The Relative Humidity Formula Explained (Without the Heavy Math)

Staring at a thermodynamics equation with exponents and natural logarithms when all you want to know is whether you need to run the dehumidifier? We've all been there.

Human brains do not naturally process saturation vapor pressures. We want a percentage that tells us if we need to call the HVAC tech or just open a window. The math behind relative humidity is frustrating because water vapor does not behave in a clean, linear way. But once you break it down, the formula actually makes perfect sense — and if you just want the answer right now, the calculator below does all of it instantly.

The Core Concept

Before the equations, you need to understand what you are actually calculating. Relative humidity is one question: how much water is currently in the air, compared to the absolute maximum that air could possibly hold at its current temperature?

If the air is holding half of its total capacity, your relative humidity is 50%. If it's holding everything it can possibly hold, it's 100% — that's full saturation, and any additional water vapor starts turning into condensation.

RH = (Actual Water Vapor / Maximum Capacity) × 100

The problem with this simple ratio is that you almost never know "Actual Water Vapor" directly. You have a thermometer reading and maybe a dew point or wet-bulb reading. That is where the formula comes in.

Saturation Vapor Pressure: The Missing Link

The "Maximum Capacity" in the formula above is what scientists call saturation vapor pressure — the maximum pressure that water vapor exerts in air at a given temperature. Above this pressure, water vapor condenses into liquid.

Here is why the formula is non-linear: saturation vapor pressure does not increase in a straight line with temperature. It grows exponentially. Air at 30°C holds roughly seven times more water vapor than air at 0°C — not three times, not two-and-a-half times. Seven times.

This exponential growth is the reason temperature dominates every humidity calculation and why a 5-degree temperature swing can dramatically change your RH reading. For more on this relationship, see our guide on how temperature affects relative humidity.

The Magnus-Tetens Formula: The Industry Standard

To get relative humidity from temperature and dew point, the gold standard is the Magnus-Tetens formula with Alduchov & Eskridge (1996) coefficients. It is used by NOAA, the UK Met Office, and our calculator:

e_s(T) = 6.112 × exp(17.625 × T / (243.04 + T))
RH = 100 × e_s(Dew Point) / e_s(Air Temperature)

Where:

• e_s(T) = saturation vapor pressure at temperature T (in hPa)
• T = temperature in Celsius
• exp() = the natural exponential function (e^x)
• 17.625 and 243.04 are the Alduchov & Eskridge constants — calibrated coefficients that make the formula accurate to within ±0.35°C

Step-by-Step Breakdown

Step 1: Calculate Maximum Capacity (e_s at Air Temperature)

Plug your air temperature into the e_s formula. This gives you the saturation vapor pressure — the maximum amount of water vapor the air can hold right now.

Example: Air temperature = 22°C

• e_s(22) = 6.112 × exp(17.625 × 22 / (243.04 + 22))
• e_s(22) = 6.112 × exp(387.75 / 265.04)
• e_s(22) = 6.112 × exp(1.463)
• e_s(22) = 6.112 × 4.319 ≈ 26.39 hPa

Step 2: Calculate Actual Moisture (e_s at Dew Point)

Plug your dew point into the same formula. This gives you the actual vapor pressure — the moisture currently in the air.

Example: Dew point = 14°C

• e_s(14) = 6.112 × exp(17.625 × 14 / (243.04 + 14))
• e_s(14) = 6.112 × exp(246.75 / 257.04)
• e_s(14) = 6.112 × exp(0.960)
• e_s(14) = 6.112 × 2.612 ≈ 15.97 hPa

Step 3: Calculate Relative Humidity

RH = 100 × (15.97 / 26.39) = 100 × 0.605 = 60.5%

At 22°C with a dew point of 14°C, your relative humidity is approximately 60.5%. This is right at the upper boundary of the ideal comfort range.

Calculating Dew Point from Temperature and RH

The inverse formula — finding dew point from air temperature and relative humidity — requires solving the equation backward:

e = e_s(T) × (RH / 100)
Dp = 243.04 × ln(e / 6.112) / (17.625 − ln(e / 6.112))

Where ln() is the natural logarithm. This is significantly more complex to compute by hand — which is exactly why the calculator at the top of this page exists.

Why the Exponent Constants Matter

The numbers 17.625 and 243.04 are not arbitrary. They are the Alduchov and Eskridge (1996) optimized coefficients derived from fitting the Magnus formula to experimental data over the temperature range -40°C to +60°C.

Earlier versions of the Magnus formula used different constants (like the classic 17.27 and 237.3). The 1996 coefficients reduce the maximum error from about ±1.3°C to ±0.35°C over that range. The difference matters in precision applications — HVAC load calculations, dew point protection for industrial systems, and meteorological data reporting.

Frequently Asked Questions

Why can't I just use a simpler formula? Linear approximations to the humidity-temperature relationship exist, but they become significantly inaccurate at temperatures above 25°C or below 5°C — which covers most practical scenarios. The Magnus formula's exponential structure is necessary because the underlying physics (Clausius-Clapeyron relation) is genuinely exponential.

Does the Magnus formula work for below-freezing temperatures? The standard Magnus formula (over liquid water) is technically accurate down to about -40°C, but ice complicates things. For temperatures below 0°C, some applications use a variant of the formula calibrated over ice rather than liquid water, which gives slightly different constants. Our calculator uses the liquid-water version, which is standard for most weather and HVAC applications.

What is the Clausius-Clapeyron equation, and how does it relate? The Clausius-Clapeyron relation is the thermodynamic equation describing how saturation vapor pressure changes with temperature. The Magnus-Tetens formula is an empirical approximation to the Clausius-Clapeyron that is accurate enough for most practical use without requiring thermodynamic integration. The Magnus formula can be derived as a simplified exponential fit to the Clausius-Clapeyron curve.

How accurate is this calculator? Our calculator uses the Alduchov & Eskridge (1996) Magnus coefficients, which give accuracy within ±0.35°C for the dew point calculation over the range 0°C to 60°C. For the wet-bulb calculation, we use the Stull (2011) approximation, accurate within ±0.65°C for 0–50°C and 5–99% RH. Both are more than sufficient for home monitoring and standard HVAC diagnostics.