Percent Error Calculator

Results

Percent error is always relative to the accepted value. To compare two of your own trials, switch to percent difference.

How to Use the Percent Error Calculator

1. 1. Pick the comparison. Choose percent error when one value is known to be right — a textbook constant, a manufacturer's specification, a theoretical prediction. Choose percent difference when you are comparing two of your own results and neither is the reference.
2. 2. Enter the values. Type the experimental value and the accepted value (or both measurements). Add a unit if you want it carried into the sentence; it does not change the arithmetic.
3. 3. Decide on the sign and the rounding. Leave the sign off for the usual absolute percent error, or keep it to show whether your measurement came out high (+) or low (−). Choose how many decimal places the percentage should carry.
4. 4. Check the working and copy the sentence. Every intermediate value is shown, so you can match it line by line against your own calculation before you paste the sentence into your report.

The Percent Error Formula

Percent error measures how far a measurement lands from the value it should have produced, as a share of that value:

percent error = |E − A| / |A| × 100%

signed percent error = (E − A) / |A| × 100%

Here E is the experimental (measured) value and A is the accepted value — also called the true, theoretical or literature value. The numerator, |E − A|, is the absolute error: the size of the miss in the measurement's own units. Dividing by |A| turns it into the relative error, a pure number, and multiplying by 100 expresses that as a percentage. Because the units cancel, a percent error lets you compare the accuracy of a length measurement with the accuracy of a mass measurement.

Most courses report the absolute value, so percent error is never negative. Some — chemistry courses especially — keep the sign instead: a negative result means the measurement was too low, a positive one too high — useful when you are explaining a systematic error such as heat lost to the surroundings or product lost during filtration. Check which convention your lab manual uses; the calculator does both.

Worked Example: Measuring g With a Pendulum

A student times a pendulum and calculates the acceleration due to gravity as 9.68 m/s². The accepted value is 9.81 m/s². These are the calculator's default inputs, and its working reads:

1. Absolute error: |9.68 − 9.81| = 0.13 m/s².
2. Relative error: 0.13 / 9.81 = 0.0132518.
3. Percent error: 0.0132518 × 100 = 1.33% (to two decimal places). With the sign kept, it is −1.33%: the measurement came out low.

The sentence the calculator writes is: “The experimental value (9.68 m/s²) was 0.13 m/s² lower than the accepted value (9.81 m/s²), a percent error of 1.33%.” Note that the relative error is carried at full precision into the last step — rounding it to 0.013 first would give 1.30% instead.

Percent Error, Percent Difference and Percent Change

Percent difference divides by the average of the two values, so swapping them gives the same answer and the result can never exceed 200%. With two pendulum timings of 12.4 s and 12.9 s, the difference is 0.5 s, the average is 12.65 s, and the percent difference is 0.5 / 12.65 × 100 = 3.95%. Percent change is a different question again — growth or decline over time — and the Percentage Calculator handles it.

Common Mistakes

• Dividing by the experimental value. The accepted value goes in the denominator. Dividing by your own measurement gives a slightly different number and is simply wrong for percent error.
• Forgetting the absolute value. If your course reports unsigned percent error, a negative answer means the bars were dropped from |E − A|.
• Rounding too early. Keep every digit of the relative error until the final step, then round once.
• Reporting false precision. A percent error quoted as 1.325178% implies far more certainty than a school-lab measurement supports. Two or three significant figures is the norm; the Significant Figures Calculator will round it for you.
• Using percent error with no true value. Comparing trial 1 with trial 2 calls for percent difference, not percent error.

Frequently Asked Questions

How do you calculate percent error?

Subtract the accepted value from the experimental value, take the absolute value, divide by the absolute value of the accepted value, and multiply by 100. For a measured 9.68 m/s² against an accepted 9.81 m/s², that is 0.13 / 9.81 × 100 = 1.33%.

Can percent error be negative?

Only in the signed convention. The usual formula takes the absolute value, so percent error is zero or positive. Some chemistry courses drop the absolute value on purpose so that the sign shows the direction of the error: negative when the measurement is below the accepted value, positive when it is above.

What is a good percent error?

There is no universal cut-off. Introductory labs often treat anything under about 5% as good and under 10% as acceptable, but the honest test is whether the accepted value falls within your measurement's uncertainty. A 0.5% error can still signal a problem if your measurement was precise to 0.1%.

What is the difference between percent error and percent difference?

Percent error compares a measurement with a reference that is assumed correct, so the reference is the denominator. Percent difference compares two values on equal terms, so their average is the denominator. Use percent difference for two trials, two students' results or two methods when neither is known to be right.

Why is percent error undefined when the accepted value is zero?

The formula divides by the accepted value, and division by zero has no answer. When the true value is zero — a balanced force, a null reading — report the absolute error, |E − A|, in the measurement's units instead.

How many decimal places should percent error have?

Match the precision of your data: two or three significant figures is typical, such as 1.33% or 4.8%. Calculate with full precision and round only the final percentage.