Spot size is nothing but the radius of the beam itself and is technically not the same as the beam diameter. The irradiance of the beam decreases gradually at the edges. The distance across the center of the beam for which the irradiance (intensity) equals 1/e 2 of the maximum irradiance (1/e 2 = 0.135) is defined as the beam diameter.
The spot size (w) of the beam is defined as the radial distance (radius) from the center point of maximum irradiance to the 1/e2 point.
where λ is the wavelength of the given laser and w0 is the radius of the beam at the narrowest point, which is termed as the beam waist.