The concept of uncertainty in measurement is very complicated due to its close relationship with measurement error. Every measurement is accurate to some extent due to the presence of uncertainty in every measurement. The term uncertainty refers to doubt. In the measurement context, it means an unavoidable error that happens due to the limitations of the measuring instrument.

The Students often find it very difficult to understand the concepts of Uncertainty of measurement. If you are also one of those students then you are at the right site. In this comprehensive article, we are going to explain the uncertainty in measurement in Very detail. All the concepts related to this topic are covered in chapter wise for your better understandings.

## Chapter 1

**Introduction to Uncertainty in Measurements**

## Chapter 3

**Steps to Calculate Uncertainty**

## Chapter 2

**Causing Factors of Uncertainty**

## Chapter 4

**Steps to Overcome Uncertainty**

### Chapter 1

**Introduction To Uncertainty in Measurement**

In this chapter, we will are going to explore an interesting topic ‘uncertainty of measurement’ in a comprehensive way.

**The following points are covered in this chapter:**

- Uncertainty and measurement
- uncertainty in measurement
- Types of uncertainty
- Solved Examples of uncertainty
- Why uncertainty is important in measurement?

Uncertainty in measurement is considered a complicated topic. Students often find it difficult to differentiate between measurement uncertainty and measurement error. After going through this article, the students will be able to distinguish between these two complicated and different concepts because we are exploring uncertainty in measurement in very detail, including its types, solved examples, and steps to calculate uncertainty. For the ease of students, we also created a comprehensive guide to measurement uncertainties available in PDF format. Click on the below download button to get the PDF version of the guide.

Before going into details, let’s briefly discuss the concepts of measurement and uncertainty.

**Measurement and Uncertainty**

Measurement is an essential component for the maintenance of life, while uncertainty refers to the extent of error. Every measurement has some level of uncertainty, hence measurement findings must contain a statement of this uncertainty. These uncertainties may be caused by a number of factors, including the measuring device, the object being measured, and environmental factors. It is essential to estimate these uncertainties using statistical analysis and knowledge of the measuring procedure. Measurement uncertainties can be reduced with the use of sound procedures, including traceable calibration, careful computation, record keeping, and checking.

## Uncertainty in Measurement Definition

Uncertainty of measurement is defined as the magnitude of error or doubt in a measurement. We are never completely sure about the exactness of a measured quantity because of the fact that every measurement contains an error. Uncertainty is an estimate of the possible range of error. It estimates whether the amount of error is small or large. As there is uncertainty in every measurement, therefore every measurement needs to be written in the below form.

Measurement = Best estimate ± Uncertainty

When we are not sure about the exactness of a value then we are sure about a range of exactness known as the uncertainty range. The uncertainty range may be defined as the quantification of doubt or the quantification of the lower and upper limits of measurement about which we are completely sure, is called the uncertainty range.

## Types of Measurement Uncertainty

Uncertainty has various types in the context of measurement. Some common and well-known types include absolute uncertainty, relative uncertainty, and percentage uncertainty. Their description is mentioned below.

**Absolute Uncertainty**

- It is defined as the least count of measurement is known as absolute uncertainty.
- It is represented by the Greek letter
**Δ**(delta). - It has the same units as quantities.
- Absolute uncertainty only depends on the least count and does not require a measured value.
- The precision of a measurement depends upon absolute uncertainty

#### Examples

- Absolute uncertainty of the meter rod is 1 mm (least count of meter rod = 1mm)
- Absolute uncertainty of the Vernier caliper is 0.01 mm (least count of Vernier caliper =0.01mm)
- Absolute uncertainty of the micrometer is 0.001 mm (least count of micrometer is 0.001 mm)

### Relative Uncertainty

- The ratio of absolute uncertainty to the measured value is known as relative uncertainty.
- It is represented by the symbol
**ε**(epsilon). - It has no unit
- The accuracy of the measurement depends upon relative uncertainty.

#### Mathematically

Mathematically relative uncertainty can be written in the below form.

\text{Relative Uncertainty } = \frac{\text{Absolute Uncertainty}}{\text{Measured Value}}

Relative uncertainty can be determined using the above equation. Let the absolute uncertainty is 1 mm and the measured value is 25 mm.

\text{Relative Uncertainty} = \frac{\text{1}}{\text{25}}

\text{Relative Uncertainty} = 0.04

#### Solved Examples

##### Example 1:

Suppose you measure the length of an object using a ruler and find it to be 15.6 cm. The ruler has an uncertainty of ±0.1 cm.

Measurement = 15.6 cm Absolute Uncertainty = ±0.1 cm

to find the relative uncertainty, put the values in the above-given expression.

\text{Relative Uncertainty} = \frac{\text{0.1}}{\text{15.6}}

\text{Relative Uncertainty} = 0.0064

##### Example 2:

Suppose You measure the weight of an object as 150.2g using a digital scale. The scale’s absolute uncertainty is ±1g. Calculate relative uncertainty.

Absolute uncertainty = ±1g Measurement value = 150.2g

Put these values in relative uncertainty mathematical expression.

\text{Relative Uncertainty} = \frac{\text{1}}{\text{150.2}}

\text{Relative Uncertainty} = 0.0067

#### Practice Problems

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