How this instrument works
Dew point is the temperature air must be cooled to, at constant pressure and constant moisture content, before it becomes saturated and water starts condensing out as dew, fog, or cloud droplets. It answers a question relative humidity alone cannot: humidity swings all day as air warms and cools even though the actual amount of water vapor in it stays fixed, while dew point tracks that vapor content directly, which is why forecasters treat it as the more honest measure of how muggy the air actually feels.
The formula comes from inverting the August–Roche–Magnus approximation for saturation vapor pressure, es(T) = 6.1094 exp(aT ⁄ (b+T)) in hectopascals. Actual vapor pressure equals RH ⁄ 100 times the saturation value at the air temperature, and dew point is defined as the temperature at which that same actual pressure would itself count as saturation. Setting the two exponential expressions equal and taking a natural log collapses a nonlinear pressure equation into the single term α, and two more lines of algebra isolate Td = bα ⁄ (a − α) — which is exactly why this page's formula looks like a fraction rather than a tidy closed form.
HVAC engineers use dew point to size cooling coils and stop supply ducts from sweating; pilots and grounds crews use it to judge how close conditions sit to fog or frost; cold-storage and greenhouse operators use it to keep produce from suffering condensation damage. The constants a = 17.27 and b = 237.7 °C used here are the classic Magnus values, accurate to roughly ±0.4 °C for air between 0 °C and 60 °C; below freezing, the vapor pressure curve over ice diverges from the curve over liquid water, and a different constant pair is needed for reliable frost-point work.
- Enter the current reading in Air temperature, °C — the actual dry-bulb temperature, not a forecast high or low.
- Enter Relative humidity, % — the 0–100 reading taken from a hygrometer, weather station, or forecast.
- Read Dew point, °C — the temperature the air must cool to before condensation begins.
- Compare the result to the overnight low: if the low is forecast near or below the dew point, expect dew, frost, or fog by morning.
Worked example — 25 °C air at 50% relative humidity
Take a room reading of 25.0 °C at 50.0% relative humidity, a fairly ordinary indoor pairing. First the intermediate term: α = 17.27 × 25 ⁄ (237.7 + 25) + ln(0.5) = 1.6435 − 0.6931 = 0.9504. That single number folds the temperature-dependence of the saturation curve and the log of the humidity ratio into one quantity.
Then Td = b·α ⁄ (a − α) = 237.7 × 0.9504 ⁄ (17.27 − 0.9504) = 225.90 ⁄ 16.3196 ≈ 13.842 °C, matching this calculator's own output of 13.842291097 °C for the same two inputs. Cool that room by about eleven degrees and moisture would start beading on a cold glass or windowpane; push it another ten degrees down and frost becomes possible once the air itself is below freezing.
Questions
Why does dew point stay steady while relative humidity swings all day?
Because relative humidity depends on both the water vapor in the air and the air's temperature, while dew point depends only on the vapor content. As the sun heats a parcel of air, its capacity to hold moisture rises, so RH falls even though nothing evaporated or condensed; the dew point barely moves because the actual amount of water vapor hasn't changed. That is why forecasters treat dew point as the steadier, more physically meaningful comfort figure.
What happens when relative humidity is 100%?
The dew point equals the air temperature exactly. At saturation the air already holds all the water vapor it can at that temperature, so no further cooling is needed to reach the condensation point — α reduces to aT ⁄ (b+T) alone, since ln(100/100) = 0, and solving Td = bα ⁄ (a−α) returns Td = T. This is the condition present inside fog and cloud.
Can the dew point ever come out higher than the air temperature?
No, not physically — a result like that points to a bad reading or a fast-moving front the sensor hasn't caught up with yet. Dew point marks the saturation point of the water vapor already present, and air can only be cooled toward that point, never past it; the algebra makes Td = T the ceiling, reached exactly at RH = 100%.
How accurate are the constants a = 17.27 and b = 237.7 °C?
To roughly ±0.4 °C for dew points between about 0 °C and 60 °C air temperature, which covers the large majority of everyday weather and indoor-climate work. These are the classic Magnus formula constants reproduced across meteorology handbooks; other constant sets trade this formula's one-line simplicity for a fraction of a degree more accuracy at sub-freezing temperatures or extremes of humidity.
Why does very low humidity push the dew point so far below air temperature?
Because the formula includes ln(RH ⁄ 100), and that term grows sharply negative as RH falls toward zero. At 25 °C and 50% RH the dew point sits about eleven degrees below air temperature, at 13.84 °C; drop RH to 10% at the same air temperature and the dew point falls to roughly −8.7 °C, a gap of nearly 34 degrees — because each halving of RH subtracts a similar chunk from α, while Td responds nonlinearly through the a − α denominator.
Is dew point the same thing as wet-bulb temperature?
No. Wet-bulb temperature is what a thermometer reads with its bulb wrapped in a wet wick while air evaporates from it, cooling the reading below the ordinary dry-bulb temperature; it always sits between the dew point and the air temperature. Dew point is a property of the water vapor content alone, independent of any evaporative cooling process, and the two only converge at 100% relative humidity, the same saturation condition where dew point equals air temperature.