Dew point: Definition of dew point & relative humidity; how to calculate the dew point.

This article explains how the wall cavity dew point, the point at which moisture condenses out of air onto a surface, is calculated for a building cavity such as inside of an insulated wall.

How to Calculate or Predict the Dew Point in a Building Wall or Ceiling Cavity

Question about how we calculate the dew point in buildings

The question-and-answer article about calculating the dew point in walls and a discussion of mathematical models of moisture condensation, quotes-from, updates, and comments an original article from Solar Age Magazine and written by Steven Bliss. Accompanying text is reprinted/adapted/excerpted with permission from Solar Age Magazine - editor Steven Bliss.

Our page top photo shows severe moisture condensation on a basement window and window frame.

All of the literature I have read on condensation within building wall cavities warns of the problem of cavity moisture (a potential source of mold contamination, insect attack, or structural rot). But the literature does not provide any clues as to how to predict wall cavity condensation.

Is there a formula which will determine the dew point inside a building wall when both inside and outside relative humilities and temperatures are known? - J.L.B., G4reenfield Center, NY.

[Click to enlarge any image including this psychometric chart]

How to Predict or Calculate a Wall Cavity Dew Point or Condensation Point in Buildings

Yes, JLB. Editor Daniel F. includes dew point calculations, formulas, and mathematic models later in this article.

First let's understand what the dew point is. The dew point and relative humidity are the two most-widely used ways that people describe the amount of moisture that is in air.

Definition of Dew Point: Why moisture condenses out of air.

The dew point, or properly, dew point temperature, is the temperature to which air will have to cool to reach its saturation point. The air saturation point is the point at which the air can hold no more water - it is fully saturated.

Warmer air can hold more water than cooler air

While it is not technically-correct, you can think of warm air as having more space between the gas molecules that comprise the air, giving room for water molecules.

What's actually the case is that there's plenty of space for water molecules in both warm and cold air. It is rather because in cooler air the water molecules (in air as a gas form) as well as other gas molecules making up air are absorbing less energy than in warmer air.

When the water molecules absorb less energy they are less excited, they zoom about less, they bang into one another with less force, so they begin to condense, first into micro-droplets (fog) and finally into visible droplets that form on first on cooler surfaces with which air is in contact (because air there is most-cooled).

When the air temperature and the dew point temperature are the same, the air is fully saturated.

If we hold the barometric pressure and water vapor content of the air constant, then when we cool the air below the dew point, the water that the air can no longer hold will be condensed out of the air and onto cooler nearby surfaces.

In fact a cool wall or ceiling surface will cool warmer moist air close to the wall surface, thus causing that air to cool and thus causing moisture to condense out of the air onto the surface.

Definition of Relative Humidity (RH) & Relationship of RH to the Dew Point

Relative humidity (RH) is defined as the actual amount of water vapor present in air expressed as a precent of the maximum quantity of water that that same air could hold at a given temperature.

The maximum amount of water that air could hold for a given temperature (and actually barometric pressure but we'll ignore that) is also defined as the saturation point of the air.

RH is the ratio of the actual water vapor pressure in air to the saturation vapor pressure of that air a fixed temperature and barometric pressure.

Relationship of Dew Point to Temperature

RH is expressed either as the ratio of actual vapor pressure to the saturation water pressure. Saturation water pressure appears in some texts as the "equilibrium water pressure" since that's the point at which the effects of temperature and vapor pressure are balanced: the air can't accept any more water. Raising the temperature will allow the air to accept more water, thus raising the dew point.

Lowering the temperature will squeeze water out of the air, lowering the dew point. However the exact relationship between temperature and dew point is not linear (look again at the psychotic chart earlier on this page). Lawrence (2005) suggests a rule of thumb that might work for ranges of temperature and relative humidity when the air is high in moisture:

t_d = t - {100 - RH / 5} for air at RH > 50%

Lawrence is saying that for moist air, the dewpoint temperature t_d will decrease about 1°C for every 5% decrease in RH (starting at t_d = t, where t = the dry bulb temperature when RH = 100%)

So what the heck, J.L.B., you can see before we even start that these relationships are not linear and not trivial. So there won't be a trivial formula either. Lawrence goes on to explore the mathematical basis of the linear approximation of the psychometric chart (Steve calls it the psychotic chart). You can find his article (Lawrence 2005) atReferences or Citations .

As Steve B. originally replied:

Mathematical models exist for computing the place and accumulation of moisture condensation inside building walls. Their usefulness, however, is limited for a number of reasons.

Dew point calculations or tables vs. real world conditions: role of air leaks vs moisture diffusion

First, the [dew point or psychometric chart] models are based exclusively on moisture diffusion theory (moisture molecules moving through building materials).

In reality, air leaks into and out of wall cavities, rather than moisture diffusion, accounts for the largest portion of moisture transmission in buildings. Because of variations in workmanship, construction details, uses of sealants and caulks, and similar variables, the relative contributions of diffusion and air leakage in building walls and ceilings is unpredictable.

Second, the moisture condensation mathematical models assume that the building wall is continuous (no holes or penetrations) and that the environmental conditions (temperature, moisture, wind, air pressure) are unchanging.

Actually, conditions constantly change inside and outside of buildings, and cold spots occur at leaks to the outdoors, lapses or omissions of insulation at building corners, air leaks occur around openings for doors and windows, and at thermal short circuits are caused by highly conductive materials such as metal, glass and concrete.

These are the places where the problematic wall or ceiling cavity condensation is likely to occur. So you can also see that the occurrence of wall or ceiling cavity is certainly non uniform in space (building walls or ceilings) and time.

Also the prediction of building wall condensation does not necessarily indicate an actual condensation problem.

The length and severity of winter and the ability of building materials to safely store and later expel moisture are important factors in determining whether a building cavity moisture problem will actually occur.

With this in mind, the best defense against building wall or ceiling moisture damage is a good offense: proper air and vapor barriers, caulking, and thermally-broken door and window components.

To do the wall condensation or dew point calculations, you need to know the temperature and vapor pressure gradients through the wall(or ceiling). These are directly proportional to the resistance's of the wall's components to heat flow and moisture vapor flow (and air leaks). At any point where the calculated vapor pressure exceeds the saturation vapor pressure (derived from the temperature at each point), condensation may occur.

Below we provide links to further information on dew point calculation from ASHRAE and the National Bureau of Standards. For greater accuracy in predicting wall cavity condensation, the vapor pressure curve is recalculated for each plane of condensation in an iterative procedure.

A Quick Look at the Psychometric Chart Relating Dew Point, Temperature, Humidity

[Click to enlarge any image]

What is the Dew Point?: the dew point (Tdp) is the temperature at which water vapor just starts to condense out of air that is cooling - for example when warm moisture-laden air contacts a cool surface inside of a wall cavity.

Above the dew point the moisture stays in the air. At or below the dew point moisture leaves the air and in buildings, condenses on the cooler surface that the air is contacting.

This also means that if you are measuring the relative humidity in a room, the RH number only has meaning if you measure the room temperature at the same time and location.

In the table above, the left-most curve, the 100% relative humidity line offers a simple case - that's air that is 100% saturated. So on the chart below, notice that on the left-most curve, the wet bulb temperature equals the dry bulb temperature - that is, when the air is fully saturated at 100% RH, no more air water can be evaporated out of the air.

Original Article

• Q&A: Condensation in Walls - Calculate the Dew Point in Building Walls - PDF version; use your browser's back button to return to this page

...

Approximate & More Accurate Formulas to Calculate the Dew Point in a Building

Question: how do I actually calculate the dew point in a building?

(May 31, 2015) Mike said:
I love how this article avoids the answer to the actual question being asked by saying yes, there is a mathematical formula but avoids giving the formula.

2015/12/28 Robin said:
What Mike said.

Reply: how to calculate the dew point if we know the relative humidity (RH) and teperature

Thanks Robin and Mike you are quite correct - I'll have added dew point calculation advice into this article.

Relative humidity is the ratio of how much moisture air is actually in the air compared with how much moisture the air could hold for a given temperture.

As you'll read in the psychometric chart above, this relationship is a logarithmic curve rather than a simple linear one.

Barometric pressure is also a factor to be considered.

That is, the dew point - or maximum amount of moisture that air can hold before water starts condensing out on cooler surfaces - is exponentially greater at higher temperatures (dry bulb temperature) and at higher vapor pressures.

If you take a look at the dew point chart given above (the psychometric chart) you'll see that the chart presents dew point data as a function of temperature and indoor relative humidity along a logarithmic scale - that is the dew point in a building is not a simple linear function. The actual calculations or formulas are themselves approximations of a more complex environment and don't consider possiblyi overwhelming effects of building air leaks and other variables.

On a review of moisture models and calculations you'll see why for practical purposes many people prefer to read the dew point off of a handy psychometric chart rather than work in log scales and calculations.

I have added your painful but fair critique along with calculation advice into the article and provide details and expert dew point resource citations below. You'll see that because the calculation is troublesome, using the psychometric chart looks ever so much more attractive.

See DEW POINT TABLE - CONDENSATION POINT GUIDE for the chart approach. That said, let's take a look at two dew point calculation approaches:

How to Calculate the Approximate Dew Point - simplified equation

Dew Point Temperature = Td = T - ((100 - RH)/5.)

where

• Td = dew point temperature
• T = temperature observed, expressed in degrees Celsius
• RH = % relative humidity

This equation is attributed to a 2005 proposal from Mark Lawrence cited below and is considered a reasonably accurate estimate provided the RH is above 50%. I also recommend Devres (1994) for an excellent article on calculating the dew point or the psychometric properties of air.

How to Calculate the Dew Point more Precisely

The following procedure is derived from information provided by Columbia University and cited below:

Relative Humidity - RH = 100% x (E / Es)

This is an approximation of a more complex and more precise Clausius-Clapeyron equation where we set E and Es as follows:

E = E0 x exp [(L/Rv) x {(1/T0) - (1/Td)}]

Es = E0 x exp[(L/Rv) x {(1/T0) - (1/T)}]

and

• E0 = 0.611 kPa, (L/Rv) = 5423 K (in Kelvin, over a flat surface of water), T0 = 273 K (Kelvin)
• T = temperature (in Kelvin)
• Td = the Dew Point Temperature in Kelvin

Given a temperature in Kelvin, solve for Es, substitute that equation into E and solve for Td to obtain the dew point.

Since these calculations work in Kelvin I include below formulas to convert from Kelvin to Celsius and from Celsius to Farenheit degrees.

To convert Kelvin to Celsius use

• T_c = t_x = 273.15

To convert Celsius (tc) to Farenheit use

• T_F = 9/5_Tc + 32

References on Dew Point Calculations

• Berglund, Larry G. "Comfort and humidity." ASHRAE journal 40, no. 8 (1998): 35.
• Brooker, D. B. "Mathematical model of the psychrometric chart." Transactions of the ASAE 10, no. 4 (1967): 558-0560.
• Devres, Y. O. "Psychrometric properties of humid air: calculation procedures." Applied energy 48, no. 1 (1994): 1-18.
  Abstract
  
  Knowledge of the psychrometric properties is essential during the designing of air conditioning, cold storage, and drying processes where humid air is a working fluid. In this study detailed procedures for calculating psychrometric properties are given. Seven main properties of the psychrometrics, namely dry-bulb, wet-buld and dew-point temperatures, atmospheric pressure, humidity ratio, relative humidity and enthalpy can be calculated using the given procedures.
  
  According to the Gibbs Phase Rule, in the humid air case, any three intensive properties will be sufficient to evaluate the remaining properties. Therefore the combination of three out of seven properties gives a total of 35 different sets. Computer software has been developed and utilised to obtain the psychrometric properties of humid air. It was found that given three input parameters, the remaining four parameters could, except in three cases, can be calculated with negligible error.
• Goodman, William. Air conditioning analysis with psychrometric charts & tables. The Macmillan Company, 1943.
• Grabon, Michel, Jackie Anderson, Peter Bushnell, Aritz Calvo, and William Chadwick. "The Sistine Chapel: New HVAC System for Cultural Preservation." ASHRAE Journal 57, no. 6 (2015): 20.
• "How do I calculate dwe point when I know the temperature and relative humidity?", IRI Q&A, Internationbal Research Institute for Climate and Society, Earth Institute, Columbia University, Lamont Campus, 61 Route 9W Monell Building Palisades, NY 10964-1000, retrieved 29 Dec 2015, original source: http://iridl.ldeo.columbia.edu/dochelp/QA/Basic/dewpoint.html
• Kodama, Akio, Tadashi Hirayama, Motonobu Goto, Tsutomu Hirose, and R. E. Critoph. "The use of psychrometric charts for the optimisation of a thermal swing desiccant wheel." Applied Thermal Engineering 21, no. 16 (2001): 1657-1674.
• Lawrence, Mark G. "The relationship between relative humidity and the dewpoint temperature in moist air: A simple conversion and applications." Bulletin of the American Meteorological Society 86, no. 2 (2005): 225-233.
  Abstract:
  
  The relative humidity (RH) and the dewpoint temperature (td) are two widely used indicators of the amount of moisture in air. The exact conversion from RH to td, as well as highly accurate approximations, are too complex to be done easily without the help of a calculator or computer.
  
  However, there is a very simple rule of thumb that can be very useful for approximating the conversion for moist air (RH > 50%), which does not appear to be widely known by the meteorological community: td decreases by about 1°C for every 5% decrease in RH (starting at td = t, the dry bulb temperature, when RH = 100%).
  
  This article examines the mathematical basis and accuracy of this and other relationships between the dewpoint and relative humidity. Several useful applications of the simple conversion are presented, in particular the computation of the cumulus cloud-base level (or lifting condensation level) as zLCL ≈ (20 + t/5) (100 − RH), where zLCL is in meters when t is in degrees Celcius and RH in percent. Finally, a historical perspective is given with anecdotes about some of the early work in this field.
• Manabe, Syukuro, and RICHARD T. WETIIERALD. "Thermal equilibrium of the atmosphere with a given distribution of relative humidity." (1967): 241-259.
• Picard, A., R. S. Davis, M. Gläser, and K. Fujii. "Revised formula for the density of moist air (CIPM-2007)." Metrologia 45, no. 2 (2008): 149.
• Singh, A. K., Harpal Singh, S. P. Singh, and R. L. Sawhney. "Numerical calculation of psychrometric properties on a calculator." Building and Environment 37, no. 4 (2002): 415-419.
• Wilhelm, Luther R. "Numerical calculation of psychrometric properties in SI units." Transactions of the ASAE 19, no. 2 (1976): 318-325.

...

Continue reading at DEW POINT TABLE - CONDENSATION POINT GUIDE or select a topic from the closely-related articles below, or see the complete ARTICLE INDEX.

Or see these

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• CONDENSATION or SWEATING PIPES, TANKS
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• MOISTURE PROBLEMS: CAUSE & CURE
• HUMIDITY CONTROL TO PREVENT MOLD
• VENTILATION in BUILDINGS.

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