measurement.
Using equipment with suitable resolution is important when an experiment requires precise results.
Problems With the Experimental Procedure
The method used to perform an experiment can also influence the final measurement.
Examples include using contaminated materials, failing to mix a solution properly, allowing a sample to lose heat before recording its temperature, or changing the procedure between trials.
Such problems can introduce systematic differences or increase variation between measurements.
A consistent procedure, properly prepared samples and careful handling of equipment help produce more dependable results.
Accuracy vs. Precision: Why They Matter When Evaluating Experimental Results
Accuracy and precision are closely related, but they describe different qualities of a measurement.
Accuracy refers to how close an experimental result is to the accepted value. Precision describes how closely repeated measurements agree with one another.
Imagine a student measuring the same metal rod five times:
49.1 cm, 49.2 cm, 49.1 cm, 49.2 cm and 49.1 cm.
These readings are very close to each other, suggesting good precision. However, if the accepted length is 50 cm, the measurements are consistently below the reference.
The results are precise but not particularly accurate.
Now consider another student who records:
49.0 cm, 50.1 cm, 49.8 cm, 50.4 cm and 49.7 cm.
These measurements vary more, but several are close to the accepted value. The student may have a less consistent measurement process.
The difference becomes easier to understand when looking at the four possible combinations:
| Measurement quality |
What it means |
| Accurate and precise |
Measurements are close to the accepted value and to each other |
| Accurate but not precise |
Results vary, but their central value may be close to the accepted value |
| Precise but not accurate |
Repeated measurements agree but are consistently away from the accepted value |
| Neither accurate nor precise |
Measurements vary and are also far from the accepted value |
Percent error helps assess the relative deviation from an accepted value. It does not independently measure precision.
If you have multiple experimental readings, examining their spread or standard deviation can provide additional information about consistency.
How to Reduce Percent Error in Laboratory Experiments
If your experimental result has a larger deviation than expected, repeating the calculation is not necessarily the solution. You need to identify where the difference might have entered the measurement process.
These practical steps can help improve the quality of experimental results.
Check instruments before taking measurements. Make sure balances, thermometers, rulers and other equipment are properly calibrated and set to zero where required.
Take repeated measurements. One reading may be affected by an accidental observation or random variation. Recording several measurements helps reveal whether the results are consistent.
Use suitable measuring equipment. Choose an instrument with enough resolution for the quantity being measured. A basic ruler may not be suitable for an experiment that requires measurements to a fraction of a millimeter.
Maintain consistent experimental conditions. Keep factors such as temperature, pressure, sample preparation and measurement procedures as consistent as the experiment requires.
Record measurements immediately. Writing down readings as they are obtained reduces the risk of forgetting values or entering incorrect numbers later.
Check calculations and units. A correct measurement can still produce an incorrect result if the wrong unit, conversion factor or numerical value is used.
Avoid rounding intermediate results. Keep sufficient decimal places during calculations and round the final reported result according to the precision of the measurements.
One important point: repeating a measurement can help reduce random variation, but it will not automatically correct a systematic problem such as an incorrectly calibrated balance.
Calculating Percent Error From Multiple Experimental Measurements
Many laboratory experiments require students to take several readings rather than rely on one measurement. Repeated trials help show whether a result is consistent and provide a more representative value for comparison with an accepted reference.
Consider a chemistry experiment in which a student measures the density of a material three times.
| Trial |
Measured density |
| 1 |
7.82 g/cm³ |
| 2 |
7.88 g/cm³ |
| 3 |
7.85 g/cm³ |
Before comparing the experimental result with the accepted density, calculate the average of the three measurements.
Average = (7.82 + 7.88 + 7.85) ÷ 3
Average = 7.85 g/cm³
Suppose the accepted density is 7.87 g/cm³.
The difference between the average experimental result and the accepted value is 0.02 g/cm³. The relative deviation is approximately 0.254%.
This gives the student a way to evaluate the average experimental result rather than relying on an individual trial.
However, there is another important consideration. The average alone does not tell you how closely the three readings agree. Two experiments could have the same average but very different levels of variation.
For this reason, laboratory analysis may also involve standard deviation or other statistical measures when evaluating repeated measurements.
How to Report Percent Error in a Laboratory Report
Calculating percent error is only part of completing a laboratory assignment. You should also explain what the result means and identify possible reasons for the difference between the experimental and accepted values.
A useful laboratory conclusion should include the measured value, the reference value, the calculated error and a short interpretation.
For example:
“During the experiment, the measured density of the material was 7.85 g/cm³, compared with an accepted reference density of 7.87 g/cm³. The calculated percent error was approximately 0.25%. The experimental result was therefore close to the accepted reference. Small differences may have resulted from measurement resolution, sample handling or limitations in the measuring equipment.”
This is more informative than simply writing that the experiment produced a 0.25% error.
When preparing your own report, remember to:
-
Include the experimental and accepted values.
-
Use the correct units for physical measurements.
-
State the percent error clearly.
-
Avoid claiming that a result is perfect simply because its error is small.
-
Discuss realistic sources of experimental deviation.
-
Use an appropriate number of significant figures.
The explanation should reflect what actually happened during the experiment. Do not automatically blame equipment or human error without considering the procedure and available evidence.
Special Cases to Understand When Calculating Percent Error
Some measurement situations require additional attention because the usual interpretation of percent error may not be sufficient.
What Happens When the Accepted Value Is Zero?
The standard percent error calculation uses the accepted value as its denominator. If the accepted value is zero, division by zero is undefined.
For example, suppose an experiment is expected to produce a measurement of zero, but the instrument records 0.05 units.
You can identify an absolute difference of 0.05 units, but you cannot calculate a conventional percent error using zero as the reference value.
In this situation, report the absolute deviation or use another measurement approach appropriate to the experiment.
Can Percent Error Be Greater Than 100%?
Yes. Percent error is not restricted to values between 0% and 100%.
Suppose the accepted value is 10 units, but the experiment produces a result of 25 units.
The absolute difference is 15 units, which is 150% of the accepted value.
A result above 100% indicates that the deviation is larger than the reference amount. It does not automatically mean the calculation is incorrect.
How Can You Tell Whether an Experimental Result Is Too High or Too Low?
The conventional absolute percent error reports the size of the deviation but removes its direction.
If you also want to understand whether the experiment produced a value above or below the accepted reference, use signed relative error:
Signed Relative Error = ((Experimental Value − Accepted Value) ÷ Accepted Value) × 100
For a positive accepted reference:
For example, if the accepted value is 50 and the experiment records 48, the signed relative error is -4%.
If the experiment records 52, the signed relative error is +4%.
Both have an absolute percent error of 4%, but they describe opposite directions of deviation.
