Fermi surfaces are essential for predicting, characterizing and controlling the properties of crystalline metals and semiconductors. Angle-resolved photoemission spectroscopy (ARPES) is the only technique directly probing the Fermi surface by measuring the Fermi momenta (k_F) from energy- and angular distribution of photoelectrons dislodged by monochromatic light. Existing apparatus is able to determine a number of k_F -vectors simultaneously, but direct high-resolution 3D Fermi surface mapping remains problematic. As a result, no such datasets exist, strongly limiting our knowledge about the Fermi surfaces. Here we show that using a simpler instrumentation it is possible to perform 3D-mapping within a very short time interval and with very high resolution. We present the first detailed experimental 3D Fermi surface as well as other experimental results featuring advantages of our technique. In combination with various light sources our methodology and instrumentation offer new opportunities for high-resolution ARPES in the physical and life sciences.