The Tetens Formula, Explained

Every result this calculator produces — relative humidity, humidity ratio, dew point, enthalpy, specific volume, wet-bulb temperature — traces back to one equation: the saturation vapor pressure of water as a function of temperature. This page shows exactly what that equation is, where it came from, and how closely it matches reality.

The formula itself

The calculator uses the Tetens formula (O. Tetens, 1930), an empirical curve fit to the physical saturation vapor pressure of water over a liquid surface:

e_s(T) = 0.61078 × exp(17.27 × T / (T + 237.3))

where T is dry-bulb temperature in °C and the result is saturation vapor pressure in kPa. This single function is the engine behind every other calculation on this site — humidity ratio, dew point (by inverting it), enthalpy, and wet-bulb temperature (by solving it inside the psychrometer equation) all start from an e_s value computed this way.

Worked check against steam-table values

At 25°C: es = 0.61078 × exp(17.27 × 25 / 262.3) = 0.61078 × exp(1.646) = 0.61078 × 5.187 ≈ 3.17 kPa. The published steam-table value for water's saturation vapor pressure at 25°C is 3.169 kPa — the Tetens approximation lands within about a tenth of a percent of the reference value at this temperature, which is well inside the precision anyone could read off a printed chart by eye.

Why an approximation instead of the full reference equation

ASHRAE's own official psychrometric chart is built from the more complex Hyland-Wexler formulation — a longer equation with several more terms, designed for maximum accuracy across an unusually wide range including sub-freezing conditions. Tetens is a simpler, single-exponential fit that trades a small amount of accuracy at the extremes for a formula that's fast to evaluate and easy to invert algebraically (which matters directly for the dew-point calculation — see below). Over the normal HVAC comfort-and-process range, roughly 0–50°C, Tetens typically agrees with the full reference equation to within about 0.1–0.2%, which is smaller than the uncertainty most field instruments themselves carry.

What it assumes, and where it stops being valid

The formula as used here assumes saturation vapor pressure over liquid water, which is correct for the temperature range this calculator targets. Saturation over ice (relevant below 0°C, since ice has a slightly different, lower saturation vapor pressure than supercooled liquid water at the same temperature) requires a different formula entirely — this calculator does not switch to an ice-phase equation, so results for dry-bulb temperatures at or below freezing should be treated as approximate rather than exact.

Downstream: how this one function drives everything else

Once e_s(T) is available, relative humidity is simply your known vapor pressure e divided by e_s(T_db). Humidity ratio, dew point, enthalpy and specific volume all follow from there — see the humidity ratio and enthalpy pages for those next steps. Wet-bulb temperature is the one output that can't be solved directly from e_s alone — it requires searching for the temperature that satisfies the psychrometer equation, which is exactly what the wet-bulb page walks through.

FAQ

Is Tetens the same formula ASHRAE charts use?

Not exactly — ASHRAE's printed charts are built from the fuller Hyland-Wexler equation. Tetens is a widely used, simpler approximation that tracks it closely (within roughly 0.1–0.2% over the normal comfort range) while being much easier to invert for dew point and solve for wet-bulb.

Does this calculator work for sub-freezing air?

It will compute a number, but the underlying formula assumes saturation over liquid water, not ice, so results below 0°C dry-bulb should be treated as approximate rather than exact.

How accurate is it in practice?

Within about 0.1–0.2% of reference steam-table values across 0–50°C — accurate enough for field HVAC work, coil selection checks, and classroom problems, though not a replacement for a certified reference instrument in a metrology lab.

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