The Small-Room Correction: What Testing at Three Metres Does to a Six-Metre Chart, and the Arithmetic That Repairs It

Schools and clinics with small rooms routinely test acuity at three or four metres with charts designed for six, often without adjusting the result. This paper computes what that shortcut costs and the two corrections it requires. Geometrically, a 6 m chart used at 3 m magnifies every letter by a factor of two in angular terms, so a line recorded as 6/12 is truly 6/24 unless the distance fraction is applied; at 4 m the same line is 6/18. Physiologically, the short distance adds accommodation demand - 0.333 D at 3 m against 0.17 D at 6 m - which flatters uncorrected myopes and penalises latent hyperopes by the excess of 0.167 D. Placement precision also degrades as rooms shrink: a 10 cm error is 3.3 percent at 3 m. The protocol that follows is to print the test distance on the result, apply the distance fraction, and reserve short-room testing for screening with corrected referral thresholds. This study is simulated, not measured.