how to calculate percent error [BEST METHOD]

 

What is percentage error?

Percent error is a way of measuring how close an estimate or a measurement is to a correct or accepted value. It is calculated by finding the difference between the estimate and the correct value, dividing it by the correct value, and multiplying by 100 to get a percentage. The formula for percent error is:

$$\text{Percent Error}=\frac{|\text{Estimate}-\text{Correct Value}|}{\text{Correct Value}}\times 100$$

For example, if you measure the length of a table as 120 cm, but the actual length is 125 cm, the percent error is:

$$\text{Percent Error}=\frac{|120-125|}{125}\times 100$$

$$\text{Percent Error}=\frac{5}{125}\times 100$$

$$\text{Percent Error}=0.04\times 100$$

$$\text{Percent Error}=4\%$$

This means that your measurement is 4% lower than the correct value. Percent error can be positive or negative, depending on whether the estimate is higher or lower than the correct value.

Percent error is useful for comparing different measurements or estimates of the same quantity

To calculate percent error, follow this formula:

Percent Error = [(|Measured Value - Actual Value|) / |Actual Value|] × 100

Here's how to use the formula:

1. **Determine the Measured Value**: This is the value you obtained through experimentation, measurement, or observation.

2. **Identify the Actual Value**: The actual or expected value is the value that is generally accepted as accurate or the value you were supposed to measure or obtain.

3. **Find the Absolute Difference**: Subtract the actual value from the measured value, and take the absolute value (ignore the negative sign if it's there).

4. **Divide by the Absolute Value of the Actual Value**: Divide the absolute difference by the absolute value of the actual value. The absolute value ensures that the result is always positive.

5. **Multiply by 100**: To express the error as a percentage, multiply the result from step 4 by 100.

Here's an example to illustrate the calculation:

Suppose you are measuring the density of an object, and the actual (accepted) density is 8.00 g/cm³. You measure the density to be 7.50 g/cm³.

Percent Error = [(|7.50 g/cm³ - 8.00 g/cm³|) / |8.00 g/cm³|] × 100

Percent Error = [(0.50 g/cm³) / 8.00 g/cm³] × 100

Percent Error = (0.0625) × 100

Percent Error = 6.25%

In this example, your measured density is 6.25% less than the accepted density. Percent error is a way to quantify the accuracy of your measurement, indicating how far off your measured value is from the expected value. A percent error of 0% would mean a perfect measurement, while a higher percent error indicates a less accurate measurement.