Measurement Error — Definition, Formula & Examples

Measurement error is the difference between the value you get when you measure something and the actual (true) value. Every measurement tool and every person using it introduces some amount of error, so no measurement is perfectly exact.

Measurement error is the signed or absolute deviation of an observed measurement from the true or accepted value of the quantity being measured, expressed as $\text{Error} = \text{Measured Value} - \text{True Value}$ .

Key Formula

\text{Error} = x_{\text{measured}} - x_{\text{true}}

Where:

$x_{\text{measured}}$ = The value obtained from your measurement
$x_{\text{true}}$ = The actual or accepted value of the quantity

How It Works

To find the measurement error, subtract the true value from your measured value. A positive result means you measured too high, and a negative result means you measured too low. You can also report the absolute error by dropping the sign, which tells you how far off you were regardless of direction. Percent error goes one step further by expressing the absolute error as a percentage of the true value, making it easier to judge how significant the error is.

Worked Example

Problem: A student measures the length of a table and gets 152 cm. The actual length is 150 cm. Find the measurement error, the absolute error, and the percent error.

Find the measurement error: Subtract the true value from the measured value.

\text{Error} = 152 - 150 = 2 \text{ cm}

Find the absolute error: Take the absolute value of the error.

|\text{Error}| = |2| = 2 \text{ cm}

Find the percent error: Divide the absolute error by the true value and multiply by 100.

\text{Percent Error} = \frac{2}{150} \times 100 \approx 1.33\%

Answer: The measurement error is +2 cm (measured too high), the absolute error is 2 cm, and the percent error is approximately 1.33%.

Why It Matters

In science labs, you compare your experimental results to known values using measurement error and percent error. Careers in engineering, medicine, and construction depend on keeping measurement errors within strict tolerances — a small error in a bridge measurement or a medicine dosage can have serious consequences.

Common Mistakes

Mistake: Dividing by the measured value instead of the true value when calculating percent error.

Correction: Always divide the absolute error by the true (accepted) value:

\frac{|\text{Error}|}{x_{\text{true}}} \times 100