What is the difference between humidity and relative humidity?

Mixing these up is the single most common psychrometry error: humidity ratio keeps climbing as air gets hotter (more mass of vapor fits before saturating), while relative humidity can fall even as the absolute amount of water in the air stays exactly the same, purely because hotter air can hold more before hitting 100%. A humidity ratio number and an RH number that both "sound high" aren't necessarily describing the same air.

How accurate is the wet-bulb temperature approximation used here?

Good enough for typical HVAC and drying-calculation conditions, but it's a fitted engineering correlation for a properly ventilated thermometer, not an exact thermodynamic identity, so don't expect it to hold at extreme humidity, unusual air velocities past the wick, or non-standard pressure.

Why does this calculator assume standard atmospheric pressure?

All the humidity and vapor-pressure relationships here (and the water Antoine constants used) are referenced to standard atmospheric pressure (760 mmHg / 101.325 kPa). At significantly different total pressures (high altitude, pressurized dryers), the humidity-ratio and wet-bulb relationships need pressure-corrected forms.

What is the valid temperature range for this calculator?

The underlying water Antoine equation is valid from about 1°C to 100°C, the same range used by this site's Antoine Equation Calculator. Results outside that range (e.g., sub-freezing or superheated-steam conditions) are not reliable.

Can I use this instead of a psychrometric chart?

Yes, for the standard-pressure calculations this calculator covers, it solves the same underlying relationships a psychrometric chart plots graphically, but returns exact numeric values instead of a graphical read-off, and shows the intermediate steps a chart can't. A physical chart is still useful for visualizing how properties move together across a wide range at a glance.

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Antoine-Based

Psychrometric
Calculator

Compute humidity ratio, relative humidity, and wet-bulb relationships for moist air, with full step-by-step solutions.

Formula

$H = \dfrac{18}{29}\cdot\dfrac{p_w}{P-p_w}$

Quick Answer

Given dry-bulb temperature and one other psychrometric property (relative humidity, humidity ratio, or wet-bulb temperature), this calculator computes the rest using the water Antoine equation for saturation vapor pressure, the standard humidity-ratio relationship, and the psychrometer equation for wet-bulb conversions, all at standard atmospheric pressure (760 mmHg).

Psychrometric Calculator

$H = \dfrac{18}{29}\cdot\dfrac{p_w}{P-p_w}$ · standard atmospheric pressure (760 mmHg)

Dry-Bulb Temperature (°C)

Relative Humidity (%)

Valid range: 1–100°C (water Antoine equation).

How to Use the Psychrometric Calculator

1
Enter the dry-bulb temperature
Enter the dry-bulb (ordinary thermometer) temperature of the air.
2
Choose your known second property
Select whether you know the relative humidity, the humidity ratio, or the wet-bulb temperature.
3
Enter that value
Enter the value for whichever property you selected.
4
Read the computed properties
Read the resulting relative humidity, humidity ratio, and saturation/actual vapor pressures, along with the full step-by-step solution.

See the drying-rate application of these properties in the Drying & Humidification topic guide, or the underlying vapor-pressure calculation in the Antoine Equation Calculator.

What Is Psychrometry?

Psychrometry describes the properties of moist air, mixtures of dry air and water vapor, using a small set of interrelated quantities: humidity ratio, relative humidity, dry-bulb temperature, and wet-bulb temperature. Because all of these connect back to the water vapor partial pressure, the Antoine equation (already used elsewhere on this site for pure-component vapor pressure) is the computational core of every psychrometric calculation.

This calculator lets you start from whichever property you actually have, relative humidity, humidity ratio, or wet-bulb temperature, and computes the rest, at standard atmospheric pressure.

A sling psychrometer with a wet-bulb thermometer covered in a wetted muslin sleeve — The instrument this calculator replaces the graphical read-off for — spin it, read both thermometers, get wet-bulb and dry-bulb temperature directly. CambridgeBayWeather, Public domain, via Wikimedia Commons.

Derivation: From Vapor Pressure to Humidity Ratio

Humidity ratio H is defined as the mass of water vapor per mass of dry air in a given volume of moist air. Using the ideal gas law for both the water vapor and dry-air partial pressures in that same volume at the same temperature, the mass ratio reduces to a partial-pressure ratio scaled by the molecular weight ratio of water to air:

H = \dfrac{m_w}{m_a} = \dfrac{M_w n_w}{M_a n_a} = \dfrac{M_w}{M_a}\cdot\dfrac{p_w}{P - p_w} \approx \dfrac{18}{29}\cdot\dfrac{p_w}{P-p_w}

For the wet-bulb case, an exact thermodynamic derivation requires a simultaneous heat-and-mass-transfer balance at the wick surface (see the Drying & Humidification topic guide). The psychrometer equation used here, $p_w = p_{ws}(T_{wb}) - A_p P (T_{db}-T_{wb})$ , is the standard engineering linearization of that balance, with the empirical constant Ap ≈ 6.66×10⁻⁴ °C⁻¹ absorbing the heat/mass transfer coefficients for a normally ventilated wet-bulb thermometer.

The Psychrometric Chart

The saturation curve and constant-RH curves below are computed live from the same humidity-ratio relationship derived above, at standard atmospheric pressure, so the amber-marked points line up exactly with the two worked examples further down this page.

Saturation and constant-RH curves computed from H = (18/29)·pw/(P−pw) with pw from the Magnus vapor-pressure relation, at standard atmospheric pressure. Amber dots mark this article's two worked examples.

When You'll Need It in GATE Chemical Engineering

Humidification & drying problems, computing the humidity of air before and after a humidifier, or the driving force for constant-rate drying, both start from this calculator's relationships.
Wet-bulb / dew point conversions, problems that give one temperature and ask for another (or for relative humidity) are a direct application of the psychrometer equation here.
Cooling tower & air-conditioning numericals, less common on GATE CH specifically, but the same humidity-ratio relationships underlie these calculations when they appear.
Mass Transfer topic guide, see the Drying & Humidification section of the Mass Transfer topic guide for the drying-rate-curve application of these properties.

Two Fully Worked Examples

Example 1: Humidity Ratio from Relative Humidity

Problem: Air at 30°C has a relative humidity of 50%. Find the humidity ratio.

p_{ws}(30°C) = 10^{8.07131 - 1730.63/263.426} = 31.86\ \text{mmHg}

p_w = 0.50 \times 31.86 = 15.93\ \text{mmHg}

H = \dfrac{18}{29}\cdot\dfrac{15.93}{760-15.93}

Answer: H ≈ 0.01331 kg water/kg dry air

Example 2: Relative Humidity from Wet-Bulb Temperature

Problem: Dry-bulb temperature is 28°C and wet-bulb temperature is 20°C. Find the relative humidity.

p_{ws}(20°C) = 17.5\ \text{mmHg}, \quad p_{ws}(28°C) = 28.3\ \text{mmHg}

p_w = 17.5 - (6.66\times10^{-4})(760)(28-20) = 17.5 - 4.05

RH = \dfrac{13.45}{28.3}\times100

Answer: RH ≈ 47.5%

Common Mistakes GATE Students Make

Confusing wet-bulb temperature with dew point. Wet-bulb is an evaporative-cooling equilibrium; dew point is where condensation would just begin, they coincide only at saturation (RH = 100%).
Using the wrong molecular weight ratio. The 18/29 factor (water/air molecular weight ratio) is easy to invert by mistake, double-check which quantity is in the numerator.
Ignoring the Antoine equation's valid temperature range. Results outside roughly 1–100°C use extrapolated vapor pressures that no longer reflect real water behavior.
Assuming humidity ratio and relative humidity scale the same way. RH depends on both actual and saturation vapor pressure (which itself depends on temperature); humidity ratio does not directly involve saturation pressure at all, the same H can correspond to very different RH values at different temperatures.

Key Takeaways

Every psychrometric property traces back to the water vapor partial pressure, via the Antoine equation.
Humidity ratio H = (18/29)·pw/(P−pw); relative humidity RH = pw/pws × 100.
The psychrometer equation converts wet-bulb readings to vapor pressure using an empirical constant Ap ≈ 6.66×10⁻⁴ °C⁻¹.
All relationships here assume standard atmospheric pressure (760 mmHg).
Valid only over the water Antoine equation's fitted range, roughly 1–100°C.

Frequently Asked Questions

Anywhere a process cares about the water vapor riding along with air rather than the air itself, sizing a dryer's driving force, checking a cooling tower's approach, or converting a wet-bulb field reading into something usable in a mass balance. See the derivation below for how every one of these properties reduces to a single underlying vapor-pressure relationship.

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When You'll Need It in GATE Chemical Engineering

Two Fully Worked Examples

Example 1: Humidity Ratio from Relative Humidity

Example 2: Relative Humidity from Wet-Bulb Temperature

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Key Takeaways

Frequently Asked Questions

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Drying & Humidification

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What Is Psychrometry?

Derivation: From Vapor Pressure to Humidity Ratio

The Psychrometric Chart

When You'll Need It in GATE Chemical Engineering

Two Fully Worked Examples

Example 1: Humidity Ratio from Relative Humidity

Example 2: Relative Humidity from Wet-Bulb Temperature

Common Mistakes GATE Students Make

Key Takeaways

Frequently Asked Questions

Related

Drying & Humidification

Antoine Equation

GATE CH Formula Sheet

GATE Practice Tests by Year

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