What is Percent Error?

In simple terms, percent error is a measurement of how inaccurate a guess or experimental value is compared to the true, accepted value. It expresses that difference as a percentage.

Nobody is perfect, and no measuring device is flawless. There will almost always be a discrepancy between what you expect to happen (the theoretical value) and what actually happens (the experimental value). Calculating the percent error gives you a standardized way to determine if that discrepancy is acceptable or if you need to recalibrate your approach.

The Percent Error Formula

To calculate the percentage error manually, you need to find the absolute difference between your experimental and theoretical values, divide that by the theoretical value, and multiply by 100.

Here is the formula you can use:

Key Definitions for the Formula:

• Experimental Value (Observed): The number you actually measured, guessed, or observed in your test.
• Theoretical Value (True/Exact): The universally accepted, known, or target number.
• Absolute Value bars ( | | ): These indicate that we ignore negative signs. We usually only care about how large the error is, not the direction.

How to Calculate Percent Error

Let’s say you are hosting an event. You estimate that 150 people will show up (Experimental Value). However, when you count the tickets at the door, exactly 200 people attend (Theoretical Value).

How far off was your guess?

1. Subtract the theoretical value from the experimental value: 150 – 200 = -50
2. Take the absolute value to remove the negative sign: |-50| = 50 (This is your Absolute Error).
3. Divide that difference by the exact theoretical value: 50 / 200 = 0.25 (This is your Relative Error).
4. Multiply by 100 to convert to a percentage: 0.25 x 100 = 25%

Your estimate had a 25% error rate.

Absolute Error vs. Relative Error vs. Percent Error

People often confuse these three terms, but they represent different stages of the same math equation:

• Absolute Error is simply the raw difference between the two numbers. If you guessed a car cost $10,000 and it actually cost $12,000, your absolute error is $2,000. It doesn’t tell you the scale of the mistake.
• Relative Error compares the absolute error to the size of the true value, represented as a decimal.
• Percent Error is just the relative error multiplied by 100 to make it easier to read and understand at a glance.

Can Percent Error Be Negative?

Usually, no. In most basic math and science applications, we use the absolute value because the goal is to measure the magnitude of the error. A 5% error is a 5% error, regardless of whether your measurement was too heavy or too light.

However, in certain fields like advanced chemistry or engineering, the direction of the error matters. If a speedometer reads consistently lower than the actual speed, keeping the negative sign tells the engineers exactly how to calibrate the instrument. If your professor or industry requires directional error, simply remove the absolute value bars from the formula above.

Why We Use It

Raw numbers lack context. Being “off by 5” means nothing until you know the target. If you are off by 5 feet when driving across the country, your accuracy is incredible. If you are off by 5 feet while parallel parking, you’ve crashed. Percent error scales your mistake to the size of the target, instantly providing the necessary context to determine if your results are viable.

FAQs

Q1. What is a “good” or acceptable percent error?

A: There is no single rule, as acceptable error margins depend entirely on your field. In a high school chemistry lab, an error rate between 5% and 10% is generally considered successful. However, in highly precise industries like aerospace manufacturing or pharmacology, the acceptable percent error is often strictly controlled to less than 1% or even 0.1%.

Q2. How do I calculate the theoretical value if I only have the percent error?

A: You can mathematically rearrange the standard formula, or you can simply use the calculator at the top of this page. Because I built this tool to work in reverse, just enter your experimental value and your percent error, and it will instantly calculate the exact theoretical value for you.

Q3. Is percent error the same as percent difference?

A: No, they are used for different scenarios. Percent error is used when you are comparing your test result to a known, universally accepted “true” value. Percent difference is used when you are comparing two experimental results against each other, and neither number is guaranteed to be the exact correct answer.

Q4. Can a percent error be over 100%?

A: Yes, absolutely. A percent error will exceed 100% if your experimental measurement is more than double the theoretical value, or if you guess a number that is drastically higher than a very small true value. For example, if you estimate a weight to be 50 grams, but the true weight is only 15 grams, your percent error is roughly 233%.

Sources: Calculator.net, CalculatorSoup, Pearson, Symbolab,, Omni Calculator, Statistics By Jim, Crystal Instruments, Inch Calculator.