How is percent error calculated?

• A. Percent error = |experimental − true| / true × 100%
• B. Percent error = (experimental − true)/true × 100%
• C. Percent error = |experimental − true| × 100%
• D. Percent error = (true − experimental)/true × 100%

Answer: (A)

Percent error measures how far your measurement is from the accepted value, shown as a percentage of that true value. To get the size of the error, you take the absolute difference between the experimental value and the true value, which gives a nonnegative magnitude regardless of whether you over- or under-estimated. Then you divide by the true value to normalize the error to the scale of the quantity you're measuring, and multiply by 100% to express it as a percent. This combination—absolute difference divided by the true value, times 100%—is why the correct form uses the absolute value of (experimental minus true) in the numerator and divides by the true value, followed by 100%.

If you drop the absolute value, you can end up with negative percentages for overestimates, which isn’t how percent error is usually reported. If you don’t divide by the true value, you aren’t expressing the error as a fraction of the quantity measured, so the result isn’t a proper percent error.