Measurement is a way to quantify an attribute of an object with respect to known standards in numerical values. The attribute of the host/object can be length, weight, height etc… There are different units of measurement followed across the world. International System of Units (SI) has become the commonly accepted standard for measurements.

There are seven fundamental units defined under the SI system. Meter is the standard unit of measurement for both length and height. It is denoted by the symbol ‘m’. Though they share the same unit for measurement, length and height have different meaning and unique definitions

**Length vs Height**

The difference between length and height is that length denotes the extension of an object in the same plane from one point to another. Whereas height represents the altitude of an object measured from a reference point or plane.

For instance, let us consider a cube occupying some space. Measuring the cube in the horizontal plane from one point to another represents the length. When the same cube is measured from one point to another in the vertical plane, it denotes the height of the cube.

**Comparison Table Between Length and Height**

Parameter of Comparison | Length | Height |

Definition | Refers measuring an object in the same plane from one edge/point to another | Refers measuring an object from top to bottom or vice-versa |

Direction in which it is measured | Horizontal direction | Vertical direction |

What does it denote | Tells us the extension or how long the target/object is | Tells us the elevation/altitude of the target/object is |

Usage in Co-ordinate geometry | Generally, the length is considered along the x-axis | Height is considered along the y-axis |

Dimension | Measured for one, two- and three-dimensional object | Height is an attribute for a three-dimensional object. |

**What is Length?**

Length can be defined as an extension of an object which is measured from one point to another in the horizontal direction. Measurement in X-axis is the general representation of length in Co-ordinate geometry.

The unit of length depends on the measurement standard followed. In the case of the SI system, the unit is the meter (denoted as ‘m’). In the British or Imperial system, it is referred to the yard. One-yard equals 0.9144 meters. While mentioning the size for a three-dimension object, the length is always written first.

Generally speaking, the distance we travel falls under the length category. But the units vary depending on the target we measure. For instance, the astronomical unit(au) is used while measuring distance in outer space. Dalton signifies the sub-atomic distance. Length is used in synonymous with distance in the field of science. Though width and breadth are measured in the horizontal direction, the longest one represents the length.

**What is Height?**

Height is another attribute of an object which denotes the altitude of the target object from a given reference. It is generally measured from the ground-level/base to the top of the object. Measurement in Y-axis is the nominal representation of height in Cartesian Co-ordinate geometry.

The unit of height matches with that of length. Meter, yard, inches, foot etc… are used to denote height as well. The way the attribute is measured signifies whether the quantity is length or height. Height always denotes the tallness of the target/object.

For example, it is incorrect to say the length of the tallest peak rather the height of the tallest peak. Height assumes significance importance concerning the health condition of a person as it is one of the parameters in calculating BMI (Body Mass Index). In anthropometry, studying about human height is one of the core areas of interest. Anthropometry assumes significance as it provides vital information while deciding the ergonomics of any object. It is considered as one of the important factors in industrial design as well.

**Main Differences Between Length and Height**

- Length is an indicator of how long the target/object is, whereas height indicates how tall the target/object is.
- Distance travelled is always attributed to length while the altitude is attributed to height.
- The direction for measuring length is horizontal and direction for measuring height is aligned to the vertical direction.
- X-axis ascertains length and Y-axis indicates the height in mathematics (Cartesian Co-ordinates)
- One- and two-dimensional objects possess length and height are considered only in three-dimensional space. Height is unique to three-dimension objects.
- Example for one-dimension quantity can be a line where it has only one attribute i.e. the length or the distance from one point to another. Example for a three-dimension quantity can be a cuboid where it is made up of three different attributes i.e. length, breadth and height.
- Height (elevation) is an important parameter in aviation. Travelling at a specific elevation becomes an essential part during landing and manoeuvre for pilots. Not maintaining the desired elevation could even lead to disaster.
- Length signifies importance while calculating the distance from one place to another. The distance we travel is either mentioned in metres or kilometres. The centimetre is used while measuring a smaller quantity
- While considering an object, the long facet is always considered as the length of the object. And the face of the object in normal orientation is denoted by height (measured upwards)
- In three-dimensional space, height is always perpendicular to the plane formed as a result of a combination of width and length.

**Conclusion**

Many assume length and height to be analogous to each other which is incorrect. They have a different definition and unique concepts of mathematics. Length and height possess a subtle difference in measurement. And this subtle difference depends on the object’s position. It is because the change in the object’s position changes the measurement and its attributes. So, proper care and attention have to be given for the position of the target/object.

Measurement of any three-dimensional(3D) object will always be incomplete without quantifying the length and height of the 3D object. Each attribute has its own significance and its impact in all the fields. Length plays a vital role in understanding the extension of any object whereas height assumes significance in tallness of the three-dimensional object.

**Reference**

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