Percent Error Calculator: Find the Accuracy of Your Measurements

How to Use Our Percent Error Calculator

To find the percent error, you only need two pieces of information. This calculation is essential for any lab report or quality check.

• Observed Value: This is the value that you measured or recorded in your experiment. It’s also sometimes called the “experimental value.”

• True Value: This is the accepted, theoretical, or scientifically established value that you are comparing your measurement against. It’s the “correct” value you were aiming for.

Understanding Your Results

The result of the calculation is the Percent Error, a value that tells you how far off your measurement was from the correct value, expressed as a percentage. A smaller percent error indicates that your observed value is very close to the true value, signifying high accuracy. A larger percent error means your measurement was less accurate.

The Formula Behind the Calculation

Our calculator uses the standard formula for percent error:

Percent Error = |(Observed Value - True Value) / True Value| × 100%

Let’s break down what each part of this formula means:

1. Find the “Error”: First, you find the difference between your measurement and the true value (Observed Value - True Value). This is the absolute error.

2. Calculate Relative Error: Next, you divide this error by the True Value. This step is crucial because it puts the error into perspective. An error of 2 cm is significant if the true value is 10 cm, but it’s very small if the true value is 1000 cm.

3. Take the Absolute Value: The vertical bars | | mean you take the absolute value of the result. This means percent error is always a positive number. It measures the size of the error, not whether you were over or under the true value.

4. Convert to a Percentage: Finally, you multiply the result by 100 to express it as a percentage.

• Example: You measure the boiling point of water to be 98.5°C. The true value is 100°C.

  • Error: 98.5 - 100 = -1.5

  • Relative Error: -1.5 / 100 = -0.015

  • Absolute Value: |-0.015| = 0.015

  • Percent Error: 0.015 × 100% = 1.5%

Frequently Asked Questions

What is considered a “good” percent error?

This completely depends on the context of the experiment.

• In a high-precision field like analytical chemistry or pharmacology, a percent error of less than 2% might be required.

• In a basic high school physics experiment with simple tools, a percent error of 10% or even 15% might be considered acceptable.

• In a complex field like ecology, where measurements are subject to many uncontrollable variables, a higher percent error might be expected. The “goodness” of a percent error is relative to the precision of the measurement tools and the complexity of the system being studied.

Can percent error be negative?

No. By standard definition, percent error is always reported as a positive value. The formula uses the absolute value of the difference to measure the magnitude of the error, regardless of whether your observed value was higher or lower than the true value. If you want to indicate the direction of the error, you would simply state that your measurement was “1.5% below the true value.”

What is the difference between percent error and percent difference?

This is a very common point of confusion.

• Percent Error is used when you are comparing your measurement to a known, true, or accepted value. There is a clear “correct” answer you are aiming for.

• Percent Difference is used when you are comparing two experimental measurements to each other, and neither is considered the “true” value. For example, if you and a lab partner both measure the length of an object and want to see how much your measurements differ. The formula is slightly different, using the average of the two measurements in the denominator.

What is the difference between accuracy and precision?

These two terms are related to measurement but mean different things.

• Accuracy refers to how close a measurement is to the true value. Percent error is a measure of accuracy. A low percent error means high accuracy.

• Precision refers to how close multiple measurements of the same thing are to each other. You can be very precise but not accurate. For example, if you measure the boiling point of water three times and get 98.5°C, 98.4°C, and 98.6°C, your measurements are precise (close together), but they are not accurate (the true value is 100°C). This often indicates a systematic error with your equipment.

What are common sources of error in an experiment?

Understanding where errors come from is key to improving your results.

• Systematic Errors: These are consistent, repeatable errors often caused by faulty equipment or flawed experimental design. For example, a scale that is not properly calibrated and always reads 0.2 grams too high. This type of error affects the accuracy of your results.

• Random Errors: These are unpredictable variations in measurements. They can be caused by limitations of the instrument, environmental factors, or slight variations in procedure. For example, slight fluctuations in reading a ruler or a thermometer. Taking multiple measurements and averaging them can help minimize random errors.

• Human Errors: These are mistakes made by the person conducting the experiment, such as misreading a scale, incorrect timing, or simple calculation mistakes.

Why do we divide by the true value instead of the observed value?

We divide by the true value because it is the stable, accepted benchmark against which we are measuring our accuracy. It serves as the standard reference point. Using the observed value would mean your error percentage would change depending on your measurement, which would be an inconsistent way to assess accuracy.

How can I reduce my percent error?

• Use more precise measuring instruments.

• Double-check that all equipment is properly calibrated.

• Take multiple measurements and calculate the average to reduce the impact of random errors.

• Carefully read and follow the experimental procedure.

• Be aware of environmental factors (like temperature or air pressure) that could affect the results.

Concrete Example: A Chemistry Lab Experiment

Imagine you are in a chemistry lab trying to determine the density of aluminum. You take a block of aluminum, measure its mass as 45.2 grams, and its volume as 17.1 cm³.

1. Calculate Observed Density:

   • Density = Mass / Volume

   • Observed Density = 45.2 g / 17.1 cm³ = 2.643 g/cm³

2. Find the True Value: You look up the accepted density of aluminum and find it is 2.70 g/cm³.

3. Use the Percent Error Calculator:

   • Observed Value: 2.643

   • True Value: 2.70

4. Result: The calculator shows a percent error of 2.11%.

5. Conclusion: You can conclude that your experimental measurement of density was quite accurate, with only a 2.11% error compared to the accepted scientific value. You could then discuss potential sources for this small error in your lab report, such as the precision of the scale or the method used to measure volume.

In what fields is percent error used?

Percent error is used across almost all scientific and engineering disciplines.

• Physics: Comparing an experimental value for the acceleration due to gravity to the accepted value of 9.8 m/s².

• Chemistry: Comparing the yield of a chemical reaction to the theoretical maximum yield.

• Engineering: Comparing the measured strength of a material to its specified strength.

• Manufacturing: Checking if a machined part is within its specified tolerance (e.g., a certain percentage of the target dimension).

What if my observed value is the same as the true value?

If your measurement is perfect, the Observed Value - True Value will be 0. Therefore, your percent error will be 0%. This indicates perfect accuracy in your measurement.

Now that you’ve calculated the accuracy of your measurement, you may need other tools for your data analysis. Our Scientific Calculator is perfect for handling complex equations in your lab reports. If you’ve taken multiple measurements, our Average Calculator can help you find the mean value.