Difference Between Length, Width, and Height: Key Concepts Explained
The concept of length plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios.
What Is Length?
Length in Maths is defined as the measurement of how long something is from one end to another. It is a fundamental concept used to describe the extent of an object in one direction. You’ll find this concept applied in areas such as geometry, measurement of objects in daily life, and even in understanding distances in physics and engineering.
Units of Length in Mathematics
The standard unit of length in the International System of Units (SI) is the metre (m). Other commonly used metric units are kilometre (km), decimetre (dm), centimetre (cm), and millimetre (mm). In the customary and imperial systems, units like inch, foot, yard, and mile are also used. Knowing how to convert between these units is often required in exams and practical life.
| Unit | Abbreviation | Equivalent (in meters) |
|---|---|---|
| Kilometre | km | 1,000 m |
| Metre | m | 1 m |
| Centimetre | cm | 0.01 m |
| Millimetre | mm | 0.001 m |
| Inch | in | 0.0254 m |
| Foot | ft | 0.3048 m |
Difference Between Length, Width, and Height
Students often confuse length with width and height. Generally, length is the longest side of an object; width (or breadth) is the shorter side, and height is how tall something stands from the base up.
| Dimension | Description |
|---|---|
| Length | Most extended/horizontal side |
| Width (Breadth) | Shorter/horizontal side (side-to-side) |
| Height | Vertical side (base to top) |
Key Formula for Length
Here are some handy formulas that use length in Maths:
- Distance between two points (\(A(x_1,y_1)\) and \(B(x_2,y_2)\)):
\( \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) - For rectangles: Length × Breadth = Area
- Perimeter using length: see Perimeter page
Length Conversion Table
Use this quick table to convert between basic units of length:
| From | To | Multiply by |
|---|---|---|
| Kilometre (km) | Metre (m) | 1,000 |
| Metre (m) | Centimetre (cm) | 100 |
| Centimetre (cm) | Millimetre (mm) | 10 |
| Inch (in) | Centimetre (cm) | 2.54 |
Tools for Measuring Length
The main tools to measure length are rulers, measuring tapes, meter sticks, and sometimes digital devices like laser measures. For very small or very large distances, callipers and odometers are used respectively. Learn more about measuring techniques on our Measurement of Objects page.
Step-by-Step Illustration: Length Word Problem
Example: Convert 250 centimetres to metres.
1. Start with the given value: 250 cm2. Know that 1 metre = 100 cm
3. Divide 250 by 100 to convert:
4. \( 250 \div 100 = 2.5 \) metres
5. Final Answer: 2.5 metres
Quick Speed Trick
To speed up length conversions, remember that you simply move the decimal point two places for every step in the metric system. For example, to go from cm to m (two steps up), move the decimal point left by two places!
Try These Yourself
- Measure the length of your desk in both centimetres and metres.
- Convert 5 km to metres.
- What is the difference in length if a string is 2 m longer than another string that is 125 cm?
- Identify whether length, width, or height is being described for the edge of a box standing upright.
Frequent Errors and Misunderstandings
- Confusing the unit conversion direction (e.g., multiplying instead of dividing).
- Mixing up length with width or height when labeling sides of an object.
- Forgetting to align units before adding or subtracting lengths.
Relation to Other Concepts
The idea of length connects closely with topics such as area, volume, and perimeter. Mastering this helps you with more advanced geometry and measurement techniques.
Classroom Tip
An easy way to remember metric length units is by “King Henry Died Many Centimetres Minus” (Kilometre, Hectometre, Decametre, Metre, Centimetre, Millimetre).
We explored length—from definition, units, formula, measurement tools, common mistakes, and how it connects with other concepts. For more practice and live doubt-solving, explore Vedantu’s online Maths classes or visit our Length Conversion page for calculators and revision tables.
You can also visit related topics such as Metric System, Centimeter, and our full guide to Units of Measurement to strengthen your Maths basics!
FAQs on Understanding Length in Mathematics: Units, Tools & Examples
1. What is length in mathematics, with a simple example?
In mathematics, length is the measurement of the distance between two points. It defines how long an object is or how far apart two locations are. For example, if you measure a pencil with a ruler, its length might be 15 centimetres. This value represents the distance from the pencil's tip to its end.
2. What are the standard units used to measure length?
The standard units for measuring length depend on the system being used. The two main systems are:
The Metric System (SI Units): This is the most widely used system globally. Its base unit is the meter (m). Other common units include the kilometre (km), centimetre (cm), and millimetre (mm).
The Imperial System: This is used in a few countries, including the United States. Common units include the inch (in), foot (ft), yard (yd), and mile (mi).
3. Which tools are commonly used to measure length?
Several tools are used to measure length, depending on the object's size and the required precision. Common tools include:
Rulers: Used for measuring short, straight lines, typically in centimetres or inches.
Measuring Tapes: Flexible tapes used for measuring longer distances or curved surfaces, common in construction and tailoring.
Odometers: Used in vehicles to measure long distances travelled, usually in kilometres or miles.
Calipers: Used for making very precise, small-scale measurements.
4. What is the difference between length, breadth, and height?
While all three are measurements of distance, they describe different dimensions of a three-dimensional object:
Length typically refers to the longest side of an object when viewed from the front.
Breadth (or width) refers to the shorter side or the distance from side to side.
Height refers to the vertical distance from the bottom to the top.
For example, in a rectangular box, the length is how long it is, the breadth is how wide it is, and the height is how tall it is.
5. How is the concept of length used to calculate the perimeter and area of a shape?
Length is a fundamental building block for both perimeter and area. For a two-dimensional shape:
Perimeter is the total length of the boundary of the shape. It is calculated by adding up the lengths of all its sides. For a rectangle with length 'l' and width 'w', the perimeter is 2l + 2w.
Area is the measure of the surface enclosed by the shape. It is often calculated by multiplying two length dimensions. For the same rectangle, the area is l × w.
Therefore, you cannot find the perimeter or area without first knowing the lengths of the sides.
6. Why is it important to convert between different units of length, such as centimetres to metres?
Converting between units is crucial for consistency and comparison. If you are working on a project where one measurement is in centimetres and another is in metres, you must convert them to the same unit before you can add, subtract, or compare them accurately. For instance, to find the total length of two ropes, one 150 cm long and the other 2 m long, you must convert both to either cm (150 cm + 200 cm) or m (1.5 m + 2 m) to get a meaningful result.
7. Can length have a value of zero or be negative in mathematics?
Yes, but the context is important. A length of zero means there is no distance between two points; they are in the exact same location. As a physical measurement of an object's size, length cannot be negative. However, in contexts like coordinate geometry or physics, a negative sign associated with a length-related value (like displacement) is used to indicate direction relative to a starting point or origin.
8. How are different metric units of length (mm, cm, m, km) related to each other?
The metric system is based on powers of 10, which makes conversions straightforward. The relationship from smallest to largest is as follows:
10 millimetres (mm) = 1 centimetre (cm)
100 centimetres (cm) = 1 meter (m)
1,000 meters (m) = 1 kilometre (km)
This base-10 structure means you can convert units simply by multiplying or dividing by 10, 100, or 1,000.
9. What are some real-world examples where we use length measurement every day?
We use length measurement constantly in our daily lives. Some examples include:
Construction: Measuring the length and height of walls to build a house.
Navigation: Calculating the distance in kilometres for a road trip.
Cooking: While not a direct length, measurements like 'a cup' are based on the dimensions (height and diameter) of the measuring cup.
Sports: Measuring the length of a swimming pool, a race track, or the distance of a javelin throw.
Shopping: Checking the screen size of a TV (measured diagonally in inches) or buying fabric (measured in metres).
10. How does understanding length help in learning more advanced topics in geometry?
Understanding length is the absolute foundation of geometry. Without it, advanced concepts would be impossible to grasp. For example:
The Pythagorean theorem is entirely about the relationship between the lengths of the sides of a right-angled triangle.
Calculating the volume of 3D shapes (like cubes or spheres) requires multiplying multiple length measurements (length, width, height, radius).
In coordinate geometry, the distance formula is used to find the length of a line segment between two points on a plane.
Essentially, length is the primary tool used to quantify and analyse the size and properties of all geometric figures.
