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Enantiomeric Excess Calculator

Calculate enantiomeric excess (ee) and the enantiomer ratio from an observed optical rotation and the specific rotation of the pure enantiomer, or from the amounts or HPLC peak areas of each enantiomer.

Calculate from

Observed rotation (α)

Path length of the cell (l)

Concentration (c)

Specific rotation of the pure enantiomer [α]

Amount of enantiomer A

Amount of enantiomer B

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How it works

specific rotation [α] = 100 α ÷ (l × c) (l in dm, c in g/100 mL) · optical purity = [α]observed ÷ [α]pure × 100% · ee = |A − B| ÷ (A + B) × 100% · major = (100 + ee) ÷ 2 %, minor = (100 − ee) ÷ 2 %

Enantiomeric excess tells how much more of one mirror-image form a sample contains than a racemic (50:50) mixture would: 90% ee means 95:5. It can be measured with a polarimeter, assuming the optical purity equals the ee (true for most compounds without strong aggregation effects), or more reliably from the peak areas of the two enantiomers on a chiral HPLC or GC column. Specific rotations depend on solvent, temperature and wavelength (usually the sodium D line, 589 nm), so compare with a reference measured under the same conditions.

Worked example

A sample at c = 10 g/100 mL in a 1 dm cell rotates light by +4.65°. Its specific rotation is 100 × 4.65 ÷ (1 × 10) = +46.50°. The pure enantiomer has [α] = +93°, so the optical purity and ee are 46.50 ÷ 93 = 50.00%: the sample is 75.00% of the (+) enantiomer and 25.00% of the (−) one, an er of 75:25.

Sources: IUPAC Gold Book — Enantiomer excess · IUPAC Gold Book — Specific rotation

Frequently asked questions

How do I calculate enantiomeric excess?

ee = (major − minor) ÷ (major + minor) × 100%. A 90:10 mixture has 80% ee. From a polarimeter, ee ≈ observed specific rotation ÷ specific rotation of the pure enantiomer × 100%.

What is the difference between ee and optical purity?

Optical purity is the ratio of observed to pure specific rotation; ee is defined from the actual composition. They are usually equal, but can differ when molecules aggregate (the Horeau effect).

How do I convert ee to an enantiomer ratio?

Major % = (100 + ee)/2 and minor % = (100 − ee)/2. So 96% ee is 98:2 and 50% ee is 75:25.

What is the ee of a racemic mixture?

Zero. A racemate contains equal amounts of both enantiomers, so it shows no optical rotation.

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This calculator is for educational purposes. Double-check important results before acting on them.