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How to calculate percentage error in chemistry, physics and business

How to calculate percentage error

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In order to be able to carry out measurements that are as accurate as possible or to be able to assess the accuracy of measurements that have already been carried out, one must know the causes of measurement errors, the size of such errors and their effects on the accuracy of the result. We outline step by step how to calculate percentage error in chemistry, physics or business.

Overview

Every measurement of a physical quantity is subject to errors for a wide variety of reasons. The reading x of a physical quantity deviates more or less strongly from the actual value of the quantity, called the true value x. In addition, one must know how to indicate the accuracy in the formulation of the result, and in many cases, you need to understand how to calculate percentage error in physics or business, or how to calculate percentage error chemistry solutions, using the steps below. Also read how to find the percentage of something with our step-by-step guide.

What is percentage error ?

Percentage error expresses as a percentage the difference between an approximate or measured value and an exact or known value. It is used in science to indicate the difference between a measured or experimental value and a true or accurate value. Here’s how to calculate percentage error using a sample calculation.

Important points

  • The purpose of a percentage error calculation is to measure how close a measured value is to a true value.
  • The percentage error (percent error) is the difference between an experimental and a theoretical value divided by the theoretical value multiplied by 100 to give a percentage.
  • In some fields, the percentage error is always expressed as a positive number. In other cases it is correct to have either a positive or a negative value. The sign can be retained to determine whether recorded values ​​are consistently above or below expected values.
  • The percentage error is a type of error calculation. Absolute and relative error are two other common calculations. The percentage error is part of a comprehensive error analysis.
  • The key to correctly reporting the percentage error is knowing whether or not to omit the sign (positive or negative) in the calculation and reporting the value using the correct number of significant numbers.

How to calculate percentage error: the formula

The percent error is the difference between a measured or experimental value and an accepted or known value, divided by the known value, multiplied by 100%.

In many applications, the percentage error is always expressed as a positive value. The absolute value of the error is divided by an accepted value and given as a percentage. Also read how to find percentage increase with our step-by-step guide.

accepted value – experimental value \ accepted value x 100%

It is common for chemistry and other sciences to keep a negative value in case one occurs. Whether the mistake is positive or negative is important. For example, you wouldn’t expect a positive percentage error when comparing actual versus theoretical yield from a chemical reaction. If a positive value were calculated, this would indicate possible problems with the procedure or reactions that were not taken into account.

If the sign for an error is retained, the calculation is the experimental or measured value minus the known or theoretical value, divided by the theoretical value and multiplied by 100%.

percentage error = [experimental value – theoretical value] / theoretical value x 100%

How to calculate percentage error: step by step guide

  • Subtract one value from another. The order doesn’t matter if you drop the sign (take the absolute value. Subtract the theoretical value from the experimental value if you keep negative signs. This value is your “error”.
  • Divide the error by the exact or ideal value (not your experimental or measured value). This results in a decimal number.
  • Convert the decimal number to a percentage by multiplying it by 100.
  • Add a percent or percent symbol to report your percentage error value.

Sample calculation for percentage error

You can get an aluminum block in a laboratory . You measure the dimensions of the block and its displacement in a container of known volume of water. You calculate the density of the aluminum block to be 2.68 g / cm 3 . To determine the density of an aluminum block at room temperature and find that they 2.70 g / cm 3 is . Calculate the percentage error of your measurement.

  • Subtract one value from the other:
  • 2.68 – 2.70 = -0.02
  • Depending on what you need, you can discard any negative sign (take the absolute value): 0.02
  • This is the error.
  • Divide the error by the true value: 0.02 / 2.70 = 0.0074074
  • Multiply this value by 100% to get the percentage error:
  • 0.0074074 x 100% = 0.74% (expressed with 2 significant numbers ).

Significant numbers are important in science. Reporting an answer with too many or too few answers can be considered incorrect even if you have properly set up the problem.

Percentage error versus absolute and relative error

The percentage error refers to the absolute error and the relative error . The difference between an experimental and a known value is the absolute error. If you divide this number by the known value, you will get a relative error . The percentage error is the relative error multiplied by 100%. In all cases, give values ​​with the appropriate number of significant digits.

How to calculate percentage error in Excel

Calculate The Percentage Change / Difference Between Two Numbers Using The Formula
As shown in the screenshot below, you need to calculate the percentage change between the new number 94 and the old number 80. The formula = (new_value-old_value) / old_value can help you quickly calculate the percentage change between two numbers. Please follow these steps.

  1. Select a blank cell to find the calculated percentage change, then type the formula = (A3-A2) / A2 in the formula bar and then press the Enter key. See the screenshot:
  1. Continue selecting the result cell and click the Percent Style button in the Number group under the Style tab to format the cell as a percentage. See the screenshot:

Now the percentage difference between two given numbers is calculated.

How to calculate percentage error – Mean Absolute Percentage Error (MAPE) in Excel

One of the metrics most commonly used for measuring the accuracy of a prediction model is MAPE — the Mean Absolute Percentage Error.

The formula for calculating the MAPE is as follows:

MAPE = (1 / n) * Σ (| actual – forecast | / | actual |) * 100

Where:

Σ – a fancy symbol that means “sum”
n – sample size
Is – the actual data value
Forecast – the forecast data value
MAPE is widely used because it is easy to interpret and explain. For example, a MAPE value of 11.5% means that the average difference between the forecast value and the actual value is 11.5%.

The lower the value for MAPE, the better a model can predict values. For example, a model with a MAPE of 2% is more accurate than a model with a MAPE of 10%.

How to calculate MAPE in Excel

To calculate MAPE in Excel, you can do the following steps:

Step 1: Enter the actual and forecast values ​​in two separate columns.

How to calculate percentage error

Step 2: Calculate the absolute percentage error for each row.

Remember that the absolute percentage error is calculated as follows: | Actual forecast | / | currently | * 100. With this formula we calculate the absolute percentage error for each line.

Column D shows the absolute percentage error and Column E shows the formula we used:

How to calculate percentage error

We will repeat this formula for each row:

How to calculate percentage error

Step 3: Calculate the mean absolute percentage error.

Calculate the MAPE by simply averaging the values ​​in column D:

=MITTELWERT(D2:D13)

How to calculate percentage error

The MAPE of this model is 6.47%.

A note on using MAPE
While MAPE is easy to calculate and easy to interpret, there are a few potential drawbacks to using it:

Since the formula for calculating the absolute percentage error | Actual forecast | reads / | currently | This means that it is undefined if any of the actual values ​​is zero.
MAPE should not be used with low volume data. For example, if the actual demand for an item is 2 and the forecast is 1, the absolute percent error value is | 2-1 | / | 2 | = 50%, which makes it appear that the forecast error is quite high, even though the forecast only deviates by one unit.

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