Enter the radius of the unit cell into the calculator to determine the HCP (hexagonal closed packing) height.

HCP Height Formula

The following equation is used to calculate the HCP Height.

H = 4*r * SQRT (2/3)
  • Where H is the hexagonal closed packing height (hcp)
  • R is the radius of the unit cell

To calculate the HCP height, multiply the radius by 4, then multiply that result by the square root of 2/3.

What is an HCP Height?


An HCP height, also known as hexagonal packing height, measures the total height of a hexagonal close packing structure of spheres.

How to Calculate HCP Height?

Example Problem:

The following example outlines the steps and information needed to calculate the HCP Height.

First, determine the radius of the unit cell. For this example, the radius is given as a value of 5.

Next, the final and last step is to calculate the HCP height using the formula above:

H = 4*r * SQRT (2/3)

H = 4*5 * SQRT (2/3)

H = 16.3299


What factors can affect the calculation of HCP height?

The primary factor that affects the calculation of HCP height is the accuracy of the radius measurement of the unit cell. Variations or errors in measuring the radius can lead to significant discrepancies in the calculated HCP height. Additionally, the precision of the mathematical constants used in the formula, such as the square root of 2/3, can also influence the result.

Why is the HCP height important in materials science?

HCP height is crucial in materials science because it provides information about the packing efficiency and density of a hexagonal close-packed structure. This measurement can influence the material’s properties, such as strength, durability, and how it interacts with other materials. Understanding the HCP height helps scientists and engineers design better materials for various applications.

Can the HCP height formula be used for any type of unit cell?

No, the HCP height formula is specifically designed for hexagonal close-packed structures. Different types of unit cells, such as cubic or tetragonal, have their unique packing arrangements and therefore require different formulas to calculate their respective heights or dimensions. It is crucial to use the appropriate formula that corresponds to the type of unit cell being analyzed.