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# Percent Error Calculator

A percent error calculator is a tool used to calculate the percentage difference between an estimated or measured value and an actual or accepted value. It is commonly used in science experiments or in situations where precise measurements are needed.

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Percent Error = [(|Accepted Value - Measured Value|) / Accepted Value] x 100%

## What is a Percentage Error?

Percentage error is a measure of the difference between an actual or measured value and a known or expected value, expressed as a percentage of the known or expected value. It is commonly used in scientific experiments, where it is important to determine the accuracy and precision of measurements.

The formula for calculating percentage error is:

Percentage error = |(measured value – expected value) / expected value| x 100%

where “|” indicates absolute value. The result is expressed as a percentage.

For example, suppose you are conducting an experiment to measure the density of a substance, and the expected value of the density is 2.5 g/cm³. If your measured value is 2.4 g/cm³, the percentage error would be:

| (2.4 – 2.5) / 2.5 | x 100% = 4%

This means that the measured value is 4% lower than the expected value. A positive percentage error would indicate that the measured value is higher than the expected value.

Percentage error can be used to determine the accuracy of a measurement. A low percentage error indicates that the measured value is close to the expected value, while a high percentage error indicates that the measured value is far from the expected value.

## The formula for calculating percentage error

The formula for calculating percentage error is:

Percentage error = |(measured value – expected value) / expected value| x 100%

where “|” indicates absolute value. The result is expressed as a percentage.

For example, suppose you are conducting an experiment to measure the length of a piece of rope, and the expected length is 10 meters. If your measured value is 9.5 meters, the percentage error would be:

| (9.5 – 10) / 10 | x 100% = 5%

This means that the measured value is 5% lower than the expected value. A positive percentage error would indicate that the measured value is higher than the expected value.

Percentage error can be used to determine the accuracy of a measurement. A low percentage error indicates that the measured value is close to the expected value, while a high percentage error indicates that the measured value is far from the expected value.

## How to calculate Percentage Error

To calculate percentage error, follow these steps:

Step 1: Determine the measured value

Determine the value that was measured in the experiment or observation. This could be a physical quantity such as length, mass, or temperature, or a numerical value such as a percentage or ratio.

Step 2: Determine the expected value

Determine the value that was expected or known beforehand, either from a theoretical calculation or from previous measurements or observations. This is the value that the measured value will be compared to in order to calculate the percentage error.

Step 3: Calculate the difference

Subtract the expected value from the measured value to determine the difference between them.

Step 4: Calculate the absolute value of the difference

Take the absolute value of the difference, ignoring any negative signs.

Step 5: Divide by the expected value

Divide the absolute difference by the expected value.

Step 6: Multiply by 100%

Multiply the quotient by 100% to express the result as a percentage.

The formula for percentage error is:

Percentage error = |(measured value – expected value) / expected value| x 100%

For example, if you measured the weight of an object and obtained a value of 2.3 kg, but the expected or true value was 2.5 kg, the percentage error would be:

| (2.3 – 2.5) / 2.5 | x 100% = 8%

This means that the measured value is 8% lower than the expected value.

## What is percent of Error, standard error and margin of error?

Percentage error, standard error, and margin of error are all statistical measures used to quantify the accuracy and precision of measurements or estimates.

Percentage error is a measure of the difference between an actual or measured value and a known or expected value, expressed as a percentage of the known or expected value. It is calculated using the formula:

Percentage error = |(measured value – expected value) / expected value| x 100%

Standard error is a measure of the variability or spread of a set of data points. It is calculated as the standard deviation of the sample divided by the square root of the sample size. It represents the degree of uncertainty associated with a sample mean or other statistical estimate. A smaller standard error indicates greater precision in the estimate.

Margin of error is a measure of the range of values within which a statistical estimate is likely to fall. It is typically used in the context of surveys or polls, where a sample of individuals is used to estimate the characteristics of a larger population. The margin of error reflects the degree of uncertainty associated with the estimate due to sampling variability. It is calculated as a function of the sample size and the level of confidence desired. A larger margin of error indicates greater uncertainty in the estimate.

In summary, percentage error is a measure of the accuracy of a single measurement or estimate, while standard error and margin of error are measures of the precision and uncertainty, respectively, associated with a sample mean or statistical estimate.