The percent error calculator formula

In quantitative science, a percent error calculator is the online statistics tool (for data analysis), which is used to compare two quantities while taking into account their sizes. When the difference between the two quantities is multiplied by 100 in the calculator, it becomes a percentage. Error found by this tool is used as a quantitative indicator of quality control and quality assurance for measurements whose outcome is expected to be the same. The percent error found by this instrument occurs when in a situation where the value of a reference is the actual value and value that is compared to it is determined experimentally. This instrument calculates the percentage of how inaccurate a measurement is standardized to how big your measurement is.

The formula is {(estimated value-actual value)/actual value}*100%. The percent error calculator formula determines how close your estimation is. Some of the causes of error include:

  • The impression of your equipment
  • A mistake in your experiment
  • Poor estimation

The first question you will ask yourself is how much you missed by which is what you g from subtracting the actual value from estimated value. In most applications, percentage error is expressed as a positive value. The percent error calculator divides the error’s absolute value by an accepted value and gives the answer in a percentage form. In chemistry and other sciences, it is a custom to keep a negative value. Whether the results gotten by this calculator is negative or positive, it is very important. For example, you cannot have a positive percent error when comparing actual to theoretical results of a chemical reaction.

How to calculate the percentage error

In using a percent error calculator, a negative value is a decrease in the percentage change while a positive value is an increase in the percentage change. If a calculator gets a negative value, the negative sign is ignored unless you want to determine if the error is over or under the actual value. This calculator also ignores the negative sign in the percentage difference because neither value is more important, so being below or above, does not make any sense.

Using this method in calculating error allows you to compare the estimated value to an actual value. To find the percentage error you first need to know the actual value and the approximate value. With the percent error calculator formula, you will calculate the absolute value of the approximate value and actual value difference. If the actual value is 9 and the estimated value is 10, you will subtract 10 from 9 to get negative 1. You will then divide -1 by 10 to get -0.1. The next step in the percent error calculator formula is to get the absolute value of the result. The absolute value of any number is the value of a positive value of that number whether it is negative or positive. For a number that is positive, its absolute value remains to be that number and the absolute value of a negative number is simply that number without including the negative sign. So the negative 0.1 above becomes positive 0.1. The last step is to multiply 0.1 by 100%. This will convert your answer into percentage. The answer will be 0.1*100=10%.

The difference between two values in a percent error calculator is used when you are interested in knowing how much you missed by and not how high or how low your value is. Other examples are 100.0 (estimated) and 105.3 (actual), 10.0 (estimated) and 15.3 (actual), 1.0 (estimated) and 6.3 (actual) and 0.1 (estimated) and 5.4 (actual). In all these examples, the difference between the actual and the estimated value is 5.3 but in the first example 100.0 (estimated) and 105.3 (actual), the guess seems a lot better. Even though the difference is the same value as the one for the last example which is 0.1 (estimated) and 5.4 (actual), missing by 5.3 out of 105.3 is not bad as missing by 5.3 out of 5.4. This simply means that the formula is concerned not only on how much you missed by but with what percentage of the actual value you missed by. This is the reason why formula divides the difference by the actual value. In the first example, 5.3/105.3 * 100% will be equal to 0.0503 * 100% which will be 5.03%. In the last example, you missed by 5.3 out of a total of 5.4:5.3/5.4 * 100% is equal to.9815 * 100% which is 98.15%. This is how to demonstrate that missing by 5.3 out of 105.3 is a good guess, but missing by 5.3 out of 5.4 is a bad guess. If the calculators gets a small percent error, then it means that the estimated value is very close to the actual value but a large percent error will mean that there is something wrong with your equipment or experiment.

Percentage error word problems

This instrument is used to find percentage change when comparing a new and an old value. It is used to calculate percentage error in comparing an estimated value to an actual value. It's also used to calculate the percentage difference when you have two values that imply the same thing where one value is not better or older than the other value. An example of a problem solved by this kind of tool is if you make a mistake while measuring the volume of something. Let’s say you get 65 liters but the actual value is 50 liters. To find the percentage error with a calculator, the amount of error is divided by the actual value. The amount of error is 65-50 =15. The percentage error will be 15/50 multiplied by 100%. The simplified form of 15/50 is 3/10 and when multiplied by 100 you will get 30%. In this solution, if the actual value was 65 and the approximate was 50, then you will still find the amount of error with a percent error calculator and your answer will remain positive as stated earlier. However, you must be careful. Since the actual value is 65 it means that the percent error calculator will find 15/65 is equal to 0.2307. Then 0.2307/1 = (0.2307 × 100)/(1 × 100) = 23.07/100. The final answer will be 23.07%.

Another word problem that can be calculated is an astronomer observes that the periods of satellites of Jupiter fluctuated depending on the distance of Jupiter from earth. When Jupiter was so far away, the satellite took too long to appear. He later on determined that this phenomenon was due to the fact that the light speed is infinite and subsequently approximated its velocity to be 220,000 km/s. The current actual value of the speed of light is 299,800 km/s. To get the percentage error of the astronomer’s approximate value, the percent error calculator will calculate 220,000 km/s = 2.2 x 108 m/s, theoretical value = 299,800 km/s 2.998 x 108 m/s. {(2.2 x 108 m/s-2.998 x 108 m/s)/ 2.998 x 108 m/s}100%. The final answer will be 26.62%.

Another example that is solved using the percent error calculator is: A multimeter is tested and its true voltage is 220V but the estimated voltage is 224V. To find the actual and the percentage error with a calculator, Actual Error = Measured Voltage -True Voltage which is 220 - 224 V. The actual error is negative 4V. The percentage error is 4/224*100% which is equal to 1.8%. If another multimeter is tested and the true voltage is 150V but the estimated voltage is 153V. The actual error and the percentage error will be 153V-150V=3V. Percentage error is 3/150*100%=2%. This second multimeter is slightly less accurate than the first one which had an accuracy of 1.8%.

This tool is used in measurement because the measuring instruments are not exact. If an estimated height is 6 feet where the actual height is 5 feet, then the percentage error will be 6-5=1, 1/5 will be converted to a percentage by multiplying by 100%. The percentage error will be 20%. Another example of solution is measuring the height of a plant to the nearest centimeter and you get 80cm. This means the error can be up to 0.5cm in that the plant could be 79.5cm or 80.5cm. Your percent error will be 0.5/80*100%. Since the actual value is not known, the percent error calculator will divide the absolute value of the difference by the measured value. The answer will be 0.625%. This tool can also calculate the error percentage without an absolute value to give a negative or positive result which is useful to know. Example:if the 20mm of rain is forecasted but 25mm of rain is gotten instead, {(20-25)/25}*100. -1/5*100% = -20%.

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