# How PIX4Dmapper calculates the Volume

This article explains how PIX4Dmapper calculate a volume by providing the functions being used within PIX4Dmapper.

PIX4Dmapper calculates the volume as follows:

1. The user draws a volume in the Volumes view. For more information about how to draw a Volume: How to draw a Volume.

Note: The volume is computed using the DSM. In order to draw a new volume, the point cloud and the DSM have to be generated.

Note: PIX4Dmapper creates the base taking into account the altitude of each vertex.

2. PIX4Dmapper projects a grid with GSD spacing on the base.

3. For each cell i of the grid, its volume (Vi) is given by:

Vi = Li * Wi * Hi

Where:

Li = the length of the cell.
Wi = the width of the cell.
Hi = the height of the cell.

The Length (Li) and Width (Wi) are equal to the project's GSD.

Li =Wi = GSD

The Height (Hi) is given by:

Hi = ZTi - ZBi

Where:

ZTi = the terrain altitude of each cell at the center of the cell.
ZBi = the base altitude of each cell at the center of the cell.

Therefore, the volume Viof cell i is given by:

Vi = GSD*GSD* (ZTi - ZBi)

Note:
• ZTi is the altitude of the 3D terrain corresponding to the center of the cell i.
• ZBi is the altitude of the base surface of the volume corresponding to the center of the cell i .

4. PIX4Dmapper calculates 2 volumes:

• The Cut volume Vc is the volume between the base and the 3D terrain, when the terrain is higher than the base.

Cut volume = VC = VC1 + VC2 +...VCN

Where:

VC1...N = Cut volume for cell i..N

• The Fill volume VF is the volume between the base and the terrain when the terrain is lower than the base.

Fill volume = VF = VF1 + VF2 +...VFN

Where:

VF1...N = Fill volume for cell i...N.

Note: The Fill Volume is given with a negative value/sign.

5. The Total volume is given by:

Total Volume = VT =VC+ VF