Alcohol Dilution Calculator — Spirit Proofing

The density function $\rho(p,T)$ implements the Wagenbreth–Blanke polynomial in OIML R22 (1975), pp. 12–13, with the published coefficients checked against Chanson (2015), Figure 1, printed p. 9 (attached PDF page 11). The polynomial is evaluated directly; no alcoholometric table is reproduced.

For ethanol mass fraction $p$ and reference temperature $T_r$, the ethanol volume fraction is

ABV input is divided by 100, and US proof input by 200. A 34-iteration bisection obtains mass fraction from strength. The reference temperature is 20 °C for ABV and 60 °F for US proof.

For an observed glass alcoholmeter reading, first infer its scale density $\rho_i$ at calibration temperature. Correct the displacement of the expanded glass using

Invert $\rho(p_s,T_s)=\rho_{obs}$ for the true starting mass fraction. Already corrected strength bypasses that correction. The spirit temperature still corrects its measured volume.

The required water follows conservation of ethanol and total mass:

The final volume is $m_f/\rho(p_t,T_r)$ and the water dose volume is $m_w/\rho(0,T_w)$. Unit conversions are explicit. Contraction compares both separate liquid volumes and the final volume at the same reference temperature. The signed difference $\Delta V=V_{s,r}+V_{w,r}-V_f$ is positive for contraction and negative for expansion. This describes dilution of an existing mixture: low-strength spirit can expand on adding water even though its original formation from pure ethanol and water involved contraction. OIV's 20 °C densities independently confirm expansion for dilution from 20% to 10% ABV. The balances and normalization are derived here.

The mass-balance approach agrees with the dilution principle in 27 CFR §30.66. Its 191-to-188 proof example rounds 95.5/94 to 1.01 too early: the printed 1.84 gal becomes 1.88745 gal if its own component values retain precision. This model gives about 1.88445 gal per 100 gal, reflecting a small difference between OIML densities and the historical TTB component values. The equations are not altered to reproduce the prematurely rounded result.

The dilution curves are parameterized by the water-dose ratio $r=V_{w,r}/V_{s,r}$, with mass fraction $p(r)=p_s/[1+r\rho_w/\rho_s]$ at the same reference temperature. The exact calculated target ratio is a retained grid point. Each interval is tested at quarter, midpoint and three-quarter positions and bisected when its linear-interpolation error exceeds one quarter of $0.001+0.00005|S|$ strength units. A separate verification samples nine interior positions in every final segment of both displayed charts and requires the error to remain below the full criterion. ABV and US-proof curves each have explicit scale, reference temperature and volume-ratio axes.

• Clear, liquid ethanol–water mixtures and pure added water; no sugar, extract, denaturant or significant other constituents.
• No loss of ethanol or water through evaporation, transfer or reaction. Ethanol mass is conserved.
• The selected reference temperature defines the starting and target strength scales. The hydrometer calibration must match it.
• An observed alcoholmeter reading assumes a glass cubic expansion coefficient of 25 × 10⁻⁶/K. Instrument calibration errors, surface-tension and meniscus corrections, air-buoyancy corrections and a different glass coefficient are outside this model. Use already corrected strength when those corrections have been made separately.
• Enter actual liquid volume at the specified spirit temperature. Vessel expansion is not included.
• The final volume is reported after thermal equilibrium at the reference temperature. No mixing-temperature or heat-release prediction is made.

Spirit and dosing-water temperatures: 0–40 °C, within the OIML polynomial's published −20 to +40 °C range. Both liquids must remain liquid. Strength: 0.1–100% ABV or 0.1–200 US proof, subject to a physically possible hydrometer density. The target cannot exceed the corrected starting strength. Very small targets imply very large water doses; numerical precision is not a statement of measurement accuracy.

This is an engineering implementation of OIML R22:1975. US proof calculations use the same density model evaluated at 60 °F; they do not implement all rounding conventions or prescribed tables of the TTB Gauging Manual. The regulatory examples follow 27 CFR Part 30, April 1, 2025 edition, reviewed for this tool on October 29, 2026. For taxation, labeling or custody transfer, check against the standard and rules in force and use the required official gauging procedure. Dissolved solids require a suitable obscuration or distillation method outside this calculator.