Enter any two of air temperature, relative humidity and dew point (leave the third blank). The blank one is calculated, along with estimates of the vapor pressure, saturation vapor pressure and absolute humidity, and a graph of humidity against the dew point.
Fill in exactly two of the three fields (the most common use is to enter the air temperature and relative humidity to find the dew point). Choose °C, °F or K for the temperatures in the menus.
Result and graph
Enter numbers in two of air temperature, relative humidity and dew point in the fields on the left and press "Calculate". The remaining one will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and graphs
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Dew point from air temperature and relative humidity (Magnus approximation)
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Relative humidity from air temperature and dew point
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Air temperature from relative humidity and dew point
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Saturation vapor pressure (Magnus approximation)
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Vapor pressure and absolute humidity (estimates from the Magnus approximation)
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the air temperature and humidity (the relative humidity in the forecast), and you get the dew point on the spot - the temperature at which water droplets (condensation) start to form when the air is cooled
- Enter any two of air temperature, relative humidity and dew point to work out the third (you can also find the humidity from the dew point, or the air temperature from the humidity and dew point)
- Temperatures can be entered in °F, °C or K, and results are shown in all three units
- You also get estimates of the vapor pressure, the saturation vapor pressure and the absolute humidity (grams of water vapor per cubic meter)
- A graph shows at a glance how much the dew point drops as the humidity goes down
The calculations on this page use the Magnus approximation (coefficients a = 17.27 and b = 237.7), which is widely used in meteorology. It is accurate enough for everyday use, but it is still an approximation and can differ from measured values at very low or very high temperatures. The vapor pressure and absolute humidity are estimates from the same approximation.
What is this calculation used for?
Preventing window condensation in winter (how cold the glass can get before it fogs)
In a room at 68°F and 60% humidity, the dew point is about 53.6°F. So once the window glass, cooled by the outside air, drops below about 54°F, condensation starts to form on it.
You can plan the fix in numbers too. At the same room temperature, lowering the humidity to 50% drops the dew point to about 48.7°F, and if the glass stays warmer than that, it stays dry. The usual advice, "don't over-humidify" and "insulate the windows (storm windows, insulating film) to keep the glass warmer", both aim for the same thing: glass surface temperature > dew point.
Preventing mold on cold walls and in closets
Even in the same room, the relative humidity is higher wherever it is colder. When air at 68°F and 60% humidity (dew point about 53.6°F) reaches a north-facing wall whose surface is cooled to 59°F, the relative humidity right at the wall is about 82%. Mold generally grows more easily at higher humidity and is often said to become active above about 80%, so mold can appear only on the wall, in the closet or behind furniture, even when the humidity in the middle of the room is fine.
Moving furniture a few inches away from the wall and airing out closets both keep moist air from sitting next to cold surfaces.
How air conditioners remove moisture, and why a cold glass "sweats"
Air at 86°F and 70% humidity has a dew point of about 75°F. Inside an air conditioner, the cooling coil is much colder than that (around 50°F), so air passing over it drops far below its dew point, water vapor turns into droplets, and the water drains outside through the condensate line. This is how an air conditioner dehumidifies, even in normal cooling mode.
A glass of iced tea "sweating" in summer is the same thing: the surface of the glass is colder than the dew point of the room air, so condensation forms on it.
Forecasting fog (fog forms when the temperature falls to the dew point)
With an evening temperature of 59°F and 85% humidity, the dew point is about 54.5°F. On a clear night with light wind, the ground keeps losing heat and the air keeps cooling. If the temperature drops close to 54.5°F by dawn, the whole layer of air becomes saturated and fog is likely.
Forecasters watch the gap between the air temperature and the dew point (the dew point depression, or spread). The smaller the spread, the more likely fog and low clouds are. When a forecast discussion mentions a small "temperature–dew point spread", it is the difference between the two temperatures on this page.
Humidity control in server rooms, factories and museums
Places that handle precision equipment or valuable collections sometimes control the air by the dew point itself, not only the relative humidity. ASHRAE's thermal guidelines for data centers state the recommended range with a dew point limit, because condensation on cold pipes or on surfaces near the outside can cause equipment failure, electrical faults and rust.
For example, a room at 75°F and 45% humidity has a dew point of about 52°F. So you can manage the condensation risk as "keep every surface in the room warmer than about 52°F (or lower the dew point further)". Air that is too dry causes more static electricity, so the humidity is kept between upper and lower limits.
Formulas and graphs
Dew point from air temperature and relative humidity (Magnus approximation)
Graph
Standard notation
(the usual math form)
\(\gamma\)
\(=\)
\(\ln\left(\dfrac{RH}{100}\right)\)
\(+\)
\(\dfrac{17.27\,T}{237.7 + T}\)
\(T_d\)
\(=\)
\(237.7\,\gamma\)
\(\div\)
\((17.27 - \gamma)\)
In words
(symbols replaced with words)
③
intermediate \(\gamma\)
\(=\)
①
humidity term
\(+\)
②
temperature term
⑥
dew point \(T_d\)
\(=\)
④
237.7 × \(\gamma\)
\(\div\)
⑤
17.27 − \(\gamma\)
The formula in words
①
Add
the humidity term ln(relative humidity \(RH\) (%) ÷ 100)
and
②
the temperature term 17.27 × air temperature \(T\) (°C) ÷ (237.7 + air temperature \(T\))
, and you get
③
the intermediate value \(\gamma\) (gamma, a number for how moist the air is)
. Next, divide
④
237.7 × \(\gamma\)
by
⑤
17.27 − \(\gamma\)
, and you get the
⑥
dew point \(T_d\) (°C)
Quick example
The dew point at an air temperature of 20°C (68°F) and 65% relative humidity is (humidity term = ln(0.65) ≈ −0.4308, temperature term ≈ 1.3403)
intermediate γ
\(=\)
humidity term (−0.4308)
\(+\)
temperature term (1.3403)
\(\gamma = -0.4308 + 1.3403 = 0.9095\)
\(T_d = \dfrac{237.7 \times 0.9095}{17.27 - 0.9095} \approx \dfrac{216.2}{16.36} \approx 13.2\ \ (^\circ C) \approx 55.8\ \ (^\circ F)\)
Key idea
The intermediate value \(\gamma\) (gamma) sums up "how moist the air is now" in one number. The higher the humidity or the air temperature, the larger \(\gamma\) and the higher the dew point.
The air temperature \(T\) goes into the formula in °C (convert °F or K to °C first: \(T_{\mathrm{C}} = (T_{\mathrm{F}} - 32) \times \dfrac{5}{9}\)). At 100% relative humidity, \(\ln(1) = 0\), so the dew point is exactly equal to the air temperature (the air already holds all the water vapor it can, and any cooling starts condensation right away).
The coefficients 17.27 and 237.7 are constants of the Magnus approximation, chosen to fit measured saturation vapor pressures of water.
Relative humidity from air temperature and dew point
Graph
Standard notation
(the usual math form)
\(RH\)
\(=\)
\(100\)
\(\times\)
\(\exp\left(\dfrac{17.27\,T_d}{237.7 + T_d}\right)\)
\(\div\)
\(\exp\left(\dfrac{17.27\,T}{237.7 + T}\right)\)
In words
(symbols replaced with words)
④
rel. humidity \(RH\)
\(=\)
③
to percent \(100\)
\(\times\)
①
dew point term
\(\div\)
②
temperature term
The formula in words
①
Take
the dew point \(T_d\) term (it matches the water vapor the air actually holds now)
,
②
divide it by
the air temperature \(T\) term (it matches the most water vapor the air can hold at that temperature)
,
③
multiply by
\(100\) to turn it into a percentage
,
④
and you get the
relative humidity \(RH\) (%)
Quick example
The relative humidity at an air temperature of 25°C (77°F) and a dew point of 15°C (59°F) is (dew point term ≈ 2.7875, temperature term ≈ 5.1733)
relative humidity \(RH\)
\(=\)
100
\(\times\)
dew point term (2.7875)
\(\div\)
temperature term (5.1733)
\(100 \times 2.7875 \div 5.1733 \approx 53.9\ \ (\%)\)
Key idea
\(\exp\) is the natural exponential function (a power of Euler's number \(e \approx 2.718\)). The two terms are each proportional to the saturation vapor pressure at their temperature (formula (4) below), so this formula is the very definition of relative humidity: "water vapor the air holds now ÷ the most water vapor it can hold".
The closer the dew point is to the air temperature, the closer the relative humidity is to 100% (damp and muggy). When the dew point is far below the air temperature, the relative humidity is low (dry).
Air temperature from relative humidity and dew point
Graph
Standard notation
(the usual math form)
\(\gamma_t\)
\(=\)
\(\dfrac{17.27\,T_d}{237.7 + T_d}\)
\(-\)
\(\ln\left(\dfrac{RH}{100}\right)\)
\(T\)
\(=\)
\(237.7\,\gamma_t\)
\(\div\)
\((17.27 - \gamma_t)\)
In words
(symbols replaced with words)
③
intermediate \(\gamma_t\)
\(=\)
①
dew point term
\(-\)
②
humidity term
⑥
air temp. \(T\)
\(=\)
④
237.7 × \(\gamma_t\)
\(\div\)
⑤
17.27 − \(\gamma_t\)
The formula in words
①
From
the dew point term 17.27 × dew point \(T_d\) (°C) ÷ (237.7 + dew point \(T_d\))
,
②
subtract
the humidity term ln(relative humidity \(RH\) (%) ÷ 100)
, and you get
③
the intermediate value \(\gamma_t\) (gamma sub t)
. Next, divide
④
237.7 × \(\gamma_t\)
by
⑤
17.27 − \(\gamma_t\)
, and you get the
⑥
air temperature \(T\) (°C)
Quick example
The air temperature at 50% relative humidity and a dew point of 10°C (50°F) is (dew point term ≈ 0.6972, humidity term = ln(0.5) ≈ −0.6931)
intermediate γt
\(=\)
dew point term (0.6972)
\(-\)
humidity term (−0.6931)
\(\gamma_t = 0.6972 - (-0.6931) = 0.6972 + 0.6931 \approx 1.3904\)
\(T = \dfrac{237.7 \times 1.3904}{17.27 - 1.3904} \approx \dfrac{330.5}{15.88} \approx 20.8\ \ (^\circ C) \approx 69.4\ \ (^\circ F)\)
Key idea
This is formula (1) (the dew point formula) solved again for the air temperature \(T\). It looks so much like formula (1) because, in the Magnus approximation, the air temperature and the dew point play symmetric roles.
The humidity is 100% or less, so \(\ln(RH \div 100)\) is 0 or negative. Subtracting it makes \(\gamma_t\) at least as large as the dew point term. So the calculated air temperature is always at or above the dew point, which fits the rule that the dew point never exceeds the air temperature.
Saturation vapor pressure (Magnus approximation)
Graph
Standard notation
(the usual math form)
\(e_s(T)\)
\(=\)
\(6.112\)
\(\times\)
\(\exp\left(\dfrac{17.27\,T}{237.7 + T}\right)\)
In words
(symbols replaced with words)
③
saturation v.p. \(e_s\)
\(=\)
①
constant \(6.112\)
\(\times\)
②
temperature term
The formula in words
①
Multiply
the constant \(6.112\) (the saturation vapor pressure at 0°C, in hPa)
by
②
the air temperature \(T\) (°C) term (a multiplier that grows with temperature)
, and you get the
③
saturation vapor pressure \(e_s(T)\) (hPa)
Quick example
The saturation vapor pressure at 20°C (68°F) is (temperature term = exp(1.3403) ≈ 3.8203)
saturation v.p. \(e_s\)
\(=\)
6.112
\(\times\)
temperature term (3.8203)
\(6.112 \times 3.8203 \approx 23.3\ \ (\mathrm{hPa})\)
Key idea
The saturation vapor pressure is the pressure of water vapor when air at that temperature holds as much as it can. It rises on a steep curve as the temperature goes up (about 23.3 hPa at 20°C/68°F, about 42.3 hPa at 30°C/86°F). This "warmer air can hold more" behavior explains condensation, fog and dehumidifying.
Formulas (1) to (3) on this page all come from this saturation vapor pressure formula (the Magnus approximation). Some science books describe the same idea as the most water vapor a cubic meter of air can hold (in g/m³) instead of a pressure (in hPa); the meaning is the same. (1 hPa is the same as 1 millibar, the unit used on US weather maps.)
Vapor pressure and absolute humidity (estimates from the Magnus approximation)
Standard notation
(the usual math form)
\(e\)
\(=\)
\(e_s(T_d)\)
\(AH\)
\(=\)
\(216.7\)
\(\times\)
\(e\)
\(\div\)
\((T + 273.15)\)
In words
(symbols replaced with words)
②
vapor pressure \(e\)
\(=\)
①
\(e_s\) at dew point
⑥
abs. humidity \(AH\)
\(=\)
③
constant \(216.7\)
\(\times\)
④
vapor pressure \(e\)
\(\div\)
⑤
absolute temp. (K)
The formula in words
①
The saturation vapor pressure at the dew point \(e_s(T_d)\) (formula (4) with the dew point put in)
is exactly
②
the vapor pressure \(e\) (hPa, the pressure of the water vapor the air actually holds now)
. Next, multiply
③
the constant \(216.7\)
by
④
the vapor pressure \(e\) (hPa)
, divide by
⑤
the absolute temperature (air temperature \(T\) + 273.15) (K)
, and you get the
⑥
absolute humidity \(AH\) (\(\mathrm{g/m^3}\))
Quick example
At an air temperature of 20°C (68°F) and a dew point of 13.2°C (about 55.8°F) (formula (4) gives \(e_s(13.2) \approx 15.2\))
abs. humidity \(AH\)
\(=\)
216.7
\(\times\)
vapor pressure (15.2)
\(\div\)
absolute temp. (293.15)
\(e = e_s(13.2) \approx 15.2\ \ (\mathrm{hPa})\)
\(AH = \dfrac{216.7 \times 15.2}{20 + 273.15} \approx 11.2\ \ (\mathrm{g/m^3})\)
Key idea
"Vapor pressure = saturation vapor pressure at the dew point" is just another way of stating what the dew point is (air cooled to its dew point holds exactly as much water vapor as it can).
The absolute humidity is the mass of water vapor (in grams) in 1 cubic meter of air. Unlike relative humidity (%), it hardly changes when the air temperature changes, so it is sometimes used to manage mold, dust mites and humidifiers. The constant 216.7 comes from the gas constant of water vapor.
The vapor pressure, saturation vapor pressure and absolute humidity on this page are all estimates calculated consistently with the Magnus approximation in formula (4) (sources that use more precise formulas can differ by up to about 1%).
The dew point is the temperature at which condensation (water droplets) starts to form as air is cooled. It can be calculated from the air temperature and relative humidity with the Magnus approximation. At 100% humidity the dew point equals the air temperature, and the lower the humidity, the lower the dew point. When the dew point is below freezing, frost forms instead of dew.
Symbols and terms
Symbols
| \(T_d\) | tee sub dee | The dew point, the temperature at which condensation (water droplets) starts to form when the air is cooled. The formulas use °C. |
| \(T\) | tee | The air temperature. All formulas on this page use °C (if you enter °F or K, it is converted to °C automatically before calculating). |
| \(RH\) | R H | Relative humidity, the "humidity" in the weather forecast. Put the percentage from 0 to 100 into the formula as is (for example, 65% humidity → 65). |
| \(\gamma\), \(\gamma_t\) | gamma, gamma sub t | Intermediate values in the calculation. Each sums up "how moist the air is now" in one number, and going through it lets you find the dew point or the air temperature with one formula. |
| \(e_s(T)\) | e sub s of T | The saturation vapor pressure at temperature T (hPa), the pressure of water vapor when air at that temperature holds as much as it can. It rises with temperature. |
| \(e\) | e | The vapor pressure (hPa), the pressure of the water vapor the air actually holds now. It equals the saturation vapor pressure at the dew point. |
| \(AH\) | A H | The absolute humidity, the mass of water vapor in 1 cubic meter of air (g/m³). |
| \(\exp\) | exponential | The natural exponential function. \(\exp(x)\) is Euler's number \(e \approx 2.718\) raised to the power \(x\). Use the EXP function in Excel or math.exp in Python. |
| \(\ln\) | natural log (L N) | The natural logarithm. \(\ln(x)\) is the power you raise \(e\) to in order to get \(x\), so it does exactly the opposite of \(\exp\). \(\ln(1) = 0\), and it is negative when \(x\) is less than 1. Use the LN function in Excel or math.log in Python. |
Terms
| dew point | The temperature at which water vapor starts to turn into droplets (condensation starts) as air is cooled. Also called the dew point temperature. The more water vapor in the air, the higher it is, so it is also a good guide to how muggy it feels (a high dew point is a muggy day). |
| relative humidity | How much water vapor the air holds, as a percentage of the most it can hold at that temperature. The "humidity" in the weather forecast is the relative humidity. With the same amount of water vapor, the relative humidity goes up when the air cools, because the limit gets smaller. |
| absolute humidity | The mass of water vapor in 1 cubic meter of air (g/m³). Unlike relative humidity, it hardly changes with the air temperature, so it is used to compare how dry the air is in different rooms, to manage mold and dust mites, and to run humidifiers. |
| saturation vapor pressure | The pressure of water vapor when the air holds as much as it can at that temperature (hPa). It rises on a steep curve as the temperature goes up. The "maximum amount of water vapor per cubic meter (g/m³)" found in some science books is the same idea expressed as a mass instead of a pressure. |
| vapor pressure | The pressure of the water vapor the air actually holds (hPa). "Vapor pressure ÷ saturation vapor pressure × 100" is the relative humidity (%). |
| condensation | What happens when air touches something colder than its dew point and the extra water vapor turns into droplets. Water on the inside of a window in winter and on the outside of a glass of iced drink are both condensation. Whether condensation forms depends on whether the surface temperature is below the dew point. |
| frost | Ice crystals that form directly from water vapor, without first becoming droplets, when the dew point is below 32°F (0°C). This temperature is sometimes called the frost point to tell it apart from the dew point. |
| Magnus approximation | An approximate formula for finding the saturation vapor pressure easily from the temperature, named after the 19th-century physicist Heinrich Gustav Magnus. There are several sets of coefficients; this page uses the classic set a = 17.27, b = 237.7 and 6.112 hPa (some sources use improved coefficients such as 17.62 and 243.12, so their values can differ slightly). |
| dew point depression | The air temperature minus the dew point, also called the temperature–dew point spread. Meteorologists use it to describe how moist the air is. The smaller the spread (the closer the air temperature and dew point), the more easily fog and clouds form. |
| °F (Fahrenheit) | The temperature unit used in the US. Water freezes at 32°F and boils at 212°F. To convert from Celsius, °F = °C × 9/5 + 32. |
| kelvin | The unit of absolute temperature used in science (symbol K). It is the Celsius temperature plus 273.15 (0°C = 273.15 K). The "T + 273.15" in the absolute humidity formula converts the air temperature to kelvins. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Percentages (Grade 6) |
|
| Variables and substitution (Grades 6–7) |
|
| Water vapor and humidity (middle school earth science) |
|
| Temperature units (middle school science) |
|
| Exponential and logarithmic functions (Algebra 2) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table for the dew point from air temperature and relative humidity
| Air temperature (°F) | 68 |
| Relative humidity (%) | 65 |
| Intermediate value γ | =LN(B2/100)+17.27*((B1-32)*5/9)/(237.7+(B1-32)*5/9) |
| Dew point (°F) | =237.7*B3/(17.27-B3)*9/5+32 |
Table for relative humidity from air temperature and dew point
| Air temperature (°F) | 77 |
| Dew point (°F) | 59 |
| Relative humidity (%) | =100*EXP(17.27*((B2-32)*5/9)/(237.7+(B2-32)*5/9)-17.27*((B1-32)*5/9)/(237.7+(B1-32)*5/9)) |
Table for air temperature from relative humidity and dew point
| Relative humidity (%) | 50 |
| Dew point (°F) | 50 |
| Intermediate value γt | =17.27*((B2-32)*5/9)/(237.7+(B2-32)*5/9)-LN(B1/100) |
| Air temperature (°F) | =237.7*B3/(17.27-B3)*9/5+32 |
Table for saturation vapor pressure, vapor pressure and absolute humidity (Magnus approximation)
| Air temperature (°F) | 68 |
| Dew point (°F) | 55.8 |
| Saturation vapor pressure (hPa) | =6.112*EXP(17.27*((B1-32)*5/9)/(237.7+(B1-32)*5/9)) |
| Vapor pressure (hPa) | =6.112*EXP(17.27*((B2-32)*5/9)/(237.7+(B2-32)*5/9)) |
| Absolute humidity (g/m3) | =216.7*B4/((B1-32)*5/9+273.15) |
After pasting, the number cells at the top are your inputs and the formula cells are calculated automatically. The Magnus approximation works in °C, so each formula converts °F to °C inside ((°F − 32) × 5/9) and converts the answer back to °F where needed.
The first table finds the dew point from the air temperature and relative humidity. With the example values (68°F, 65%), B3 (the intermediate value γ) shows about 0.9095 and B4 about 55.8 (°F).
The second table works out the relative humidity. With the example values (77°F air, 59°F dew point), B3 shows about 53.88 (%).
The third table works out the air temperature. With the example values (50% humidity, 50°F dew point), B4 shows about 69.5 (°F).
In the fourth table, the example values (68°F air, 55.8°F dew point) give a saturation vapor pressure of about 23.3 (hPa), a vapor pressure of about 15.2 (hPa) and an absolute humidity of about 11.2 (g/m3).
The first table finds the dew point from the air temperature and relative humidity. With the example values (68°F, 65%), B3 (the intermediate value γ) shows about 0.9095 and B4 about 55.8 (°F).
The second table works out the relative humidity. With the example values (77°F air, 59°F dew point), B3 shows about 53.88 (%).
The third table works out the air temperature. With the example values (50% humidity, 50°F dew point), B4 shows about 69.5 (°F).
In the fourth table, the example values (68°F air, 55.8°F dew point) give a saturation vapor pressure of about 23.3 (hPa), a vapor pressure of about 15.2 (hPa) and an absolute humidity of about 11.2 (g/m3).
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table for the dew point from air temperature and relative humidity
| Air temperature (°F) | 68 |
| Relative humidity (%) | 65 |
| Intermediate value γ | =LN(B2/100)+17.27*((B1-32)*5/9)/(237.7+(B1-32)*5/9) |
| Dew point (°F) | =237.7*B3/(17.27-B3)*9/5+32 |
Table for relative humidity from air temperature and dew point
| Air temperature (°F) | 77 |
| Dew point (°F) | 59 |
| Relative humidity (%) | =100*EXP(17.27*((B2-32)*5/9)/(237.7+(B2-32)*5/9)-17.27*((B1-32)*5/9)/(237.7+(B1-32)*5/9)) |
Table for air temperature from relative humidity and dew point
| Relative humidity (%) | 50 |
| Dew point (°F) | 50 |
| Intermediate value γt | =17.27*((B2-32)*5/9)/(237.7+(B2-32)*5/9)-LN(B1/100) |
| Air temperature (°F) | =237.7*B3/(17.27-B3)*9/5+32 |
Table for saturation vapor pressure, vapor pressure and absolute humidity (Magnus approximation)
| Air temperature (°F) | 68 |
| Dew point (°F) | 55.8 |
| Saturation vapor pressure (hPa) | =6.112*EXP(17.27*((B1-32)*5/9)/(237.7+(B1-32)*5/9)) |
| Vapor pressure (hPa) | =6.112*EXP(17.27*((B2-32)*5/9)/(237.7+(B2-32)*5/9)) |
| Absolute humidity (g/m3) | =216.7*B4/((B1-32)*5/9+273.15) |
The same formulas as in Excel work as is (LN and EXP work the same). Copy the whole table, paste it into cell A1, and replace the input values with your own.
How to calculate it in Python
import math
air_temperature_f = 68 # air temperature (°F)
relative_humidity = 65 # relative humidity (%)
magnus_a = 17.27 # Magnus coefficient a
magnus_b = 237.7 # Magnus coefficient b (°C)
air_temperature_c = (air_temperature_f - 32) * 5 / 9 # the Magnus approximation works in °C
# --- dew point from air temperature and relative humidity ---
gamma = math.log(relative_humidity / 100) + magnus_a * air_temperature_c / (magnus_b + air_temperature_c)
dew_point_c = magnus_b * gamma / (magnus_a - gamma)
print(f"Dew point: {dew_point_c * 9 / 5 + 32:.1f} °F ({dew_point_c:.1f} °C)")
# --- to find the relative humidity from the air temperature and dew point, remove the # from the next two lines ---
# dew_point_c = (59 - 32) * 5 / 9 # dew point (59°F in °C)
# relative_humidity = 100 * math.exp(magnus_a * dew_point_c / (magnus_b + dew_point_c) - magnus_a * air_temperature_c / (magnus_b + air_temperature_c))
# --- to find the air temperature from the relative humidity and dew point, remove the # from the next two lines ---
# gamma_t = magnus_a * dew_point_c / (magnus_b + dew_point_c) - math.log(relative_humidity / 100)
# air_temperature_c = magnus_b * gamma_t / (magnus_a - gamma_t)
# --- vapor pressure, saturation vapor pressure and absolute humidity (estimates from the same Magnus approximation) ---
saturation_vapor_pressure = 6.112 * math.exp(magnus_a * air_temperature_c / (magnus_b + air_temperature_c)) # hPa
vapor_pressure = 6.112 * math.exp(magnus_a * dew_point_c / (magnus_b + dew_point_c)) # hPa
absolute_humidity = 216.7 * vapor_pressure / (air_temperature_c + 273.15) # g/m3
print(f"Saturation vapor pressure: {saturation_vapor_pressure:.1f} hPa / Vapor pressure: {vapor_pressure:.1f} hPa / Absolute humidity: {absolute_humidity:.1f} g/m3")
Runs with the standard library (math) only. Change the air temperature and relative humidity at the top and run it to see the dew point and the estimated vapor pressure and absolute humidity. To work out the relative humidity or the air temperature instead, remove the
How to write it in LaTeX and other math languages (copy and paste)
Dew point from air temperature and relative humidity (Magnus approximation)
γ = ln(RH/100) + 17.27T/(237.7 + T), Td = 237.7γ/(17.27 − γ)
\gamma = \ln\left(\dfrac{RH}{100}\right) + \dfrac{17.27\,T}{237.7 + T}, \quad T_d = \dfrac{237.7\,\gamma}{17.27 - \gamma}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>γ</mi>
<mo>=</mo>
<mi>ln</mi>
<mo>(</mo>
<mfrac><mi>RH</mi><mn>100</mn></mfrac>
<mo>)</mo>
<mo>+</mo>
<mfrac>
<mrow><mn>17.27</mn><mi>T</mi></mrow>
<mrow><mn>237.7</mn><mo>+</mo><mi>T</mi></mrow>
</mfrac>
<mo>,</mo>
<msub><mi>T</mi><mi>d</mi></msub>
<mo>=</mo>
<mfrac>
<mrow><mn>237.7</mn><mi>γ</mi></mrow>
<mrow><mn>17.27</mn><mo>−</mo><mi>γ</mi></mrow>
</mfrac>
</mrow>
</math>
gamma = ln(RH/100) + (17.27 T)/(237.7 + T), T_d = (237.7 gamma)/(17.27 - gamma)
gamma = Log[rh/100] + 17.27*t/(237.7 + t); td = 237.7*gamma/(17.27 - gamma)
g := ln(RH/100) + 17.27*T/(237.7 + T); Td := 237.7*g/(17.27 - g);
g = log(RH/100) + 17.27*T/(237.7 + T); Td = 237.7*g/(17.27 - g);
γ = ln(RH/100) + 17.27T/(237.7 + T), T_d = 237.7γ/(17.27 − γ)
Relative humidity from air temperature and dew point
RH = 100 × exp(17.27Td/(237.7 + Td)) ÷ exp(17.27T/(237.7 + T))
RH = 100 \times \dfrac{\exp\left(\dfrac{17.27\,T_d}{237.7 + T_d}\right)}{\exp\left(\dfrac{17.27\,T}{237.7 + T}\right)}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>RH</mi>
<mo>=</mo>
<mn>100</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mi>exp</mi>
<mo>(</mo>
<mfrac>
<mrow><mn>17.27</mn><msub><mi>T</mi><mi>d</mi></msub></mrow>
<mrow><mn>237.7</mn><mo>+</mo><msub><mi>T</mi><mi>d</mi></msub></mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>exp</mi>
<mo>(</mo>
<mfrac>
<mrow><mn>17.27</mn><mi>T</mi></mrow>
<mrow><mn>237.7</mn><mo>+</mo><mi>T</mi></mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mfrac>
</mrow>
</math>
RH = 100 exp((17.27 T_d)/(237.7 + T_d)) / exp((17.27 T)/(237.7 + T))
rh = 100*Exp[17.27*td/(237.7 + td)]/Exp[17.27*t/(237.7 + t)]
RH := 100*exp(17.27*Td/(237.7 + Td))/exp(17.27*T/(237.7 + T));
RH = 100*exp(17.27*Td/(237.7 + Td))/exp(17.27*T/(237.7 + T));
RH = 100 exp(17.27T_d/(237.7 + T_d))/exp(17.27T/(237.7 + T))
Air temperature from relative humidity and dew point
γt = 17.27Td/(237.7 + Td) − ln(RH/100), T = 237.7γt/(17.27 − γt)
\gamma_t = \dfrac{17.27\,T_d}{237.7 + T_d} - \ln\left(\dfrac{RH}{100}\right), \quad T = \dfrac{237.7\,\gamma_t}{17.27 - \gamma_t}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>γ</mi><mi>t</mi></msub>
<mo>=</mo>
<mfrac>
<mrow><mn>17.27</mn><msub><mi>T</mi><mi>d</mi></msub></mrow>
<mrow><mn>237.7</mn><mo>+</mo><msub><mi>T</mi><mi>d</mi></msub></mrow>
</mfrac>
<mo>−</mo>
<mi>ln</mi>
<mo>(</mo>
<mfrac><mi>RH</mi><mn>100</mn></mfrac>
<mo>)</mo>
<mo>,</mo>
<mi>T</mi>
<mo>=</mo>
<mfrac>
<mrow><mn>237.7</mn><msub><mi>γ</mi><mi>t</mi></msub></mrow>
<mrow><mn>17.27</mn><mo>−</mo><msub><mi>γ</mi><mi>t</mi></msub></mrow>
</mfrac>
</mrow>
</math>
gamma_t = (17.27 T_d)/(237.7 + T_d) - ln(RH/100), T = (237.7 gamma_t)/(17.27 - gamma_t)
gammat = 17.27*td/(237.7 + td) - Log[rh/100]; t = 237.7*gammat/(17.27 - gammat)
gt := 17.27*Td/(237.7 + Td) - ln(RH/100); T := 237.7*gt/(17.27 - gt);
gt = 17.27*Td/(237.7 + Td) - log(RH/100); T = 237.7*gt/(17.27 - gt);
γ_t = 17.27T_d/(237.7 + T_d) − ln(RH/100), T = 237.7γ_t/(17.27 − γ_t)
Saturation vapor pressure (Magnus approximation)
es(T) = 6.112 × exp(17.27T/(237.7 + T))
e_s(T) = 6.112 \times \exp\left(\dfrac{17.27\,T}{237.7 + T}\right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>e</mi><mi>s</mi></msub>
<mo>(</mo><mi>T</mi><mo>)</mo>
<mo>=</mo>
<mn>6.112</mn>
<mo>×</mo>
<mi>exp</mi>
<mo>(</mo>
<mfrac>
<mrow><mn>17.27</mn><mi>T</mi></mrow>
<mrow><mn>237.7</mn><mo>+</mo><mi>T</mi></mrow>
</mfrac>
<mo>)</mo>
</mrow>
</math>
e_s(T) = 6.112 exp((17.27 T)/(237.7 + T))
es = 6.112*Exp[17.27*t/(237.7 + t)]
es := 6.112*exp(17.27*T/(237.7 + T));
es = 6.112*exp(17.27*T/(237.7 + T));
e_s(T) = 6.112 exp(17.27T/(237.7 + T))
Vapor pressure and absolute humidity (estimates from the Magnus approximation)
e = es(Td), AH = 216.7e/(T + 273.15)
e = e_s(T_d), \quad AH = \dfrac{216.7\,e}{T + 273.15}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>e</mi>
<mo>=</mo>
<msub><mi>e</mi><mi>s</mi></msub>
<mo>(</mo><msub><mi>T</mi><mi>d</mi></msub><mo>)</mo>
<mo>,</mo>
<mi>AH</mi>
<mo>=</mo>
<mfrac>
<mrow><mn>216.7</mn><mi>e</mi></mrow>
<mrow><mi>T</mi><mo>+</mo><mn>273.15</mn></mrow>
</mfrac>
</mrow>
</math>
e = e_s(T_d), AH = (216.7 e)/(T + 273.15)
e = 6.112*Exp[17.27*td/(237.7 + td)]; ah = 216.7*e/(t + 273.15)
vp := 6.112*exp(17.27*Td/(237.7 + Td)); AH := 216.7*vp/(T + 273.15);
e = 6.112*exp(17.27*Td/(237.7 + Td)); AH = 216.7*e/(T + 273.15);
e = e_s(T_d), AH = 216.7e/(T + 273.15)
How to have ChatGPT do the calculation
You are a weather calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). Find the dew point at an air temperature of 68°F and a relative humidity of 65%, using the Magnus approximation (coefficients a = 17.27, b = 237.7). Steps: 1. Convert the air temperature to °C: T = (°F − 32) × 5/9 2. Calculate γ = ln(RH ÷ 100) + a × T ÷ (b + T) (T in °C, RH in %) 3. Calculate the dew point Td = b × γ ÷ (a − γ) and convert it back to °F (°F = °C × 9/5 + 32) 4. Also calculate the saturation vapor pressure es = 6.112 × exp(a × T ÷ (b + T)) (hPa), the vapor pressure e = 6.112 × exp(a × Td ÷ (b + Td)) (hPa) and the absolute humidity AH = 216.7 × e ÷ (T + 273.15) (g/m³) 5. Give the results to one decimal place Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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