A carbon catalyst, comprising a carbon structure in which area ratios of three peaks f broad, f middle, and f narrow obtained by separating a peak in a diffraction angle of from 23° to 27° in an X-ray diffraction pattern obtained by powder X-ray diffraction, each ratio being calculated based on an area of each peak f broad, f middle, and f narrow, satisfy the following conditions (a) to (c): (a) f broad observed within a range of diffraction angle of 24.0° ±4.0°: 75% or more and 96% or less; (b) f middle observed within a range of diffraction angle of 26.3°±1.5°: 3.2% or more and 15% or less; and (c) f narrow observed within a range of diffraction angle of 26.5°±1.0°: 0.4% or more and 15% or less, wherein the peak separation is performed by the following steps: (i) the X-ray diffraction pattern is subjected to intensity correction of a polarization factor, a Lorentz factor, and an atom scattering factor of carbon, and is also subjected to background correction in which a straight line connecting the diffraction angle of around from 10° to 20° to the diffraction angle of around from 30° to 40° is defined as a background, and the background is subtracted from each diffraction intensity after the intensity correction; and (ii) in the corrected X-ray diffraction pattern, the peak having a peak top within a range of the diffraction angle of from 23° to 27° is superimposed onto a Gaussian basic waveform to be approximated, to thereby optimize a peak intensity, a peak half width, and a peak position, and each of three superimposed peaks included in the peak is subjected to curve fitting, wherein the curve fitting is performed so that a residual sum of squares becomes smallest, wherein the residual square refers to a square of a residual error at each measured diffraction angle, wherein the residual sum of squares refers to a sum of residual squares, and wherein the residual error refers to a difference between the intensity of the peak having a peak top within a range of the diffraction angle of from 23° to 27° in the corrected X-ray diffraction pattern, and the sum of intensities of the three separated peaks f broad, f middle, and f narrow. (a) f broad observed within a range of diffraction angle of 24.0° ±4.0°: 75% or more and 96% or less; (b) f middle observed within a range of diffraction angle of 26.3°±1.5°: 3.2% or more and 15% or less; and (c) f narrow observed within a range of diffraction angle of 26.5°±1.0°: 0.4% or more and 15% or less, (i) the X-ray diffraction pattern is subjected to intensity correction of a polarization factor, a Lorentz factor, and an atom scattering factor of carbon, and is also subjected to background correction in which a straight line connecting the diffraction angle of around from 10° to 20° to the diffraction angle of around from 30° to 40° is defined as a background, and the background is subtracted from each diffraction intensity after the intensity correction; and (ii) in the corrected X-ray diffraction pattern, the peak having a peak top within a range of the diffraction angle of from 23° to 27° is superimposed onto a Gaussian basic waveform to be approximated, to thereby optimize a peak intensity, a peak half width, and a peak position, and each of three superimposed peaks included in the peak is subjected to curve fitting,