Error analysis is the study of how and why measurements differ from the true value. In physics, no measurement is ever perfectly exact because every tool has limits and every person makes small mistakes.

Understanding Types of Errors

There are two main types of errors in experiments. Systematic errors happen because of a problem with the measuring device, like a scale that starts at 1 gram instead of 0. These errors pull your results in one specific direction every time. Random errors occur because of unpredictable changes, like a sudden breeze affecting a balance scale. You can reduce random errors by taking multiple readings and calculating their average.

Absolute and Relative Error

Absolute error is the difference between your measured value and the true value. If a stick is actually 10 cm long and you measure 10.2 cm, the absolute error is 0.2 cm. Relative error compares this mistake to the size of the object. It is calculated by dividing the absolute error by the true value. This tells you how significant the mistake is relative to the measurement.

Calculating Percentage Error

Percentage error turns your relative error into a percentage to make it easier to understand. You calculate it using this formula:

• Percentage Error = (Absolute Error / True Value) × 100

If you have a percentage error of 2%, it means your measurement is very close to the truth. If it is 20%, your measurement might not be reliable.

Why Precision and Accuracy Matter

Accuracy is how close your measurement is to the actual, true value. Precision is how close your repeated measurements are to each other. You could measure the same table five times and get 100 cm every time; this is high precision. However, if the table is actually 105 cm, your measurement is not accurate. Good experiments aim for both high accuracy and high precision by using quality tools and careful techniques.