In physics, every measurement has some uncertainty. An error is simply the difference between the true value and the measured value of a physical quantity.

Absolute Error

Absolute error is the magnitude of the difference between the individual measurement and the true value. If you measure the length of a table as 10.2 cm, but the actual length is 10.0 cm, the absolute error is |10.2 - 10.0| = 0.2 cm. It tells you exactly how much your measurement deviates from the real value in the units you used.

Relative Error

Relative error helps us understand the importance of an error compared to the size of the measurement. You calculate it by dividing the absolute error by the true value. For our table example, the relative error is 0.2 / 10.0 = 0.02. This value is a ratio and does not have any units, making it perfect for comparing the accuracy of different types of measurements.

Percentage Error

Percentage error is just the relative error expressed as a percentage. You simply multiply the relative error by 100. Using our previous example, 0.02 × 100 = 2%. This provides a very clear picture of how much the measurement is off. A 2% error means that for every 100 units, the measurement is incorrect by 2 units.

Why Errors Matter

• Precision: Understanding errors helps you know how reliable your data is.
• Comparison: It allows you to see which measuring instrument is more accurate.
• Safety: In engineering, knowing the percentage error prevents machines or structures from failing.