Specific Rotation Calculator (Polarimetry: [α], Observed Rotation & Concentration)

How it works

[α] = α / (l · c) · α = observed rotation in degrees, l = path length in decimetres, c = concentration in g/mL (g/100 mL ÷ 100) · α = [α]·l·c · c = α / ([α]·l) · reported with temperature and wavelength, e.g. [α]²⁰_D (sodium D line, 589 nm)

A chiral compound rotates the plane of polarized light. The observed angle grows in proportion to how many molecules the light passes, so it is normalised by the tube length (in decimetres, by convention) and the concentration (in g/mL) to give the specific rotation, a characteristic physical constant. Polarimetry uses the same relation in reverse to measure sugar concentration (saccharimetry) or to check the identity and optical purity of drugs. The definition follows IUPAC (Gold Book, “specific optical rotatory power”) and the USP general chapter ⟨781⟩ Optical Rotation.

Worked example

A sucrose solution of 10 g/100 mL (0.1000 g/mL) in a 2 dm tube rotates the light +13.3°. [α] = 13.3 / (2 × 0.1) = +66.50°, dextrorotatory, matching the literature value for sucrose (+66.5°). Reversed: a reading of +6.65° in a 1 dm tube would mean c = 6.65 / (66.5 × 1) = 0.1 g/mL.

Sources: IUPAC Gold Book — specific optical rotatory power · Wikipedia — Specific rotation

Frequently asked questions