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Enantiomeric Excess Calculator

Chemistry
°C
°C

ΔΔG‡ assumes kinetic control, one selective pathway, no background reaction and a ΔΔG‡ that doesn't change with temperature (ΔΔS‡ ≈ 0).

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What was measured

Enantiomers give identical responses on UV, FID and MS detectors, so their areas compare directly. Peaks that aren't baseline-resolved (Rs < 1.5) bias the ratio: check them with the Chromatography Resolution Calculator.

Peaks

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The assigned pair is 96.7 % of all integrated area

Result

Enantiomeric excess

95.1 % ee

(R) major

er

97.6 : 2.4

N : 1

40.1 : 1

% major

97.6

% minor

2.4

Composition

The excess is the part that is not racemic. The boundary between major and minor above lands on the middle of the racemic part below, because the minor species makes up half of the racemic part and the major species the other half plus the excess.

Selectivity ruler

Equal distances on this ruler are equal selectivity. Each extra nine (90 → 99 → 99.9 % ee) costs about RT ln 10 ≈ 5.7 kJ/mol at 25 °C.

About This Tool

Enantiomeric Excess Calculator – ee, er and de from Peak Areas, NMR or Optical Rotation

This enantiomeric excess calculator turns the numbers you already have, chiral HPLC or GC peak areas, NMR integrals or a polarimeter reading, into ee, er, N : 1 and, for a given temperature, ΔΔG‡. The same peak table handles diastereomers (de and dr) and products with two stereocentres. Everything is calculated in your browser.

ee is the part that is not racemic

A sample that is 97.6 % of one enantiomer and 2.4 % of the other is not "97.6 % pure". Its minor enantiomer pairs off with an equal amount of the major one to form a racemic part, and only what is left over is excess:

ee = 100 · |A₁ − A₂| / (A₁ + A₂) = % major − % minor

The composition bar draws exactly that: the racemic part is twice the minor percentage, and the boundary between major and minor lines up with its middle.

er, and why many chemists report it

The enantiomer ratio is the plain ratio of the two species, er = 97.6 : 2.4. It carries the same information as ee, since ee = 100 · (r − 1) / (r + 1) with r = N : 1, but it does not compress near 100 %: 99 % and 99.8 % ee look alike, yet the minor enantiomer differs fivefold. Reporting er is common practice in the asymmetric-synthesis literature for that reason.

Measuring by chiral chromatography

Enantiomers respond identically on UV, FID and MS detectors, so their areas compare directly. The ratio is only as good as the integration, though: peaks that are not baseline-resolved bias it, so check Rs with the Chromatography Resolution Calculator. When the minor peak is not detected, a result of "100 % ee" says nothing about your method. State a bound from the reporting threshold instead, such as > 99.9 % ee.

Why this tool never shows 100 % by rounding
A non-zero minor amount that rounds to 0 is shown as "< 0.1", and a value below 100 that rounds to 100 is shown as "> 99.9". "100 %" appears only when no minor peak was integrated at all, with a reminder to enter your reporting threshold.

NMR, shift reagents and Mosher esters

With a chiral shift reagent or a derivatising agent, the two enantiomers give separate signals. Integrate one well-separated signal per species, using the same number of protons. A Mosher ester measures the diastereomeric excess of the derivatives, and a substrate of ee x reacted with an agent of ee y gives an observed de of x · y, so ee = de / ee_CDA. This assumes complete conversion and no kinetic resolution, which is why the agent's purity matters.

Optical rotation and optical purity

The specific rotation is [α] = α / (l · c), with l in dm and c in g/mL, usually reported with c in g/100 mL as in [α]D20 +39.2 (c 1.05, CHCl3). Dividing by the literature value for the pure enantiomer gives the optical purity, which equals ee only if rotation is linear in composition and the conditions match. Self-association (the Horeau effect), chiral impurities and a different solvent or wavelength all break that, and a small readout error becomes a large ee error at low concentration. Use polarimetry as a check, not as the number you report.

ΔΔG‡ and the cost of each nine

For a kinetically controlled reaction, N : 1 = exp(ΔΔG‡ / RT). The selectivity ruler plots ln(N : 1), so equal distances mean equal energy: going from 90 to 99 to 99.9 % ee costs about RT ln 10 ≈ 5.7 kJ/mol each time at 25 °C. Extrapolating the same ΔΔG‡ to another temperature assumes it does not change with T, which often fails.

Diastereomers and two stereocentres

Two diastereomers use the same formulas as de and dr, with an optional relative response factor if the detector treats them differently. A product with two stereocentres has four stereoisomers: the tool gives dr and de between the two diastereomers, the ee inside each one, and the share of every stereoisomer in the total.

Frequently Asked Questions

Is the Enantiomeric Excess Calculator free?

Yes, Enantiomeric Excess Calculator is totally free :)

Can I use the Enantiomeric Excess Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Enantiomeric Excess Calculator?

Yes, any data related to Enantiomeric Excess Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

How do I calculate enantiomeric excess from chiral HPLC peak areas?

Integrate the two enantiomer peaks and use ee = 100 × |A₁ − A₂| / (A₁ + A₂). For areas of 2456.8 and 61.2 that is 100 × 2395.6 / 2518.0 = 95.1 % ee. Enantiomers respond identically on UV, FID and MS detectors, so the areas compare directly, but only if the peaks are baseline-resolved (Rs of 1.5 or more).

What is the difference between ee and er, and why do many chemists now prefer er?

ee is the excess of one enantiomer over a racemic mixture, as a percentage. er is the plain ratio of the two enantiomers, such as 97.6 : 2.4. They carry the same information (ee = 100 × (r − 1) / (r + 1)), but er avoids the compression near 100 %, where 98 % and 99.8 % ee differ by a factor of ten in the minor enantiomer. It also maps directly onto ΔΔG‡.

Is optical purity the same as enantiomeric excess?

Only if rotation is linear in composition. Optical purity is 100 × [α] / [α]ref, so it assumes the reference value was measured under the same wavelength, solvent, temperature and concentration, and that the sample has no chiral impurities. Self-association (the Horeau effect) can break the linearity. A polarimeter is also a poor way to measure high ee, because a small readout error becomes a large ee error.

How do I calculate de and dr for diastereomers, or for a product with two stereocentres?

For two diastereomers the formulas are the same: de = 100 × |D₁ − D₂| / (D₁ + D₂) and dr = D₁ : D₂. With two stereocentres you get four stereoisomers: sum each diastereomer's pair to get dr and de, then take the ee inside each pair separately. If the detector responds differently to the two diastereomers, enter a measured relative response factor.

Why shouldn't I report 100 % ee?

A measurement can only show that the minor enantiomer is below the detection or reporting limit, not that it is absent. If no minor peak is integrated, state a bound such as > 99.9 % ee (minor < 0.05 %) from your method's reporting threshold. Rounding is the same trap: 99.96 % ee displays as > 99.9 % at one decimal, never as 100 %.

How is ee related to ΔΔG‡ and the reaction temperature?

For a kinetically controlled reaction with one selective pathway, N : 1 = exp(ΔΔG‡ / RT), so ΔΔG‡ = RT ln(major / minor). At 25 °C, 90 % ee (19 : 1) corresponds to 7.3 kJ/mol. Each extra nine of ee costs about RT ln 10 ≈ 5.7 kJ/mol. Extrapolating to another temperature assumes ΔΔG‡ does not change with T, which often fails.