What is Depth of cut and how do you calculate it?

Depth of Cut (DOC) is one of many important factors to consider in Polycrystaline Diamond Compact (PDC) drill bit design.

The depth at which the cutter penetrates the formation is Depth of Cut (DOC), as the image below describes.

Depth of Cut Cutter View
Coupled to the rotation of the PDC drill bit, Depth of Cut (DOC) is usually measured in millimeters and is .

It is more versatile and easier to back calculate from historical or live outputs at the rig site if we use the units DOC/revolution or mm/REV.

DOC/REV is related to the Rate of Penetration (ROP) of the PDC drill bit, usually measured in meters per hour.

Depth of Cut Equation

DOC/mm can be easily calculated using the following formula:

Depth of Cut Equation

*For all you engineers, drilling superintendents and directional hands out there keep this formula handy.

The Depth of Cut (DOC) formula is a generalization of how fast the PDC drill bit penetrates the formation in one revolution.

The bit is made up of multiple PDC cutters that are coupled to the blades.

The PDC drill bit cutters are the elements responsible for removing the formation and thus generating Rate of Penetration (ROP).

This Rate of Penetration (ROP) per revolution can be translated to the cutters via DOC/mm.

PDC Drill Bit Wear Grooves

If a PDC Drill Bit  is designed without considering its target ROP and revolutions per minute (RPM) serious performance limitations can be inadvertently placed on the bit.

If the DOC is too high the PDC blades may end up riding on the formation,

which hinders performance and wears the blades down.

PDC Drill Bit Depth of Cut

PDC Cutter Exposure

Once blade contact has been established the PDC drill bit simply cannot drill any faster without further damaging the blade.

One method to maximize DOC is to increase the cutters’ exposure from the supporting blade material.

An example of a PDC drill bit with a high and low exposure are depicted below.

PDC Drill bit Cutter Exposure

PDC drill bit Cutters that are largely exposed will have the ability to drill faster however there is a downside.

The PDC dill bit cutters have less surface area and pocket to be brazed to.

The mechanical lock between the cutter and pocket is largely reduced.

The PDC drill bit cutters will be more susceptible to complete pull out from the pocket during an impact event.

A lost PDC drill bit cutter will certainly mean reduced performance from the bit.

If the bit continues to drill for much longer, a severely damaged bit that cannot be repaired is a near certainty.

It is important that PDC drill bit cutter exposure is determined for optimum DOC and ROP while also considering cutter retention by not carelessly over exposing them.

As a rule of thumb most PDC drill bit cutters are not exposed more than half of their diameter, although this may not always be the case.

For instance a 16 mm cutter will not have an exposure of more than 8 mm.

An example whether or not a PDC drill bit with a cutter exposure of 6 mm will have blade contact is as follows.
Instantaneous ROP of the bit: 120 m/hr
Downhole RPM of the PDC: 200 RPM

PDC Drill Bits Canada - Depth of Cut

In this case since the cutter is exposed 6 mm from the blade and the depth of cut (DOC) is 10 mm there is a good possibility that the bit blades will rub on the formation.


Most PDC bits are designed such that each cutter is in a unique position along the profile of the bit.

In other words, most PDC drill bits do not have plurality in their cutter positions.

In the image below each cutter is located in a unique position along the bits profile also know as a single set design.

The depth of cut (DOC) formula can be used to generalize this bit.

If for instance a bit is designed where 2 cutters are in the same radial position or a plural set then this formula cannot be used.

However, if the plural cutters are 180 degrees away then dividing the depth of cut (DOC) formula by 2 will give you a more accurate generalization.

Single Set Cutter Layout

Depth of Cut Single Set Cutter Layout

Depth of Cut (DOC) is one of many important factors that must be considered when designing a PDC drill bit.

Selecting the cutter exposure correctly based on how the bit is expected to perform will ensure that blade contact will not impede high performance drilling that our customers expect.

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