How to Calculate Percent Error – Formula + Real Examples

Have you ever tried to follow a recipe, only for it to turn out slightly off? Maybe your cookies spread out too much, or your sauce might have been a little too thin. Or maybe you are in a science lab aiming for a precise result, but your findings appear to be a little different from what you had initially expected. This “off” or “different” outcome is a result of an ‘error.’ When it comes to developing an understanding of the error and how great or small the error is, ‘percent error’ is the best tool to do so. In this blog, you will learn how to calculate percent error, what percent error is, and what are some common percentage error examples.

What Is Percent Error?

The term percent error refers to a method that quantifies the deviation between the actual value of an experiment and its true or accepted value. In simple terms, it measures the level of “off” or “difference” that we discussed earlier. Usually, when conducting an experiment, you look for a specific outcome. This outcome, known as either the theoretical or accepted value, is what serves as the standard for comparison.

Because of many reasons, including but not limited to human error, instrument limitations, or environmental conditions, your experimental values might end up differing from the accepted value. Percentage error is not just used to measure the raw numerical value that results from this deviation, but the percentage of the accepted value that was achieved.

Percent error has different implications for different experiments. A 1-gram discrepancy in a kilogram of sugar is nothing to be worried about; however, a 1-gram mistake while conducting a chemical experiment can be disastrous. Percent error puts these deviations into perspective, telling you the relative accuracy of your experiment.

Percent Error Formula

Understanding how to calculate percent error is easy once you break down its components. This formula provides a standardized way to observe the differences between what you observed and what you expected in the form of a percentage.

Percent Error  ×100%

Let us look at each of the elements of this equation: -

Experimental Value: -

This is the result you obtained from the experiment; it is the actual result of your findings.

Accepted Value: -

This is the true, theoretical, and standard value. It is the value that should have been obtained. This value is typically established through highly accurate measurements, published data, or scholarly consensus.

Absolute Value Bars (|...|): -

The absolute value ensures that your percent error is always a positive value. Whether your value is too high or too low, it doesn’t matter; what matters is the magnitude of difference between accepted values and experimental values.

Multiplication by 100: -

This step converts the decimal ratio into a more easily understandable percentage.

How To Calculate Percent Error Step-by-Step

There is a simple method on how to find out percent error step-by-step. You need to follow these four steps, and it will be easy to calculate the percent error at the tips of your fingers: 

Step 1) Find the Difference: -

First, you need to subtract the accepted value from your experimental value.

Step 2) Take the Absolute Value: -

Then you have to make the value positive; if there is already a positive value at hand, then there is no need to remove the minus sign.

Step 3) Divide by the Accepted Value: -

Now you have to divide the absolute difference by the accepted value.

Step 4) Convert to Percentage: -

Lastly, multiply the result by 100 and obtain the percentage error.

Real-Life Example of Percent Error

Let us think out of the box. Percent error is not just used for scientific research; it can be observed in multiple everyday situations and is unknowingly used by people who aren’t exactly researchers. Let us look at the multiple different instances of percent error being used in real life and see which real-life example of percent error you have noticed in your everyday life: -

Following a Recipe in the Kitchen: -

While trying to bake a cake, maybe you add too much water to the flour, and it ends up becoming unsuitable for baking. This percentage error is quite common because of the high porosity of flour. Want to know ‘what is porosity?’ Then check out another blog of ours.

Manufacturing and Quality Control: -

In industries like automotive, electronics, or aerospace, parts must meet extreme specifications. Even a tiny deviation can lead to malfunctions or safety issues.

Financial Projections and Budgeting: -

Businesses and individuals often make financial forecasts, but actual spending or revenue rarely matches projections perfectly.

Sports Performance: -

 Even in sports, where athletes aim for peak performance, percent error can be a useful tool to analyze how far off a new attempt is from a personal best or a world record.

Common Mistakes to Avoid

While calculating percentage error, there are a few common mistakes you need to avoid. If you are having trouble with percent error, you can get assignment help from us. These are some of the common mistakes you should avoid: -

Forgetting the Absolute Value: -

This is perhaps the most common mistake. Always perform the subtraction first, then ensure the result is positive before proceeding with the division.

Swapping Experimental and Accepted Values: -

While the numerator's subtraction uses the absolute value, the denominator must be the accepted value.

Calculation Errors: -

Even with the perfect figures and formula, a minor mistake can throw off the findings and cause yet another error.

Ignoring or being inconsistent with Units: -

Although units cancel out in the division stage, thinking about them helps prevent errors and helps avoid misunderstanding.

When is a Percent Error Acceptable?

It is tricky to determine when exactly a percent error is considered acceptable. The correct answer would be that it depends. A percent error can be negligible or not particularly noteworthy in one instance, but in other instances, it can have catastrophic consequences. For high school science experiments, a percent error in physics lab of 5% to 10% is generally acceptable. In specialized university programs, your experiments are not supposed to have a percent error greater than 1% to 2%.

On the other hand, when it comes to precise manufacturing or engineering concerned with maximum safety products/services (for example: medical supplies, aviation, etc.), the percent error is supposed to be less than 0.001%. In construction, percent error tends to vary between 1% and 5% and so on.

Percentage Error vs Percentage Difference

The terms ‘percentage error’ and ‘percentage difference’ sound similar to a lot of people; however, they are not. Let us look at the differences between the two terms.

Conclusion

We hope that you have learned a lot about percentage errors, how to calculate percent errors, and how to apply them in real-life situations. If you are still not clear or you need help with an assignment that requires you to utilize the percentage error formula, then feel free to contact Do My Assignment to get homework/assignment help with just about anything.