Dew Point

How the Magnus Formula Estimates Dew Point

Dew point is the temperature air would need to cool to for it to become fully saturated with the moisture it already holds. It’s a more reliable “how humid does it actually feel” indicator than relative humidity alone, since relative humidity changes with temperature even when the actual amount of moisture in the air doesn’t — the same air reads as a much higher relative humidity percentage on a cold morning than on a warm afternoon, while its dew point stays roughly constant.

Enter the air temperature and relative humidity, and this calculator estimates the dew point using the Magnus formula, a widely-used meteorological approximation.

The Formula

The Magnus formula first computes an intermediate value $\alpha$ from temperature and relative humidity, then solves for dew point from it:

$$\vC{\alpha} = \ln\left(\frac{\vB{RH}}{100}\right) + \frac{17.625 \times \vA{T}}{243.04 + \vA{T}}$$ $$\text{Dew Point} = \frac{243.04 \times \vC{\alpha}}{17.625 - \vC{\alpha}}$$

where $\vA{T}$ is air temperature in Celsius and $\vB{RH}$ is relative humidity as a percent (0–100]. The constants 17.625 and 243.04 are the Magnus formula’s standard coefficients, accurate to within about 0.35°C across the -45°C to 60°C range this calculator supports.

Worked Example

At 25°C with 60% relative humidity:

1. $\vC{\alpha} = \ln(0.6) + {\displaystyle\frac{17.625 \times \vA{25}}{243.04 + \vA{25}}} = -0.510826 + 1.643895 = \vC{1.133069}$.
2. $\text{Dew Point} = {\displaystyle\frac{243.04 \times \vC{1.133069}}{17.625 - \vC{1.133069}}} \approx \mathbf{16.70°C}$ (about 62.1°F) — a widely-cited reference value for this exact temperature/humidity pairing.

Key Factors to Consider

• A dew point above roughly 65°F (18°C) is commonly considered the point where humidity starts to feel noticeably uncomfortable. Values climbing into the low-to-mid 70s°F are often described as “muggy” or “oppressive,” and above about 75°F as extreme — these are commonly-cited comfort thresholds, not precise physical boundaries.
• The dew point can never exceed the actual air temperature. By definition, dew point is the temperature air would need to cool TO in order to become saturated — it’s always at or below the current air temperature, and the two become equal only when the air is already at 100% relative humidity (fully saturated, as in fog).
• A frost point applies below freezing, a subtly different concept from dew point. When air temperature is below 0°C, moisture condenses directly as frost rather than liquid dew — the Magnus formula used here estimates the equivalent saturation temperature regardless, but the physical process it describes differs slightly below freezing.
• Indoor condensation problems are directly related to dew point. A cold surface (a window, an uninsulated wall) below the indoor air’s dew point will collect condensation — this is the same underlying physics behind window fogging and can be a useful diagnostic when troubleshooting moisture issues in a home.

Common Mistakes

• Confusing dew point with relative humidity when comparing two locations or times of day. A 90% relative-humidity reading on a cool morning can represent far less actual moisture in the air than a 50% reading on a hot afternoon — dew point is the number that tracks actual moisture content directly, so it’s the better one for a true apples-to-apples comparison.
• Expecting the formula to stay accurate well outside its calibrated -45°C to 60°C range. The Magnus formula’s coefficients were fitted to real vapor-pressure data within that band — pushing it further doesn’t fail loudly, it just quietly produces a less trustworthy number, which is exactly why this calculator declines to compute one outside that range rather than showing a false sense of precision.
• Assuming a high dew point always means rain is coming. Dew point measures how saturated the air already is, not whether precipitation will occur — a muggy, high-dew-point day can stay completely dry, while an actual storm depends on separate factors like lift and instability.

Useful to Know

Dew point and frost point describe the same underlying saturation concept but apply on opposite sides of freezing: above 0°C, excess moisture condenses as liquid dew; below it, the equivalent process deposits moisture directly as frost instead. The Magnus formula computes one continuous saturation-temperature estimate either way, so a dew point result below 0°C is really describing a frost point in practice, even though the calculator doesn’t relabel it as such.