Scientific Ethanol Dilution Calculator
Auto Contraction Table & Explanation
The table below lists volumetric contraction percentages measured at various ABV/Proof levels at 20 °C (68 °F). Values for intermediate strengths are calculated by linear interpolation between these data points:
| ABV (%) | Proof | Contraction (%) |
|---|---|---|
| 10 | 20 | 0.8 |
| 20 | 40 | 1.5 |
| 30 | 60 | 2.2 |
| 40 | 80 | 2.7 |
| 50 | 100 | 3.2 |
| 60 | 120 | 3.1 |
| 70 | 140 | 2.5 |
| 80 | 160 | 1.7 |
| 90 | 180 | 1.0 |
Formula Explanations
1. Temperature-Based Density Correction
The densities of ethanol and water decrease with temperature due to thermal expansion. These changes affect dilution accuracy, so they are compensated using temperature-adjusted densities:
- ρethanol(T) = 0.80615 − 1.497 × 10-3 T + 6.35 × 10-6 T² [g cm-3]
- ρwater(T) = 0.999842594 + 6.793952 × 10-5 T − 9.09529 × 10-6 T² + 1.001685 × 10-7 T³ − 1.120083 × 10-9 T⁴ + 6.536332 × 10-12 T⁵ [g cm-3]
The density expressions above are non-linear 2nd- and 5th-order polynomial fits to NIST/IAPWS data, giving ≤ 0.05 % error from 0 – 50 °C for ethanol and from 0 – 40 °C for water.
2. ABV/Proof Temperature Correction
Hydrometers and alcohol meters are calibrated to 20 °C. When the solution temperature differs, the measured ABV or Proof must be corrected to reflect the actual ethanol content. The corrected alcohol fraction is:
Ccorr = Cmeas × [ (Cmeas·ρethanol(T) + (1−Cmeas)·ρwater(T)) ÷ (Cmeas·ρethanol(20) + (1−Cmeas)·ρwater(20)) ]
3. Volume from Mass
Using the corrected alcohol fraction, the actual volume of the solution is calculated by:
V = mass ÷ [ Ccorr·ρethanol(T) + (1−Ccorr)·ρwater(T) ]
4. Dilution Calculation
To dilute the solution to a lower ABV/Proof without changing the alcohol mass, we calculate the required target volume as:
Vtarget = (V × Ccorr) ÷ [ Dtarget × (1 − contraction) ]
Water to add = Vtarget − V
5. Volumetric Contraction
When ethanol and water are mixed, the final volume becomes slightly less than the sum of the parts due to molecular interactions — this is known as volumetric contraction.
- Contraction can be applied automatically using interpolated values based on ABV/Proof.
- Alternatively, a manual contraction factor can be entered if known.
- Note: When solution temperature correction is enabled, contraction is also adjusted with temperature using:
contraction(T) = contraction(20 °C) × [1 + 0.00065 × (T − 20)]