Measuring fault offsets preserved at the ground surface is of primary importance to recover earthquake and long-term slip distributions and understand fault mechanics. The recent explosion of high-resolution topographic data, such as Lidar and photogrammetric DEMs, offers an unprecedented opportunity to measure dense collections of fault offsets. We have developed a new Matlab code, 3D_Fault_Offsets, to automate these measurements. In topographic data, 3D_Fault_Offsets mathematically identifies and represents nine of the most prominent geometric characteristics of common sub-linear markers along faults (especially strike-slip) in 3D, such as the streambed (minimum elevation), top, free face and base of channel banks or scarps (minimum Laplacian, maximum gradient and maximum Laplacian), and ridges (maximum elevation). By calculating best-fit lines through the 9 point clouds on either side of the fault, the code computes the lateral and vertical offsets between the piercing points of these lines onto the fault plane, providing 9 lateral and 9 vertical offset measures per marker. Through a Monte Carlo approach, the code calculates the total uncertainty on each offset. It then provides tools to statistically analyze the dense collection of measures, and to reconstruct the pre-faulted marker geometry in the horizontal and vertical planes. We applied 3D_Fault_Offsets to re-measure previously published offsets across 88 markers on the San Andreas, Owens Valley, and Hope faults. We obtained 5454 lateral and vertical offset measures. These automatic measures compare well to prior ones, field and remote, while their rich record provides new insights on the preservation of fault displacements in the morphology.