# What is the dew point?

Computes the dew point from air temperature and relative humidity with the Magnus formula, or the relative humidity or air temperature from the other two.

- Page: https://www.acalculator.org/physics/dew-point-calculator
- JSON spec: https://www.acalculator.org/physics/dew-point-calculator.json
- Version: 0a266617fbe9

## Default answer

Example with the default inputs (Air temperature 67.9999999999999 °F, Relative humidity 50%): At 68 °F and 50% relative humidity, the dew point is 48.7 °F.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| t | Air temperature | The dry-bulb air temperature. |
| rh | Relative humidity | The relative humidity over water, in percent. |
| td | Dew point | The temperature to which the air must cool, at the same pressure, to become saturated. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| temp | Air temperature | The dry-bulb air temperature. |
| rh | Relative humidity | The relative humidity over water, in percent. |
| dewPoint | Dew point | The temperature to which the air must cool, at the same pressure, to become saturated. |

## Method

Td = b·γ ÷ (a − γ), where γ = ln(RH ÷ 100) + a·T ÷ (b + T), a = 17.625 and b = 243.04 °C, with T and Td in °C (Magnus formula, Alduchov and Eskridge 1996).

## Assumptions

- Saturation is over liquid water, also below 0 °C. Over ice, the frost point is a little higher than this dew point.
- The Magnus coefficients a = 17.625 and b = 243.04 °C fit the saturation vapor pressure from −40 °C to 50 °C, so the air temperature and the dew point must both be in that range.
- Relative humidity is between 0% (not included) and 100%.

## Worked examples

1. t = 293.15, rh = 50% gives td = 282.411107. Source: hand calculation in content.mdx: γ = ln 0.5 + 17.625 × 20 ÷ 263.04 = 0.64695; Td = 243.04 × 0.64695 ÷ (17.625 − 0.64695) = 9.26 °C (Alduchov and Eskridge 1996 coefficients).
2. t = 303.15, rh = 70% gives td = 297.080468. Source: hand calculation in content.mdx: γ = ln 0.7 + 17.625 × 30 ÷ 273.04 = 1.57985; Td = 243.04 × 1.57985 ÷ (17.625 − 1.57985) = 23.93 °C.
3. t = 298.15, td = 298.15 gives rh = 100%. Source: definition of the dew point (WMO No. 8): at T = Td the air is saturated, RH = 100%.
4. rh = 40%, td = 278.15 gives t = 292.047809. Source: hand calculation in content.mdx: s = 17.625 × 5 ÷ 248.04 − ln 0.4 = 1.27158; T = 243.04 × 1.27158 ÷ (17.625 − 1.27158) = 18.90 °C.

## FAQ

### What is the dew point?

The dew point is the temperature the air must cool to, at the same pressure and moisture content, before it is saturated and water starts to condense as dew, fog or cloud. The higher the dew point, the more water vapor is in the air.

### How is the dew point calculated?

With the Magnus formula: γ = ln(RH ÷ 100) + 17.625 × T ÷ (243.04 + T), then Td = 243.04 × γ ÷ (17.625 − γ), with temperatures in °C. At 20 °C and 50% humidity, the dew point is 9.26 °C (48.7 °F).

### Can the dew point be higher than the air temperature?

No. When the air cools to its dew point it is saturated (100% relative humidity), and extra vapor condenses. So the dew point is at most the air temperature, and equal to it only at 100% humidity.

### What dew point feels humid?

The US National Weather Service uses this rough summer guide: a dew point of 55 °F (13 °C) or lower feels dry and comfortable, 55 to 65 °F (13 to 18 °C) starts to feel sticky, and 65 °F (18 °C) or higher feels oppressive. Relative humidity alone can mislead, because the same humidity holds much more water on a hot day than on a cold one.

### How accurate is the Magnus formula?

With the Alduchov and Eskridge (1996) coefficients, the saturation vapor pressure it uses is within about 0.4% of reference values from −40 °C to 50 °C. Outside that range, for the air temperature or the dew point, the calculator gives no answer.

## Sources

- Alduchov, O. A., and R. E. Eskridge (1996). Improved Magnus form approximation of saturation vapor pressure. Journal of Applied Meteorology 35(4), 601–609. https://doi.org/10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2
- World Meteorological Organization, Guide to Instruments and Methods of Observation (WMO-No. 8), Volume I, Chapter 4, Measurement of humidity: definitions of dew point and relative humidity. https://library.wmo.int/idurl/4/68695
- National Weather Service, The Dew Point vs Humidity: comfort guide for summer dew points. https://www.weather.gov/arx/why_dewpoint_vs_humidity
- NIST Special Publication 811 (2008), section 4.2.1.1: T/K = t/°C + 273.15, and Appendix B.8: t/°C = (t/°F − 32) ÷ 1.8. https://www.nist.gov/pml/special-publication-811