How to Calculate Dew Point: Formula from Room Temperature and Humidity, Excel Formula and Chart
Dew point is the starting point for thinking in numbers about moisture problems, from window condensation and closet mold to condensation control in painting and on job sites and storage of precision equipment. But look it up and you meet daunting terms like "Magnus formula" and "saturation vapor pressure," and it's hard to know which formula to use. With concrete numbers, this article covers what dew point means, how to find it by hand and in Excel, a simple mental formula and its error, a chart by room temperature and humidity, the link to absolute humidity and saturation water vapor, and the frost point used below 0°C.
Dew point: the temperature where cooled air reaches 100% humidity
If you lower only the temperature of air while keeping its water vapor the same, at a certain temperature the air can't hold any more vapor, and the excess turns into water droplets. That temperature is the dew point. For air at 20°C and 60% humidity, the dew point is 12.0°C. When this air touches window glass, a wall or a cold glass below 12.0°C, droplets form on the surface.
The key point is that dew point depends only on how much water vapor the air contains. For the same room air, raising or lowering the temperature with a heater doesn't change the dew point unless vapor is added or removed. A hygrometer's percentage changes with temperature, but dew point doesn't, so it's a handy yardstick for comparing moisture across places and times.
- High dew point = lots of water vapor in the air (a little cooling causes condensation)
- Low dew point = dry air (condensation only with a lot of cooling)
- Small gap between room temperature and dew point = high relative humidity (no gap means 100% humidity)
- Surface temperature < dew point = condensation on that surface
Steps to calculate dew point (Magnus formula)
Dew point is found in three stages: first find the most water vapor air can hold at that temperature (saturation vapor pressure), then multiply by humidity to get the vapor present now (vapor pressure), and finally work back to the temperature at which that vapor pressure is exactly saturated. There are several saturation vapor pressure formulas, but in everyday temperature ranges the Magnus formula (Magnus–Tetens) is simple and accurate enough.
- 1
Find the saturation vapor pressure e_s
e_s = 6.112 × exp(17.62 × T ÷ (243.12 + T)) [hPa], where T is the room temperature (°C). At 20°C, 6.112 × exp(352.4 ÷ 263.12) ≈ 23.3 hPa.
- 2
Find the vapor pressure e
e = e_s × humidity (%) ÷ 100. At 20°C and 50% humidity, 23.3 × 0.5 ≈ 11.7 hPa. This expresses the vapor in the air now as a pressure.
- 3
Find g = ln(e ÷ 6.112)
ln is the natural logarithm. 11.7 ÷ 6.112 ≈ 1.91, so g ≈ 0.646.
- 4
Find the dew point Td
Td = 243.12 × g ÷ (17.62 − g). 243.12 × 0.646 ÷ (17.62 − 0.646) ≈ 9.3°C is the dew point at 20°C and 50% humidity.
The coefficients 17.62 and 243.12 are the values over a water surface (liquid water). Some textbooks use 17.27 and 237.7, or 17.625 and 243.04, but in the range of about −20 to 50°C the answers differ by only around 0.1°C, which doesn't matter when thinking about condensation.
Dew point formulas for Excel and spreadsheets
To get dew points for many rows at once, such as temperature and humidity logger data, a spreadsheet formula is the quickest way. With room temperature (°C) in column A and humidity (%) in column B, enter the following in cell C2 and copy it down. The same formula works in both Excel and Google Sheets.
- Dew point (°C): =243.12*(LN(B2/100)+17.62*A2/(243.12+A2))/(17.62-(LN(B2/100)+17.62*A2/(243.12+A2)))
- Absolute humidity (g/m³): =216.7*(6.112*EXP(17.62*A2/(243.12+A2))*B2/100)/(273.15+A2)
- Saturation water vapor (g/m³): =216.7*6.112*EXP(17.62*A2/(243.12+A2))/(273.15+A2)
The dew point formula combines the third and fourth steps. ln(humidity ÷ 100) + 17.62T ÷ (243.12 + T) equals g in the steps above, so one cell can do the calculation without putting saturation vapor pressure in a separate column. A cell with 0% humidity makes LN fail with an error, so leave missing logger values blank.
A mental formula, room temperature − (100 − humidity) ÷ 5, and its error
When you want a rough figure on the spot, the simple formula dew point ≈ room temperature − (100 − humidity) ÷ 5 is handy. At 20°C and 60%, 20 − 40 ÷ 5 = 12°C, exactly matching the Magnus formula's 12.0°C. However, this formula is more accurate at high humidity, and drifts further off in dry air.
| Temperature and humidity | Magnus formula | Simple formula | Difference |
|---|---|---|---|
| 20°C, 80% | 16.4°C | 16.0°C | −0.4°C |
| 20°C, 70% | 14.4°C | 14.0°C | −0.4°C |
| 20°C, 60% | 12.0°C | 12.0°C | 0°C |
| 25°C, 60% | 16.7°C | 17.0°C | +0.3°C |
| 20°C, 50% | 9.3°C | 10.0°C | +0.7°C |
| 20°C, 40% | 6.0°C | 8.0°C | +2.0°C |
At 50% humidity or above, the error stays within 1°C, but below 40%, as in a heated room in winter, it's off by 2°C or more. The simple formula errs toward overestimating the dew point, which is on the safe side if you're simply being cautious about condensation, but for calculations where a few degrees change the result, such as judging window condensation, the Magnus formula or the tool is recommended.
Dew point chart by room temperature and humidity
This table shows dew points calculated with the Magnus formula. Rows are room temperature and columns are humidity, and condensation forms on any surface colder than the temperature where they meet. Negative values are calculated dew points (over water), and in practice frost starts forming at the slightly higher frost point.
| Temperature \ humidity | 30% | 40% | 50% | 60% | 70% | 80% |
|---|---|---|---|---|---|---|
| 10°C | −6.8°C | −3.0°C | 0.0°C | 2.6°C | 4.8°C | 6.7°C |
| 15°C | −2.5°C | 1.5°C | 4.7°C | 7.3°C | 9.6°C | 11.6°C |
| 18°C | 0.1°C | 4.2°C | 7.4°C | 10.1°C | 12.4°C | 14.5°C |
| 20°C | 1.9°C | 6.0°C | 9.3°C | 12.0°C | 14.4°C | 16.4°C |
| 22°C | 3.6°C | 7.8°C | 11.1°C | 13.9°C | 16.3°C | 18.4°C |
| 24°C | 5.3°C | 9.6°C | 12.9°C | 15.8°C | 18.2°C | 20.3°C |
| 26°C | 7.1°C | 11.4°C | 14.8°C | 17.6°C | 20.1°C | 22.3°C |
| 28°C | 8.8°C | 13.1°C | 16.6°C | 19.5°C | 22.0°C | 24.2°C |
| 30°C | 10.5°C | 14.9°C | 18.4°C | 21.4°C | 23.9°C | 26.2°C |
Here's a summer example. A room at 26°C and 70% humidity has a dew point of 20.1°C, so droplets will certainly form on air conditioner vents, cold pipes and a plastic bottle from the fridge (around 5°C). In winter, against a dew point of 9.3°C at 20°C and 50%, a single-pane window on a 0°C morning cools to around 7°C on its surface, so condensation forms. How to find window surface temperature is explained in detail in Humidity Levels That Avoid Condensation.
Absolute humidity and saturation water vapor
What we usually call humidity is relative humidity: the percentage of the most the air can hold at that temperature (saturation water vapor). Absolute humidity (by volume), by contrast, is how many grams of water vapor are actually in 1 m³ of air. It's found with 216.7 × vapor pressure (hPa) ÷ (273.15 + room temperature).
| Temperature | Saturation water vapor | Saturation vapor pressure |
|---|---|---|
| −10°C | 2.4 g/m³ | 2.9 hPa |
| −5°C | 3.4 g/m³ | 4.2 hPa |
| 0°C | 4.8 g/m³ | 6.1 hPa |
| 5°C | 6.8 g/m³ | 8.7 hPa |
| 10°C | 9.4 g/m³ | 12.3 hPa |
| 15°C | 12.8 g/m³ | 17.0 hPa |
| 20°C | 17.2 g/m³ | 23.3 hPa |
| 25°C | 23.0 g/m³ | 31.6 hPa |
| 30°C | 30.3 g/m³ | 42.3 hPa |
| 35°C | 39.5 g/m³ | 56.1 hPa |
Air at 20°C can hold up to 17.2 g of water vapor per 1 m³, so at 50% humidity it holds about 8.6 g/m³. When this air cools past the temperature where saturation water vapor is 8.6 g, the dew point of 9.3°C, the excess vapor becomes droplets. The method taught in school science of reading the dew point from a saturation water vapor table is just this relationship looked up in reverse.
- The air in a 6-tatami room with a 2.4 m ceiling (about 23 m³) holds about 200 g of water at 20°C and 50%, and about 160 g at 40%. That's only about a glassful
- Saturation water vapor roughly doubles for every 10°C rise (9.4 g at 10°C, 17.2 g at 20°C, 30.3 g at 30°C)
- Air conditioning and factories often use grams per 1 kg of dry air (humidity by weight, mixing ratio, g/kg). At 20°C and 50%, it's about 7.2 g/kg
Below 0°C, use the frost point
In air dry enough for the dew point to fall below 0°C, frost (ice) forms on cold surfaces instead of water droplets. An ice surface attracts water vapor more readily than a water surface, so the temperature where frost starts to form (the frost point) is slightly higher than the dew point. Saturation vapor pressure over ice is calculated with the Magnus formula using the coefficients 22.46 and 272.62.
| Temperature and humidity | Dew point (over water) | Frost point (over ice) |
|---|---|---|
| 20°C, 20% | −3.7°C | −3.2°C |
| 20°C, 15% | −7.5°C | −6.6°C |
| 10°C, 30% | −6.8°C | −6.0°C |
| 0°C, 80% | −3.0°C | −2.7°C |
The difference is under 1°C, but for windows and sashes in cold regions, around freezers, and frost on outdoor equipment in winter, judging by frost point is closer to reality. The Condensation & Dew Point Calculator automatically compares using the formula for ice when the surface temperature is below 0°C.
What to look up once you know the dew point
- At what humidity window glass and aluminum sashes get condensation: What Humidity Avoids Condensation? A Chart by Window Type and Outdoor Temperature
- Ways to reduce condensation, most effective first: Preventing Window Condensation: Inner Windows, Insulation Film and Ventilation
- Why closets and north-facing rooms get moldy: Condensation and Mold in Closets
- What humidifier output in mL/h you need: Guide to Humidifier Output
FAQ
- What's the dew point at 20°C and 50% humidity?
- About 9.3°C. Condensation starts on any surface 10.7°C colder than the room. At 60% humidity it's 12.0°C, and at 40% it's 6.0°C.
- Is there an easy way to calculate dew point?
- You can estimate it with room temperature − (100 − humidity) ÷ 5. At 50% humidity or above, the error stays within 1°C, but at 40% or below it's off by 2°C or more, so use the Magnus formula or a calculator when you need accuracy.
- What's the Excel formula for dew point?
- With room temperature in column A and humidity (%) in column B: =243.12*(LN(B2/100)+17.62*A2/(243.12+A2))/(17.62-(LN(B2/100)+17.62*A2/(243.12+A2))). If 20°C and 50% gives 9.3, you've entered it correctly.
- What's the difference between dew point and frost point?
- Dew point is the temperature where water droplets (liquid water) start to form, and frost point is where frost (ice) starts to form. On surfaces below 0°C, judge by frost point, which is a little under 1°C higher than the dew point.
- Does raising the room temperature with a heater change the dew point?
- Not unless water vapor is added or removed. Relative humidity (%) falls as the room warms, but the air holds the same amount of vapor, so the surface temperature where condensation starts stays the same.
Tools in this article
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