How to Calculate Percent Error (Formula + Examples)

Percent error compares a measured or estimated value with a known true value. Use percent error = |measured − true| ÷ |true| × 100. The absolute value makes the result positive, and dividing by the true value puts the miss on a percentage scale.

For adjacent percentage work, use the percentage calculator to check percent-of, percent-change, and reverse-percent problems.

What percent error measures

Percent error answers one practical question: how far was your result from the accepted value, relative to the accepted value itself? The raw difference tells you the size of the miss. The percent error tells you whether that miss is large for the scale of the problem.

The accepted value is the anchor. In a science lab, that might be a published value. In an estimate, it might be the actual measurement you got afterward. The measured value is your observation, estimate, or experimental result.

How to calculate percent error step by step

Use the same order every time. Subtract first, take the absolute value, divide by the true value, then convert the decimal to a percent.

Do not divide by the measured value. Percent error is measured against the answer you should have reached. Changing the denominator changes the meaning of the result.

Worked example

Suppose a measured weight is higher than the accepted weight. The sign of the first subtraction does not matter because the absolute value removes it.

That means the measurement was about fourteen percent above the accepted value. If you subtract in the other order, the raw difference changes sign but the percent error stays the same.

When percent error is useful

Percent error is useful when there is a known correct value. That makes it different from percent difference, where neither value is treated as the official answer.

Science labs use it to compare experimental results with accepted values. A student might measure a density, boiling point, or acceleration and compare it with the expected result. The percent error shows the accuracy of the measurement without hiding the scale.

Estimates use the same math. If you estimate a time, weight, cost, or distance and later learn the true value, percent error tells you how close the estimate was.

Percent error versus percent change

Percent error and percent change look similar because both divide a difference by a reference value. The reference value is what separates them.

Use percent error when one value is accepted as correct. Use percent change when a value moves from old to new. Use percent difference when you are comparing two values without declaring either one the true answer.

Common mistakes

Skipping the absolute value changes the interpretation. Percent error is usually reported as a non-negative amount. A signed version can tell you whether the measurement was high or low, but that is normally called signed error or relative error.

Rounding too early can move the final percent. Keep extra precision through the subtraction and division, then round the final result.

A true value of zero is a special case. The formula divides by the true value, so a true value of zero makes ordinary percent error undefined. Use absolute error or another context-specific metric instead.