100 micrometres!
The smallest object a person can make out without a microscope or magnifying glass is about 0.1 millimeters, or 100 micrometers, across. A micrometer is a millionth of a meter. This is a limit of human eyesight, not an object, and the figure is approximate: it depends on the viewer's eyes, the lighting and how close the object is held.
The limit comes from visual acuity, the eye's ability to see fine detail. A person with normal vision, called 20/20, can make out a detail that spans 1 minute of arc, one-sixtieth of a degree. On an eye chart, each stroke of the letters on the 20/20 line spans that angle.
How large a detail that angle covers depends on distance. A person with ideal vision can focus on objects as close as about 25 centimeters (10 inches), a distance called the near point. At 25 centimeters, 1 minute of arc spans about 73 micrometers. Rounded up, that gives about 0.1 millimeters, the size the OpenStax textbook Microbiology gives for an object to be visible without a microscope.
Several things push the limit up. The near point moves farther away with age, so older eyes cannot bring small things as close. Dim light, low contrast and uncorrected nearsightedness or farsightedness all reduce acuity too.
Visual acuity is limited by three things. Light spreads out slightly as it passes through the pupil, an effect called diffraction. The eye's optics do not focus perfectly, and these flaws, called aberrations, also blur the image. And the retina, the light-sensitive layer at the back of the eye, records the image with separate cells, whose spacing sets a limit of its own.
Detail is sharpest at the center of the retina, where light-sensing cells called cones are packed about 2.5 micrometers apart. Only a few minutes of arc away from the center, acuity is already measurably worse. A pupil about 3–5 millimeters wide gives the best balance between diffraction and blur.
The 0.1-millimeter figure is for making out detail, such as the strokes of the letters on an eye chart. Other tasks can go further. Telling whether a dot or a line is there at all, or whether two lines are out of line, can succeed with details finer than the normal acuity limit. Noticing a dot or line needs only that it is there, not any of its detail.