Measurement Errors

Measurements play an important role in scientific experiments, research and physical measurements. While measuring, errors are unavoidable. No measurement is perfectly accurate. This leads to deviation from the true value. Understanding, analysing and minimising errors helps improve the accuracy and reliability of results.

Error

Error is the difference between the measured value and the true (or accepted) value. Since the true value is often unknown, repeated measurements are used to estimate it. Errors can arise due to limitations in instruments, human observation, or environmental factors.

Types of Error

Errors are generally categorised into three categories according to their origin.

Systematic Error

This error is caused by a faulty instrument or method. It can be further sub-grouped:

Instrument Error: This error arises due to a construction and calibration issue of the instrument. There could also be zero error in the instrument.
Observation Error: This error arises due to improper setup of the apparatus, parallax error or carelessness in measuring the readings.
Environmental Error: This error is due to the environment conditions affecting the measurements, like temperature, pressure, humidity or air resistance.

Random Error

These errors vary as they occur irregularly and unpredictably; therefore, they are called random errors. For example, fluctuation in the voltage supply

Gross Error

This error includes the mistakes made by humans while doing the measurements, like recording data incorrectly, using the wrong instruments, or misreading scales. These are generally large errors.

Error Calculation

The common ones are:

Absolute Error

Absolute error is the difference between the measured value and the true value. It is always positive.

Formula: Absolute Error = Measured Value - True Value

Percentage Error

Percentage error expresses the relative error in percentage form.

Formula:

Formula

Combination of Errors

When a result is calculated from two or more measured quantities, the errors in those measurements also combine. The rules for the combination of errors depend on the mathematical operation involved (addition, subtraction, multiplication, division, or powers).

Addition and subtraction:

If Q = A B then,

ΔQ = ΔA + ΔB

Multiplication or Division:

Formula

Power Rule:

If Q = Aⁿ then,

Formula

Reducing Errors

errors cannot be eliminated, but they can be minimised by:

Using instruments with higher precision
Avoiding parallax by taking readings at eye level
Calibrating instruments properly
Repeating measurements and taking the average
Performing experiments in controlled environments

Summing Up

Measurement errors are unavoidable and are caused by faulty instruments, human mistakes, or environmental conditions. Error is the difference between the measured and true values. They are categorised as systematic, random, or gross errors. Errors can be calculated as absolute, relative, or percentage. Errors can't be eliminated, but using precise instruments, proper calibration, repeated measurements, and careful observation, errors can be reduced, and more accurate measurements can be taken.