📖 Dew Point — Theory
Mathematical explanation of dew point using the August-Roche-Magnus formula. ↓ Download as PDF
What is the Dew Point?
The dew point temperature (Td) is the temperature to which air must be cooled at constant pressure and humidity until water vapor begins to condense — forming dew, frost, or fog.
Unlike relative humidity, the dew point is an absolute measure of atmospheric moisture. A dew point of 20 °C always means the same amount of water vapor regardless of air temperature.
The August-Roche-Magnus Formula
The Magnus formula is the most widely used practical approximation for dew point:
Step 1 — Intermediate variable α
α(T, RH) = ln(RH / 100) + (a · T) / (b + T)
Step 2 — Dew Point Td
Td = (b · α) / (a − α)
Accuracy: ±0.1 °C over −40 °C to 60 °C. Source: Alduchov & Eskridge (1996), J. Applied Meteorology.
Worked Example
T = 25 °C, RH = 60 %:
α = ln(60 / 100) + (17.625 × 25) / (243.04 + 25)
α = ln(0.6) + 440.625 / 268.04
α = −0.5108 + 1.6440 = 1.1332
Td = (243.04 × 1.1332) / (17.625 − 1.1332)
Td = 275.39 / 16.4918 = 16.70 °C
Interactive Visualisation
Hover over the chart to see dew point values. Each line represents a fixed relative humidity.
Temperature Spread
The spread (T − Td) indicates how far the air is from saturation:
- ● Spread < 3 °C — Near saturation. Mist, fog, or dew likely.
- ● Spread 3–10 °C — Moderate humidity. Comfortable but noticeable moisture.
- ● Spread > 10 °C — Dry air. Low risk of condensation.