Errors in Measurement (Physics)

In physics, error does NOT mean mistake.
It means:

The difference between the measured value and the true value.

Since no instrument is perfect, every measurement has some error.

🔎 Types of Errors

There are three main types:

1️⃣ Systematic Error

This error happens in the same direction every time.

Causes:

• Faulty instrument

• Wrong calibration

• Zero error in instruments

Example:

If a scale shows +0.5 kg even when empty, all measurements will be 0.5 kg extra.

👉 These errors can often be corrected.

2️⃣ Random Error

This happens due to unpredictable changes.

Causes:

• Human reaction time

• Slight environmental changes

• Small observational variations

Example:
If you measure length 5 times and get:

• 10.1 cm

• 10.3 cm

• 10.2 cm

• 10.4 cm

• 10.2 cm

The small differences are random errors.

👉 Reduced by taking the average of many readings.

3️⃣ Gross Error (Human Mistake)

This happens due to carelessness.

Examples:

• Reading the wrong scale

• Writing 12 instead of 21

• Using wrong units

👉 Avoided by being careful.

📐 Important Terms

Absolute Error

Absolute Error=∣Measured Value−True Value∣\text{Absolute Error} = | \text{Measured Value} - \text{True Value} |Absolute Error=∣Measured Value−True Value∣

It tells how much the value differs.

Relative Error

Relative Error=Absolute ErrorTrue Value\text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}}Relative Error=True ValueAbsolute Error

It shows how large the error is compared to the true value.

Percentage Error

Percentage Error=Relative Error×100\text{Percentage Error} = \text{Relative Error} \times 100Percentage Error=Relative Error×100

🎯 Why Errors Matter

Physics depends on accuracy. Even famous scientists like
Isaac Newton
and
Galileo Galilei
had to carefully reduce experimental errors to get correct laws.

💡 Simple Summary