This article will help you examine how to calculate percentage errors and apply this to measurements used in both the sciences of physics and the chemistry field. Both the sciences of chemistry and physics are dependent upon measurements.
While conducting experiments, it’s expected to get precise results. However, the instruments we use have limitations. Because our instruments aren’t exact, they can cause errors in our measurements. This error is the difference between the true/accepted value and the measured/experimental value.
What is Meant by Percent Error?
When an experiment is conducted and obtained, they align with the actual value or differ from what happens. The error refers to the gap between the estimated value as well as the real value. Measurement errors are caused by non-preventable flaws in the measuring instrument, as well as the limits of our eyes.
They can be of all sizes, and, at times, we have to determine whether the error in our measurement is big enough to render the measurement unusable. The smaller error means that we’re close to the exact value. Thus, scientists have come up with an approach to determine the degree of error in estimation.
Now, let’s move to our crucial part – the definition in the percentage error formula.
Percentage Error Definition
Percentage error refers to an error in the gap between the real and estimated value compared to the value. It is expressed in an arithmetic format.
Also, you look for the difference between the real answer and the guess, then subtract it from the answer you got, and then convert it into a percentage. Percentage errors show how big our mistakes are when we evaluate the value of something.
For instance, an error of 5% means that we came very close to the agreed number, whereas 60% signifies that we were away from the true value.
Percentage Error Calculation Steps
- Subtract one value and subtract another. It doesn’t matter if you’re dropping the sign (taking the absolute value).
- Add the theory value to the experimental value if you’re keeping negative signs. This will be what you call your “error.”
- The error is divided by your ideal value (not the measured or experimental value). This will result in an exact decimal.
- Convert the decimal value into Percentage using the multiplier 100.
- You can use a Percentage symbol to display your error rate in Percentage.
Percentage Error Formula
Percentage error is the variance between an exact and measured value, divided by the value multiplied by 100 Percentage. In many cases, percentage error is expressed as a positive number. While in other cases, the total magnitude of an error can be calculated by an accepted number and then expressed as a percentage.
That’s how you come to the Percent Error Formula.
You can also apply to do this without using the Absolute Value. In chemistry, as well as other disciplines, it is important to keep an error of minus. This can result in a negative or positive result that could be helpful to be aware of.
The error can be negative or positive; it’s crucial. For instance, we could not anticipate the positive percent error when comparing actual. If a positive result was determined, this could be a sign of issues with the method or unaccounted for reactions.
When calculating the measured or experimental value minus, the actual or theoretical value will always be considered absolute. So, the Percent Error Formula will be,
In many measurement instruments, the measurement is not 100% accurate. Therefore, we can utilise the Percentage Error to determine the possibility of error when taking measures.
Percent Error Calculation Steps:
- Subtract one value from the other values. In this case, the order doesn’t matter. This will be what is called the error.
- Dividing the error into the theoretical amount.
- Convert the decimal value above into a percentage value by adding 100. This will give you the percentage error.
Solved Examples
Q.1: I thought that 70 people would show up at the concert I organised. However, on that day, the date of show attendance was only around 80. Check out how many errors I made in my calculations.
Solution: We will first discover the absolute difference, i.e. 70 – 80 = 10
Then, apply the formula.
You get an error of 12.5%.
Can a percentage error be negative?
The majority of us consider the percentage error as positive due to the quantity of error which is more important than its appearance. Certain sciences, like chemistry, require that we specify the nature of the error. In this scenario, you should not consider the absolute value differences between the two values.
Subtraction order also affects the way you subtract the calculated value from the real value. Therefore, if your error in percentage falls below a certain level, your measured value is greater than the actual value. But until it is your intention, you should always use the total value and report percentage errors as an integer.
For instance, suppose you estimated how long the table was and took an estimate of 22 centimeters. A friend measures the length of the board well and comes up with a figure of 18cm.
It is important to determine the “true” or “accepted value” of the length of the board find the percentage error for every measurement. When you looked over the manual of the manufacturer and determined its length was 20 cm long. This is the acceptable value for our estimation.
Percent Error Versus Absolute and Relative Error
Percent error is a result of absolute and relative errors. The difference between an experiment and a known number is the absolute error. If you divide that number by the value that is known, you will get the relative error. A percent error is a relative error multiplied by 100%. In all cases, you must report figures using the proper number of significant figures.
Conclusion
Before closing, let’s summarise all we’ve read into 3 points:
Percent error refers to an error in the ratio between the estimate when compared against the value. It is expressed in the form of a percentage.
Percent Error = x 100
Percent errors show how big our mistakes are when we are measuring the accuracy of something. The conclusion is that calculating a percent error is to assess the degree of accuracy a given value is to the true value. In some areas, percent error is expressed in positive numbers. In other fields, it’s appropriate to use either the negative or positive number.
