Dew Point & Relative Humidity Calculator (Magnus)

Understanding the dew point and humidity calculator — concept and principle

The dew point is the temperature to which air must be cooled, at constant pressure and moisture content, for water vapour to start condensing. This calculator finds it from air temperature and relative humidity using the Magnus formula, and also reports absolute humidity, vapour pressure and humidity ratio.

Cooling shrinks how much vapour air can hold; at 16.69 °C the 18.96 hPa already there fills it.

How it is calculated

Saturation vapour pressure: e_s = 6.112 · exp(17.62·T / (243.12 + T)) hPa.
Actual vapour pressure: e = e_s · RH/100.
Dew point: with γ = ln(RH/100) + 17.62·T/(243.12 + T), T_d = 243.12·γ / (17.62 − γ).
Absolute humidity: 216.7 · e / (T + 273.15) g/m³ (e in hPa).
Humidity ratio: 622 · e / (1013.25 − e) g/kg dry air, assuming sea-level pressure.

The principle

Air at a given temperature can hold water vapour only up to its saturation vapour pressure, which rises steeply, roughly exponentially, with temperature. Relative humidity is the actual vapour pressure divided by that limit. Cooling air does not change its vapour content, so the dew point is simply the temperature at which the existing vapour pressure equals saturation. The Magnus form is an empirical fit to the Clausius–Clapeyron behaviour that is easy to invert; the constants 17.62 and 243.12 °C are those recommended by the WMO for water surfaces.

Worked example

Inputs: T = 25 °C, RH = 60%.
e_s = 6.112 · exp(17.62 × 25 / 268.12) ≈ 31.601 hPa; e = 0.6 × 31.601 ≈ 18.960 hPa.
γ = ln 0.6 + 1.64292 ≈ 1.55830; T_d = 243.12 × 1.55830 / (17.62 − 1.55830) ≈ 16.69 °C.
Absolute humidity: 216.7 × 18.960 / 298.15 ≈ 13.78 g/m³.
Humidity ratio: 622 × 18.960 / (1013.25 − 18.960) ≈ 11.86 g/kg.

Each point is the calculator re-run with only “Air temperature (°C)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Air temperature (°C)	Dew point (°C)
6.25	-0.951258051
12.5	4.938718461
18.8	10.82018133
25	16.69314901
31.2	22.55763988
37.5	28.41367229
50	40.10043481

How to read the result

Where does your result fall?

The dew point is a direct measure of how much moisture is in the air, unlike RH, which changes with temperature. As a rough guide, dew points below about 10 °C feel dry, mid-teens feel comfortable to slightly humid, and above about 20 °C feel muggy. Any surface colder than the dew point, such as a cold window or pipe, will collect condensation, which is the key test for mould and condensation risk.

Common mistakes

Using the formula for frost point below 0 °C, where saturation over ice is lower.
Forgetting that the humidity ratio depends on air pressure (it rises at altitude).
Comparing RH values taken at different temperatures.
Trusting extra decimals: sensor RH is often only accurate to ±2–3%.

Keep in mind: The Magnus formula is accurate to a small fraction of a degree in normal weather ranges, but humidity sensors carry their own errors. Building condensation assessments should follow the relevant standards and professional advice.

Frequently asked questions

Why can RH be high on a cold morning and low in the afternoon with the same air?

The moisture content stays the same, but warming raises e_s, so RH falls; the dew point barely changes.

What does 100% RH mean?

The air temperature equals the dew point, so the air is saturated and fog, dew or condensation can form.

Sources: WMO Guide to Instruments and Methods of Observation (WMO-No. 8), Annex on humidity formulae

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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