import math


def calculate_tail_correction(num_particles, box_length, cutoff):
    """
    The tail correction associated with using a cutoff radius.
    
    Computes the tail correction based on a cutoff radius used in the LJ energy calculation in reduced units.
    
    Parameters
    ----------
    num_particles : int
        The number of particles in the system.
    
    box_length : int
        Size of the box length of the system, used to calculate volume.
    
    cutoff : int
        Cutoff distance.
    
    Returns
    -------
    tail_correction : float
        The tail correction associated with using the cutoff.
    """
    
    brackets = (1/3*math.pow(1/cutoff,9)) - math.pow(1/cutoff,3)
    volume = box_length**3
    
    constant = ((8*math.pi*(num_particles**2))/(3*volume))
    
    tail_correction = constant * brackets
    
    return tail_correction