Domain conversions and dimensional blind spots

Values below were produced with pint 0.26.1 and SciPy 1.18.1 (CODATA 2022). Anything marked exact is fixed by definition and carries zero uncertainty.

Dimensional analysis does not catch these

Two quantities with the same dimensions convert freely, whether or not the conversion means anything.

The last two raise because they are dimensionally distinct. The first four are the dangerous ones: no tool will warn you.

Energy ladder

Molecular science quotes the same energy in at least six units, three of which are per-mole and therefore need the Avogadro constant.

Two traps. First, per-mole and per-particle units are not dimensionally interchangeable: eV is an energy, kJ/mol is an energy per amount of substance, and the conversion needs N_A. Pint will refuse Q(1, "eV").to("kJ/mol") and accept Q(1, "eV * N_A").to("kJ/mol"). Second, there are two calories and a factor of 1.00067 between them; thermochemical is the default in chemistry, IT in engineering.

Q(1, "eV * N_A").to("kJ/mol")            # 96.48533212331002 kilojoule / mole
Q(1, "1/cm").to("eV", "sp")              # 0.00012398419843320026 electron_volt
Q(298.15, "K").to("eV", "boltzmann")     # 0.02569257912108585 electron_volt

Spectroscopy

Wavelength, frequency, wavenumber, and photon energy are related by physics, not by dimensional analysis, and wavelength-frequency/energy relations are reciprocal — an uncertainty does not convert by the same factor as the value.

Q(532, "nm").to("THz", "sp")     # 563.5196578947367 terahertz
Q(532, "nm").to("1/cm", "sp")    # 18796.992481203004 / centimeter
Q(532, "nm").to("eV", "sp")      # 2.3305300457368467 electron_volt

Because E = hc/λ, a constant wavelength uncertainty becomes an energy uncertainty that scales as 1/λ². Propagate through the relation, do not scale the uncertainty by the value's conversion factor. scripts/convert_units.py --uncertainty does this with the conversion's local derivative.

The sp context assumes vacuum unless given a refractive index. With n=1.33, 532 nm is interpreted as the wavelength in that medium, giving 423.7 THz. A photon crossing an interface retains its frequency; its wavelength changes. Do not apply n to a vacuum wavelength merely because the experiment contains water.

Concentration

"ppm" alone is ambiguous: mass/mass, volume/volume, and mol/mol differ by the ratio of densities or molar masses. In environmental water chemistry ppm conventionally means mg/L, which equals mg/kg only because dilute water is close to 1 kg/L. In gas analysis it conventionally means volume/volume. State which.

Pint treats ppm and percent as plain dimensionless scale factors (1e-6 and 0.01), which is right for arithmetic and gives no protection against mixing the three senses. Defining ureg.define("ppm_v = 1e-6 = ppmv") only adds an alias-like scale; it provides no dimensional protection. To enforce semantic separation, use a custom base dimension (for example volume_fraction_kind = [volume_fraction_kind], then ppm_v = 1e-6 * volume_fraction_kind) and explicit adapters to physical dimensionless fractions. This is an application convention, not a new SI dimension.

Mass and amount of substance need the chemistry context and a molar mass:

Q(1, "g").to("mol", "chemistry", mw=Q(180.156, "g/mol"))   # 0.005550744909966918 mole

Pressure

Gauge and absolute pressure need an explicit reference pressure. Pint can define custom offset units, but a static offset cannot infer the actual ambient pressure. "psig" and "psia" have the same dimensions; a gauge reading needs the ambient pressure added before it can be used in a gas law. Vacuum work, autoclave protocols, and chromatography backpressures are where this bites.

Radiation, magnetism, rotation

Q(1, "Ci").to("Bq")               # 37000000000.0 becquerel   (exact by definition)
Q(1, "gauss").to("T", "Gaussian") # 9.999999999338245e-05 tesla
Q(1, "rpm").to("rad/s")           # 0.10471975511965977 radian / second

Gauss fails without the Gaussian context: CGS electromagnetic units have different dimensions from SI ones, not merely different scales. Magnetic field strength H (A/m, oersted) and magnetic flux density B (T, gauss) are distinct quantities that literature routinely calls "the field".

Mass spectrometry

The unified atomic mass unit and the dalton are the same thing: 1 Da = 1.66053906892e-27 kg (CODATA 2022, relative standard uncertainty 3.1e-10).

m/z is conventionally reported as a dimensionless number: the ratio of mass in daltons to charge number. The thomson (Th) exists but is not SI and is rarely used. Treating m/z as a mass is wrong for any ion with z > 1, which is most of a protein spectrum.

Logarithmic quantities

pH, pKa, dB, and magnitudes are logarithms of ratios. They do not add, average, or propagate like ordinary quantities:

• the arithmetic mean of pH 5 and 7 is pH 6 on the pH scale. If the target is mean hydrogen-ion activity, transform to activity first. Mixing two solutions needs volume, activity coefficients, acid-base equilibria and buffering, not merely averaging;
• pH is minus log10 of hydrogen-ion activity, not generally concentration. Locally, u(a)/a = ln(10)*u(pH); large uncertainties give asymmetric transformed intervals;
• adding two dB quantities multiplies the underlying linear quantities (see pint-recipes.md);
• decibel scales differ by reference: dBm references 1 mW, dBW references 1 W, dBV references 1 V, and dB alone references nothing until you say so.

Temperature

Kelvin and rankine are ratio scales and behave normally. Celsius and Fahrenheit are interval scales: 20 degC is not "twice" 10 degC, and their differences live in delta_degC / delta_degF. See pint-recipes.md for what pint permits.

Absolute zero is exactly 273.15 K below 0 degC — scipy.constants.zero_Celsius.

Constants: which values, and which uncertainties

The 2019 SI redefinition fixed several constants exactly, so their relative standard uncertainty is zero and no future CODATA release will change them:

These are five of the seven SI defining constants; the cesium frequency and luminous efficacy complete the set. Quantities derived only from exact defining constants are also exact (for example R = N_A*k and the Faraday constant N_A*e). Electron mass, the gravitational constant, fine-structure constant, and Rydberg constant are measured. Check each uncertainty rather than declaring all other constants measured.

import scipy.constants as constants

constants.value("electron mass")       # 9.1093837139e-31
constants.unit("electron mass")        # kg
constants.precision("electron mass")   # 3.07e-10  relative standard uncertainty
constants.precision("Planck constant") # 0.0       exact by definition

scipy.constants in SciPy 1.18.1 defaults to CODATA 2022; SciPy 1.11 and earlier served CODATA 2018; SciPy 1.15 introduced the CODATA 2022 data. Hard-coding a constant pins you to whichever release you copied it from and discards its uncertainty entirely. scripts/audit_units.py flags literals that match a known constant (CONST001).

Note also that constants.precision returns a relative standard uncertainty. The absolute standard uncertainty is abs(value) * precision. Nominal constants used in Pint definitions do not automatically carry the measured constant's uncertainty.

Primary definitions reviewed 2026-10-01: BIPM SI Brochure, updated 2026, NIST CODATA 2022, IUPAC pH, and Pint 0.26.1 definitions.