Percentage Error — Definition, Formula & Examples

Percentage error is a way to describe how far off a measured or estimated value is from the exact (true) value, written as a percentage. A smaller percentage error means your measurement or estimate was more accurate.

Percentage error is the absolute difference between an experimental (or approximate) value and a known true value, divided by the true value, then multiplied by 100%.

Key Formula

\text{Percentage Error} = \frac{|V_A - V_E|}{|V_E|} \times 100\%

Where:

$V_A$ = The approximate (measured or estimated) value
$V_E$ = The exact (true or accepted) value

Worked Example

Problem: You estimate the length of a table to be 150 cm, but the actual length is 160 cm. What is the percentage error?

Find the absolute error: Subtract the exact value from the approximate value and take the absolute value.

|150 - 160| = 10 \text{ cm}

Divide by the exact value: Divide the absolute error by the true value.

\frac{10}{160} = 0.0625

Convert to a percentage: Multiply by 100% to express it as a percentage.

0.0625 \times 100\% = 6.25\%

Answer: The percentage error is 6.25%.

Why It Matters

Percentage error shows up in science labs whenever you compare an experimental result to a known value — for example, measuring the boiling point of water or the density of a material. It also matters in everyday tasks like estimating costs or distances, where knowing how far off you were (in relative terms) is more useful than just knowing the raw difference.

Common Mistakes

Mistake: Dividing by the approximate value instead of the true value.

Correction: Always divide the absolute error by the exact (true) value. The true value is your reference point for judging how large the error is.