# Percent Error Formula

## Introduction to Percent Error Formula

Whenever the measuring products are manufactured, it is not feasible for them to be completely accurate. Oftentimes, there is a slight manufacturing error that causes errors in the values. You can never consider that the values you get are exact.

## Error Formula

To know the level and percentage of error in the measuring instruments, you can use the error formula. It is a useful tool to determine the precision of your calculations. But, before understanding how to find error, let us define percentage error and a few other basic things.

### Accuracy:

It is defined as the extent to which the measured value is close to the exact value of the measurement quantity. Accuracy usually occurs due to calibration, errors in designing, or even human errors.

### Precision:

It is defined as the degree of exactness of an instrument. Precision errors usually occur due to measuring instruments.

### Error:

The result obtained through every measurement using the measuring instruments contains some levels of uncertainty, which is defined as errors. There are several types of errors in measurement. One of them is the percentage error.

### What is the Percentage Error?

To define a percentage error, it is expressed as the difference between the exact and measured values of an instrument. It is used to determine the closeness of the measured value to the exact value. For example, if there is a 2% error in the value, it means it is quite close to the exact value. However, a 60% error means that the measuring instrument has some major errors.

It is also defined as the relative error in a measuring instrument multiplied by 100.

### How to Calculate Percent Error?

The error calculation formula consists of the difference between the measured and exact value divided by the exact value, further multiplied by 100 to obtain the percentage value. Many times, during the application, the percentage error is positive. Now let us see how to calculate percent error.

The Percent Error formula is given by:

Absolute difference = Exact value - Experimental value

Percent error= (Absolute difference/Exact value)*100

Once you know how to find a percent error, you can calculate it easily and incorporate the error percentage in your experiments to get the correct values. This allows you to get your experiments done correctly.

### Steps on How to Calculate Error:

1. Note the values, and subtract one value from the other. Here, it does not matter in which order the values are being calculated.

2. Divide the error value with the theoretical value.

3. The value so obtained is in the form of decimals. Convert it into a percentage by multiplying it by 100, to obtain the percentage.

### Conclusion:

Once you know how to find an error, you can easily conduct your experiments and avoid any mistakes in finding the values accurately. So, go ahead and perform your experiments.

1. While Taking Down the Measurements, the Scale Measures the Value Wrongly as 12 cm. However, the Actual Measurement is 8 cm. Find the Percentage Error.

Ans: Using the percentage error formula:

Percent error = ({Experimental Value - Actual Value}/Actual Value) * 100

Percent error = ({12 - 8}/8) * 100

= 4/8 * 100 = 50%

Therefore, there is a 50% error in the measuring instrument.

2. What are the Different Types of Errors Observed During Measurements?

Ans: The various types of errors of measurements are listed as follows:

• Systematic errors

• Instrumental errors

• Personal errors

• Random errors

• Least count errors

• Percentage errors

• Absolute errors

• Relative errors