Errors in science and math can happen due to faulty observation or instruments. Knowing the percentage error helps to determine the exactness of the calculations, and how far off the measured value concerns the exact value in a percentage.

The formula for percent error or percentage error is:
% error = [(Approximate Value – Exact Value)/Exact Value] * 100
The approximate value is the estimated or the measured value, and the exact value is the actual or the real value.
Example: If you predict that your football team will score 4 goals and the team scores 3, then the actual value is 3, and the estimated value is 4.

To Calculate the Percentage Error do the Following:

• Find the difference between the exact and the estimated value: In the above example, you will subtract 4 which is the actual number of goals scored with 3 which is the estimated value. The result is 4-3 = 1. This gives you the amount of deviation the result was from what was expected.
  In the above formula, even if the difference in magnitude produced a negative number, take the absolute value. That essentially means that in statistics, it does not matter if the guess was high or low, what is needed is to know how much difference was there in the estimated value from the real value.
• Divide the numerator by the real value: The result that you get after finding the difference of actual and estimated value should be divided by the exact value. In the above example, you divide 1 by 4. The numerator/denominator = ¼. If the numerator was a negative number, you could discard the sign.
• Convert the resultant fraction into a decimal: The easiest method to convert a fraction into a percentage is to convert into decimal. ¼ = 0.25 for the example above. You can either use a calculator for this purpose or do the long division by hand. To round off a number you can go up to 4 or 5 decimal places.
• Multiply the result by 100: To convert the number into a percentage, multiply the result that you get from the above step by 100. In the above example, you have to multiply 0.25 by 100. 0.25 * 100 = 25. Adding the percentage symbol to the result gives the percentage error which is 25%.
  Cross-check the answers you have derived for any calculation errors. To verify if your answer is correct.

Key Points to Know About Percent Error:
1. A percentage error calculation is done to find if the measured value is close to the actual value.
2. The percent error is shown as a positive value, but in some fields, it can be shown either as a positive or negative value. When the absolute of the value is not taken it shows whether the actual value you derived is less or higher than the expected result.
3. It is essential to know when to consider keeping the -ve sign and when to ignore when reporting values.
4. There are other types of error calculations like relative error and absolute error calculation other than percent error.

These are some points to keep in mind while calculating percent error!