This percent error calculator calculates the relative difference between the real value and the observed value discovered in a measurement. Thanks to this tool, you’ll be able to quickly determine whether your measurement was correct. Continue reading to determine how to calculate percent error and the percent error formula. You may also use the Percentage calculator to help you understand the notion of percents.

Percent error definition

We may attempt to estimate the value of a quantity by taking many measurements. By calculating the period of free fall from a certain height, we may figure out the gravitational acceleration.

The difference between an observed and a true or accepted value is measured in percentage error. When analyzing data, the final output frequently differs from the real value. The error can occur for various causes, including human error, but also due to estimates and limits of the instruments employed in the measurement.

Regardless, calculating the percentage inaccuracy might be useful in situations like these. First, the absolute error, which is just the difference between the observed and actual value, is used to calculate the percentage error. The relative error is then multiplied by 100 to get the percentage error, which is obtained by dividing the absolute error by the real value.

Percent error formula

Percent error shows how far off you are from the precise number when estimating the value of something. These mistakes may occur due to equipment imprecision, measurement (human or tool error), or modifications made to computation procedures (rounding off, etc.). This % error we calculate using the method below, which is basic and straightforward:

Percent \; Error = \frac {TV - OV} {TV} \times 100 \%

where:

  • TV is the true value, and
  • OV is the observed value.

How to calculate percent error?

We’ll look at a basic example to help you better grasp what percent error is. Let’s pretend we’re figuring out how much of a difference between the measured and genuine sound speed.

  • Find out what the true value of sound speed is. It’s 343 m/s in the air at 20°C.
  • Take an accurate measurement. You discovered that it was 329 m/s.
  • Take the observed value and subtract it from the real value = 14 m/s = 343 – 329 m/s. The absolute inaccuracy is 14 m/s.
  • Divide the correct number by the percent error to get the percent error, percentage mistake = 14 / 343 x 100% = 4.082 percent
  • The relative error, often known as the percent error, equals 4.082 percent.

Percent error chemistry

It might be accurate or incorrect depending on how near a measurement is to the genuine value. For example, assume you’re experimenting with estimating the density of an aluminum metal sample. The actual or accurate value is determined by broad agreement with a reputable reference. The acceptable density for aluminum is 2.70 g/cm3.

The value of a measurement measured during the experiment is called the experimental value. For example, assume you found an experimental value of 2.42 g/cm3 for the aluminum density in your experiment. The discrepancy between the experimental and accepted values is the experiment’s error.

Percent error formula chemistry

It is usual in chemistry and other fields to maintain a negative value if one occurs. It matters whether the mistake is positive or negative. For example, when comparing real to theoretical yield in a chemical process, you would not anticipate having a positive percent error. If a positive number is computed, there may be issues with the technique or unexplained reactions.

Percent \; Error = \frac {Experimental \; Value - Theoretical \; Value} {Theoretial \; Value} \times 100 \%

Percent error, a margin of error, and standard error

Other words are similar to percent mistake. We’ve included a brief description of each of them below to ensure you don’t get them together.

The relative difference between the observed and real value is what percent error, or relative error, is all about. To compute it, use the percent error calculation given before.

The standard error of data collection is a number that can determine. It’s a statistical word for the precision of a sample that accurately represents the entire population.

On the other hand, the confidence interval is strongly connected to the margin of error. It’s derived by multiplying the standard error by the z-score for a particular confidence level.

Percent error example

John measured himself and discovered that he was 5 feet tall. However, after a thorough investigation, he discovered that his true height is 4.5 ft. Determine the percentage of inaccuracy he made when measuring his height.

Solution:

Before we begin to solve the problem, let us first identify the information:

Actual value: 4.5 feet, estimated value: 5 feet

Step 1: To calculate the absolute value of the mistake, subtract one value from the others.

|4.5 5| = 0.5 \; Error

Step 2: Subtract the mistake from the real amount.

0.5 \div 4.5 = 0.1111 (up to 4 decimal places)

Step 3: To represent the answer as a percentage, multiply the number by 100 and add the percent sign.

100 \times 0.111 = 11.11

Error \; rate = 11.11 \%

FAQ

How to find percent error?

Percent error is calculated by taking the difference between the precise and estimated values of a number, dividing it by the exact value, then multiplying it by 100 to express it as a percentage of the exact value.

Can percent error be negative? 

The error is negative if the experimental value is smaller than the acceptable value. Conversely, the error is positive if the experimental value is greater than the accepted value.

What is a good percent error?

The measurement may be so difficult that a 10% error or greater is acceptable in some circumstances. In some circumstances, a 1% mistake may be excessive. Most high school and initial university lecturers will allow a 5% inaccuracy.

What does percent error tell you? 

When you measure anything in an experiment, the percentage of mistakes shows how significant your errors are. Smaller numbers indicate that you are getting nearer to the acceptable or true value.

Can percent error be over 100?

When doing tests, there is always the potential of obtaining a result that is either less or more than the genuine value due to experimental or human error.