Error

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.

Percentage Error

Then find the Percentage Error:
Show the error as a percent of the exact value, so divide by the exact value and make it a percentage:

Example continued: 65/325 = 0.2 = 20%

Percentage Error is all about comparing a guess or estimate to an exact value. See percentage change, difference and error for other options.

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How to Calculate Percent Error

Percent error is also known as approximation error. It equals the absolute value of the experimental value minus the theoretical value, divided by the theoretical value, multiplied by 100.

1. Subtract theoretical value from experimental value
2. Take the absolute value of the result
3. Divide that by the theoretical value
4. Multiply by 100 to get a percentage

In terms of experimental and theoretical values the percent error formula is:

You may notice that this formula is similar to the way you would calculate percent change as in our Percentage Change Calculator.

Absolute Error Formula

The absolute error is the absolute value of the difference between measured and true values. If your scale weighs something as 1.2 pounds but the actual value is 1.5 pounds your scale is off by 0.3 pounds. The absolute error is 0.3 pounds.

Relative Error Formula

The relative error is the absolute error relative to what the true value should be. If your scale is off by 0.3 pounds and the true value is 1.5 pounds, the relative error is 0.3 / 1.5 = 0.2.

Notes on the Percent Error Calculations

The Theoretical value in chemistry, physics or science experimentation in general, is the established ideal value you would expect as a result of an experiment. Other terms you may see to represent this value are accepted, actual, expected, exact and true. This value is in the denominator of the percent error equation.

The Experimental value is the observed result of an experiment. Other terms you may see to represent this value are measured, observed, estimated and approximate.

In the numerator of the error formula you are calculating the absolute difference between the experimental value and the theoretical value or the absolute distance between the two values on a number line. The order of the values does not matter because you are taking the absolute value.

If you encounter percent error formulas that are somewhat different from the formulas here, note the alternate terms above and remember that | a — b | = | b — a |.

Experimental Value Formula

Use the percent error formula to solve for E, the experimental or observed value. In this equation P stands for percent error. Note there are two possible solutions.

Theoretical Value Formula

You can use the experimental error formula derived above to solve for T. Here again P stands for percent error. Note there are two possible solutions.

Percent Error Calculation Example

Suppose you did an experiment to measure the boiling point of water and your average result is 101.5°C. This is your experimental or measured value. Since the actual boiling point of water is 100°C this would be your theoretical value.

You want to find the % error of the average boiling point of water in your experiment, 101.5°C relative to 100°C.

Plug your numbers into the percent error formula:

So your experimental boiling point has 1.5 percent error compared to the theoretical boiling point of water.

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.

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Источники:

https://www.mathsisfun.com/numbers/percentage-error.html&rut=a415f2d0580cb05718ca62aa6be2f3022c49ee4fe9b941c0f4b9085915b6d660
https://www.thefreedictionary.com/errored&rut=4f61683c2bbb23eaa8d12fbd7febb2dfbad93fa0b02c2e80aefa6a1bd4e78f7d
https://support.microsoft.com/en-us/topic/error-codes-in-device-manager-in-windows-524e9e89-4dee-8883-0afa-6bca0456324e&rut=520d1a4719cd7be4f0e2ab8b8a2771efeb7bac4f97b318ddfb99731ed778667b
https://www.calculatorsoup.com/calculators/algebra/percent-error-calculator.php&rut=0c9603f46e5affe1418e24ae2ac4a444d4c0d4dcd8924c842b9a70fc80c153a5
https://www.calculator.net/percent-error-calculator.html&rut=b5f1dd286f740fd9a3ed4bde1952fba251a8ecab54bbe9f97f24bae3c54bd99c
https://www.britannica.com/science/error-mathematics&rut=eadd59bc1cca280dc78667e8bdc9111ec4e22b32a6744322441d6fb4c54ee8dc