experimental value percent error

Percent Error Calculator

Related Percentage Calculator | Scientific Calculator | Statistics Calculator

Percentage Error

Percentage error is a measurement of the discrepancy between an observed (measured) and a true (expected, accepted, known etc.) value. It is typically used to compare measured vs. known values as well as to assess whether the measurements taken are valid.

When measuring data, whether it be the density of some material, standard acceleration due to gravity of a falling object, or something else entirely, the measured value often varies from the true value. Error can arise due to many different reasons that are often related to human error, but can also be due to estimations and limitations of devices used in measurement. Calculating the percentage error provides a means to quantify the degree by which a measured value varies relative to the true value. A small percentage error means that the observed and true value are close while a large percentage error indicates that the observed and true value vary greatly. In most cases, a small percentage error is desirable, while a large percentage error may indicate an error or that an experiment or measurement technique may need to be re-evaluated. If, for example, the measured value varies from the expected value by 90%, there is likely an error, or the method of measurement may not be accurate.

Computing percentage error

The computation of percentage error involves the use of the absolute error, which is simply the difference between the observed and the true value. The absolute error is then divided by the true value, resulting in the relative error, which is multiplied by 100 to obtain the percentage error. Refer to the equations below for clarification.

For example, if the observed value is 56.891 and the true value is 62.327, the percentage error is:

The equations above are based on the assumption that true values are known. True values are often unknown, and under these situations, standard deviation is one way to represent the error. Please refer to the standard deviation calculator for further details.

Negative percentage error

Based on the formula above, when the true value is positive, percentage error is always positive due to the absolute value. In most cases, only the error is important, and not the direction of the error. However, it is possible to have a negative percentage error. This occurs if we do not take the absolute value of the error, the observed value is smaller than the true value, and the true value is positive. For example, given an observed value of 7, a true value of 9, and allowing for a negative percentage, the percentage error is:

A negative percentage error simply means that the observed value is smaller than the true value. If the observed value is larger than the true value, the percentage error will be positive. Thus, in the context of an experiment, a negative percentage error just means that the measured value is smaller than expected. It does not indicate that the observed value is somehow better than expected, since the best possible outcome for percentage error is that the observed and true values are equal, resulting in a percentage error of 0.

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• Science Experiments for Kids
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science
• Chemistry Problems With Answers
• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

Calculate Percent Error 5

Percent Error Definition

Percent error, sometimes referred to as percentage error, is an expression of the difference between a measured value and the known or accepted value . It is often used in science to report the difference between experimental values and expected values.

The formula for calculating percent error is:

Note: occasionally, it is useful to know if the error is positive or negative. If you need to know the positive or negative error, this is done by dropping the absolute value brackets in the formula. In most cases, absolute error is fine. For example, in experiments involving yields in chemical reactions, it is unlikely you will obtain more product than theoretically possible.

Steps to Calculate the Percent Error

• Subtract the accepted value from the experimental value.
• Take the absolute value of step 1
• Divide that answer by the accepted value.
• Multiply that answer by 100 and add the % symbol to express the answer as a percentage .

Example Calculation

Now let’s try an example problem.

You are given a cube of pure copper. You measure the sides of the cube to find the volume and weigh it to find its mass. When you calculate the density using your measurements, you get 8.78 grams/cm 3 . Copper’s accepted density is 8.96 g/cm 3 . What is your percent error?

Solution: experimental value = 8.78 g/cm 3 accepted value = 8.96 g/cm 3

Step 1: Subtract the accepted value from the experimental value.

8.78 g/cm 3 – 8.96 g/cm 3 = -0.18 g/cm 3

Step 2: Take the absolute value of step 1

|-0.18 g/cm 3 | = 0.18 g/cm 3

Step 3: Divide that answer by the accepted value.

Step 4: Multiply that answer by 100 and add the % symbol to express the answer as a percentage.

0.02 x 100 = 2 2%

The percent error of your density calculation is 2%.

Related Posts

5 thoughts on “ calculate percent error ”.

Percent error is always represented as a positive value. The difference between the actual and experimental value is always the absolute value of the difference. |Experimental-Actual|/Actualx100 so it doesn’t matter how you subtract. The result of the difference is positive and therefore the percent error is positive.

Percent error is always positive, but step one still contains the error initially flagged by Mark. The answer in that step should be negative:

experimental-accepted=error 8.78 – 8.96 = -0.18

In the article, the answer was edited to be correct (negative), but the values on the left are still not in the right order and don’t yield a negative answer as presented.

Mark is not correct. Percent error is always positive regardless of the values of the experimental and actual values. Please see my post to him.

Say if you wanted to find acceleration caused by gravity, the accepted value would be the acceleration caused by gravity on earth (9.81…), and the experimental value would be what you calculated gravity as :)

If you don’t have an accepted value, the way you express error depends on how you are making the measurement. If it’s a calculated value, like, based on a known about of carbon dioxide dissolved in water, then you have a theoretical value to use instead of the accepted value. If you are performing a chemical reaction to quantify the amount of carbonic acid, the accepted value is the theoretical value if the reaction goes to completion. If you are measuring the value using an instrument, you have uncertainty of the instrument (e.g., a pH meter that measures to the nearest 0.1 units). But, if you are taking measurements, most of the time, measure the concentration more than once, take the average value of your measurements, and use the average (mean) as your accepted value. Error gets complicated, since it also depends on instrument calibration and other factors.

Comments are closed.

• Percent Error Calculator

Calculate the percent error between a theoretical and experimental value, expressed as a percentage. The theoretical value is the expected value of measurement, while the experimental value is the actual value measured.

Have a Question or Feedback?

Percent error:, steps to solve percent error.

Chevron Down Icon scroll down

On this page:

How to calculate percent error, percent error formula, what is percent error, error terminology, frequently asked questions.

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

Full bio Chevron Right Icon

Pateakia has worked in education for 15 years and has three degrees, including a PhD, Master's degree, and Bachelor's degree. She specializes in mathematics.

Percentage error is the margin of error in a measurement between the expected and actual values measured. It is used to express the difference between the expected values and actual values in an experiment as a percentage.

Measuring percent error is important because it illustrates how close a measured or actual value is to the expected, theoretical value in an experiment. In chemistry, it’s often used in tandem when measuring the percent yield of a reaction.

The expected value can also be called the theoretical, true, or accepted value. The actual value is sometimes referred to as the experimental value.

You can find the percentage error using the following formula:

error = |theoretical – experimental| / |theoretical| × 100%

Thus, percent error equals the absolute value of the theoretical value minus the experimental value, divided by the theoretical value, multiplied by 100%. [1]

To use the formula, first, find the difference by subtracting the experimental value from the theoretical value. Next, divide the difference by the theoretical value to find the relative error. Lastly, multiply by 100 to find the error as a percentage.

Our percent change calculator may also be useful for finding the amount of change between 2 values.

Example: Find the percent error between a theoretical value of 99 and an experimental value of 98.

% error = |theoretical – experimental| / |theoretical| × 100% % error = |99 – 98| / |99| × 100% % error = 1 / 99 × 100% % error = .010101 × 100% % error = 1.01%

Since it is impossible to avoid measurement errors completely, there needs to be a way to define how much error there is when measuring.

Percent error is a measurement of the relative error between measurements in an experiment. You can find the precision, accuracy, or size of the error between measurements in an experiment from the percent error.

When conducting an experiment, the theoretical value is often referred to as the true value. This is the value expected to be seen when conducting a measurement.

The experimental value can also be called the observed value and is the value measured when conducting a measurement.

You might have also heard the term absolute error. Be mindful that absolute error and percent error are not the same thing.

Absolute error is the difference between the theoretical and experimental values.

absolute error = theoretical – experimental

Relative error is the difference between the theoretical and experimental values, divided by the theoretical value. Relative error is thus the amount of error relative to the whole.

relative error = theoretical – experimental / theoretical

Standard error is a statistical measure of error based on the standard deviation of the results. You can use our standard error calculator to find it.

Now you can solve percentage error using the formula above or our handy calculator. Use our percentage calculator for more tools to calculate percentages.

Is percent error the same as percent difference?

No, percent error is the margin of error in a measurement between the expected and actual values measured, while percent difference uses true values.

How is the percent error different from the margin of error?

The percent error is an absolute value, whereas the margin of error is a range of values.

When should you use percent error?

You should use percent error when trying to compare measured versus known values.

Can percent error be negative?

Yes, if the observed value is smaller than the true value, the percent error will be negative.

Recommended Percentage Resources

• Percentage Calculator Right Arrow Icon
• Marks Percentage Calculator Right Arrow Icon
• Percent Yield Calculator Right Arrow Icon
• Percent to Fraction Calculator Right Arrow Icon
• Percent to Ratio Calculator Right Arrow Icon
• Wu, G., Baraldo, M., Furlanut, M., Calculating percentage prediction error: A user's note, Pharmacological Research , October 1995, 32(4), 241-248. https://doi.org/10.1016/S1043-6618(05)80029-5

Advertisement

How to Calculate the Percent Error Formula

• Share Content on Facebook
• Share Content on LinkedIn
• Share Content on Flipboard
• Share Content on Reddit
• Share Content via Email

We all make mistakes. Sometimes, if you play your cards right, they can become valuable learning opportunities. It's called "human error" for a reason; even the best of us leave a "t" uncrossed or an "i" undotted now and then. Such is life.

Before trying to correct a blooper , gaffe or snafu (did you know a thesaurus makes a great gift?), it's usually a good idea to find out what went wrong in the first place.

The size of the error is a key detail. How badly did you miss the mark? Was it a close shave or wildly off-base?

Picture a violinist in a philharmonic orchestra. On the night of a big concert, he misses an important cue and plays some notes too late. If he missed the cue by half a second, it might not be a huge deal. But if he missed it by half a minute , that's a different can of worms.

When there's a difference between the value you expected and the value you actually got — and you express that difference as a mathematical percentage — it's called a percent error or percentage error . Calculating percentage error involves comparing an expected value and an actual value to determine how far reality deviated from theoretical expectations.

Today, we're going to take the mystery out of reporting the percent error correctly and show you how to use it in real life.

What Is the Percent Error Formula?

The equation couldn't be much simpler. Here it is:

Percent Error = | Experimental Value – Actual Value | / Actual Value x 100%

The value you originally projected goes by many names, including exact value, accepted value, estimated value, theoretical value, approximate value or experimental value, depending on the context. For instance, a physics student calculating speed will refer to an accepted value based on the velocity formula , but the approximate or measured value of speed in her experiment may differ. In another scenario, a business owner may refer to an estimated value when forecasting revenue.

Similarly, there are multiple labels for your real-life result, including actual value, measured value, and exact or known value. No matter what you call it, the spirit behind the actual number itself remains the same.

Some people find written instructions more helpful than mathematical formulas. If you're one of them, no worries. Here's a step-by-step walkthrough for percent error calculation:

• Step One: Take the experimental value and subtract the actual value from it. This is called the relative error.
• Step Two: Take the absolute value of the number you arrived at in Step One (that's what those two vertical lines indicate). This new number is called the absolute error and ensures that your final percentage does not include a negative sign.
• Step Three : Divide that number by the actual value.
• Step Four: Multiply your result by 100.
• Step Five: Write out your final answer as a percentage.

Examples of How to Calculate Percent Error

We're now ready to take the percentage error formula out for a test drive.

Let's say you're a bookworm with a long vacation coming up. You go to the library to grab some reading material. Before you open the front door, you assume you'll check out three books. But instead, for whatever reason, you only take home two books. What's the percentage error of your estimate?

In our example, the experimental value is 3 and the actual value is 2. Plug in the numbers, and you get this:

Percent Error = (3 – 2)/2 x 100

If you're old enough to read this article, we're guessing you already knew that 3 minus 2 equals 1. Which leaves us with:

Percent Error = 1/2 x 100

Divide 1 by 2 and you get the following:

Percent Error = 0.5 x 100

And 100 times 0.5 equals 50. But remember, we have to express our final answer as a percentage. When we do that, we learn the original guess you made had a percent error of 50%.

This example was all about quantity (i.e., the number of library books). But the percent error formula can also be applied to lots of other values — like speed, distance, mass and time.

Bearing that in mind, let's go through the formula again.

Suppose a college athlete thinks he'll need 45 seconds to finish a hardcore workout challenge. But when he hits the gym, the routine takes him 60 seconds to complete. What was the percent error of the time estimate he started out with (45 seconds)?

Percent error = (45 – 60)/60 x 100

Right off the bat, we've hit a complication. If you subtract 60 from 45, you get a negative number (-15 to be exact).

Divide -15 by 60 and you'll get -0.25, which is another negative value. And we can't stop there; we still need to multiply the -0.25 by 100, giving us an answer of -25. Does that mean the percent error is -25%?

The percent error between an estimated value and the actual value cannot be expressed as a negative . It's always written out as a positive value, whether the starting estimate was way too big or way too small.

Here's where our old friends "absolute error" and "relative error" come into play. The value of -15 is only the relative error. You need to take the absolute value of that before proceeding with the calculation. Once you have the absolute error of 15, you can divide that by 60 and multiply by 100 for a percent error of 25%.

New York Yankees legend Lawrence Peter Berra — better known by his nickname "Yogi" — has been credited as saying , "Baseball is 90 percent mental. The other half is physical." Math teachers are still chuckling about that one.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

Percent Error Calculator

What is percent error.

Percent error measures the accuracy of a measurement by comparing the experimental value to the accepted (theoretical) value. It's commonly used in science labs, quality control, and experimental research to determine how far off your measured value is from the expected result.

Percent Error Formula

The formula for calculating percent error is:

Percent Error = |Experimental Value - Accepted Value| ÷ Accepted Value × 100%

• Experimental Value = Your measured or observed value
• Accepted Value = The theoretical or known value
• | | = Absolute value (makes the result positive)

How to Calculate Percent Error

• Subtract the accepted value from your experimental value
• Take the absolute value of this difference
• Divide by the accepted value
• Multiply by 100 to get the percentage

Common Questions About Percent Error

Can percent error be negative.

No, percent error is typically expressed as a positive number. The absolute value in the formula ensures this.

What's a good percent error?

A lower percent error indicates more accurate results. In most school labs, less than 5% is considered good, while professional settings may require even lower errors.

What's the difference between percent error and percentage error?

These terms mean the same thing and are used interchangeably in scientific calculations.

Why do we use absolute value?

The absolute value tells us how far off the measurement is, regardless of whether it's higher or lower than the expected value.

Examples of Percent Error Calculations

Example 1: Experimental Value: 52 grams Accepted Value: 50 grams Percent Error = |52 - 50| ÷ 50 × 100 = 4%

Example 2: Experimental Value: 9.8 meters Accepted Value: 10 meters Percent Error = |9.8 - 10| ÷ 10 × 100 = 2%

Tips for Reducing Percent Error

• Use calibrated instruments
• Take multiple measurements and average them
• Control environmental conditions
• Follow proper measurement techniques
• Record values with appropriate significant figures
• Percent Change Calculator
• Percent Increase Calculator
• Percent Difference Calculator
• Percent Yield Calculator
• Percent Off Calculator
• Percent Decrease Calculator
• X is What Percent of Y Calculator
• What is X Percent of Y Calculator
• X is Y Percent of What Calculator
• How to Find the Percent of a Number

Percent Error Calculator

Understanding percent error, what is percent error.

Percent error is a measure of how inaccurate a measurement is, expressed as the relative difference between the experimental value and the accepted theoretical value. It is commonly used in scientific experiments to quantify the precision of measurements or the accuracy of predictions.

The formula for percent error is:

\[ \text{Percent Error} = \left|\frac{\text{Experimental Value} - \text{Theoretical Value}}{\text{Theoretical Value}}\right| \times 100\% \]

• Experimental Value is the measured or observed value
• Theoretical Value is the expected or accepted value
• The vertical bars \( | \) indicate absolute value

Calculation Steps

Let's calculate the percent error for an experiment where the theoretical value is 10 and the experimental value is 9.5:

• Experimental Value = 9.5
• Theoretical Value = 10
• Apply the percent error formula: \[ \text{Percent Error} = \left|\frac{9.5 - 10}{10}\right| \times 100\% \]
• Calculate: \[ = \left|\frac{-0.5}{10}\right| \times 100\% = 0.05 \times 100\% = 5\% \]
• The percent error is 5%

Example and Visual Representation

Let's visualize a percent error of 5%:

This diagram represents:

• The full circle represents 100% or no error
• The blue sector represents the 5% error
• The larger the blue sector, the greater the percent error

Need a Custom Calculator?

We can create a free, personalized calculator just for you!

Contact us and let's bring your idea to life.

Percent Error — Overview & Calculation - Expii

Percent error — overview & calculation, explanations (3), what is percent error.

Percent Error is a calculation that determines how much error occurred during an experiment

There are multiple types of error that cause an increase in the percent error. Error can come from a range of mistakes such as technique or a problem with using the equipment. Error is completely normal, and expected!

The Formula for Calculating Percentage Error Is:

|Accepted−Experimental|Accepted X 100%

Experimental Value : The value determined from conducting the experiment

Accepted Value : The value derived from a source (typically a known value that can be found from a reliable source)

Here's A Step-by-Step Example:

The melting point of gold is 1,064°C, however, when a student went to determine the melting point of gold, they measured the melting point to be 1,011°C. What is the percent error?

1) Determine which number is the experimental value and which number is the accepted value

Experimental Value: 1,011°C because this is the value the student found while conducting the experiment

Accepted Value: 1,064 because this is the literature melting point of gold

2) Plug the numbers into the equation

(|1064−1011|1064)⋅100%=4.981%

3) Boom you're done!

The percent error for this experiment was 4.981%

Try out a problem!

A student was conducting an experiment to determine the density of platinum. During the experiment, the student found that the density of platinum was 19.89 g/mL. The student checked online and found that the density of platinum is 21.45 g/mL. What is the student's percent error for the experiment?

Related Lessons

Visual Percent Error

Notice the absolute value sign; it does not matter what order the numerator is computed in, as long as the denominator is the correct comparator, the magnitude of percent error will be correct.

(Video) Calculating Percent Error

by Professor Dave Explains

In this video, professor Dave explains how to calculate error. There are actually a few types of error that you should know about. Maybe the simplest is absolute error . This is what you get when you subtract the actual value from the measured value . However, this value is not very descriptive.

Instead, we usually present something called the relative error . This value is calculated with the following formula:

relative error=|measured value−actual value|actual value

When we multiply this value by 100, we get the percent error or percentage error.