Some branches of the Science of Geology, are pretty heavy in math and physics. Hydrogeology, Seismology, Geophysics and Structural Geology are some of them.
Here we present you the 10 equations that a Geology Student should know and use.

1. Darcy's Law formula

The most important law in Hydrogeology, by far. When your professor is willing to go easy on you in an exam, he is going Darcy's Law. It is fundamental knowledge for every geologist.
It describes the flow of a fluid through a porous medium, for slow, viscous flow. The total discharge, is equal to the product of the intrinsic permeability of the medium, the cross-sectional area to flow, and the total pressure drop, all divided by the viscosity, and the length over which the pressure drop is taking place.

2. Porosity

In Hydrogeology, people care mostly for how much fluid can be stored in a rock. So, porosity which is the volume of the voids of a soil over the total volume of the sample defines the porosity of a soil, is pretty important.
It is used in geology, hydrogeology, soil science, and building science. The porosity of a porous medium (describes the fraction of void space in the material, where the void may contain.
Porosity is a fraction between 0 and 1, typically ranging from less than 0.01 for solid granite to more than 0.5 for peat and clay. It may also be represented in percent terms by multiplying the fraction by 100.

3. Volumetric water content

If you read the 2 above paragraphs, you pretty much know why this formula is important. This equations calculates the Water content or moisture content  inside a solid. It practically is the ratio of the volume of water to the total volume (that is soil volume + water volume + air space).

4. Effective diffusivity in porous media

In a porous medium, the skeletal portion of the material is often called the “matrix” or “frame” which is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media. The effective diffusion coefficient describes diffusion through the pore space of porous media. It is macroscopic in nature, because it is not individual pores but the entire pore space that needs to be considered. 

5. Hydraulic conductivity

Last but not least in the Hydrogeology section of our list, we got Hydraulic Conductivity. It is  a property of vascular plants, soils and rocks, that describes the ease with which a fluid (usually water) can move through pore spaces or fractures. It depends on the intrinsic permeability of the material and on the degree of saturation, and on the density and viscosity of the fluid.

6. Seismic moment

Another strongly related with equations branch of geology is Seismology. Let's start with the Seismic moment. It is a quantity to measure the size of an earthquake and is proportional to the area of the rupture times the average slip that took place in the earthquake. Simple as that.
Read HERE a blog about this equation.

7. Richter magnitude scale

In 1930, the Richter scale was developed. It is a base-10 logarithmic scale, which defines magnitude as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor amplitude. This scale saturates at around M=7, because the high frequency waves recorded locally have wavelengths shorter than the rupture lengths of large earthquakes.
HERE you can read another post specifically about the Richter magnitude scale.

8. P-wave Velocity

P-waves are a type of elastic wave, called seismic waves in seismology, that can travel through a continuum. The continuum is made up of gases (as sound waves), liquids, or solids, including the Earth. They can be produced by earthquakes and recorded by seismographs. The name P-wave is often said to stand either for primary wave, as it has the highest velocity and is therefore the first to be recorded; or pressure wave, as it is formed from alternating compressions and rarefactions. 
More about P-waves HERE.

9. S-wave Velocity

Another type of elastic wave strongly related to seismology, is the S-wave, secondary wave, or shear wave . It is one of the two main types of elastic body waves with its P-Wave pal. The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation. The wave moves through elastic media, and the main restoring force comes from shear effects. Read more about S-Wave HERE.

10. Crystal Structures of Metals

Mineralogy and Crystallography are two geology branches that use lots of, chemistry and geometry related equations. This one will come pretty handy to any undergraduate geology student.
Metals are crystallized in four crystal structures: simple cubic (sc); body-centered cubic (bcc); face-centered cubic (fcc) or cubic-close-packing (ccp); and hexagonal-close-packing (hcp).
Face-centered cubic (fcc) system (or cubic close-packed or ccp) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell (1⁄8 × 8 from the corners plus 1⁄2 × 6 from the faces). The lattice is not a primitive one since there are 4 lattice points (atoms) per unit cell, one at the vertices (one eighth at each vertex) and three other on the 6 faces. The lattice constant can be calculated by the radius of the atom. 

You can try to search whatever you want just by clicking on the “Browse Formulas” button on the top left of your screen and find a full list of Geology Equations HERE.

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