Relative Humidity (Vapor Pressure)
Relative humidity is the ratio of actual water vapor pressure to the saturated vapor pressure at the same temperature, expressed as a percentage. This approach uses direct pressure measurements.
RH = (e / eₛ) × 100
Dewpoint Equation
The Magnus-formula dewpoint method relates temperature, dewpoint temperature, and relative humidity. It is widely used in meteorology when a thermometer and hygrometer provide temperature and dewpoint readings.
RH = 100 × exp(17.271·Tᵈ/(237.7+Tᵈ)) / exp(17.271·T/(237.7+T))
How It Works
Relative humidity (RH) is the ratio of actual water vapor in the air to the maximum it could hold at that temperature, expressed as a percentage. This calculator supports two approaches: the vapor-pressure ratio (RH = AVP/SVP × 100) and the Magnus-formula dewpoint method, which relates temperature, dewpoint, and RH.
Example Problem
The actual vapor pressure is 12 mbar and the saturated vapor pressure is 20 mbar. What is the RH?
- Identify the knowns. Actual vapor pressure e = 12 mbar, saturation vapor pressure eₛ = 20 mbar at the measured air temperature.
- Identify what we're solving for. We want the relative humidity RH — the fraction of saturation moisture currently in the air, expressed as a percent.
- Write the vapor-pressure ratio: RH = (e / eₛ) × 100. The pressure units cancel, leaving a percentage.
- Substitute the values: RH = (12 mbar / 20 mbar) × 100.
- Simplify the arithmetic: 12 / 20 = 0.6, then 0.6 × 100 = 60.
- **The relative humidity is RH = 60%** — the air is holding 60% of the moisture it could carry at this temperature before condensation begins.
At 60% RH, the air holds 60% of the maximum moisture it could carry at that temperature.
When to Use Each Variable
- Solve for RH (Vapor Pressure) — when you have actual and saturated vapor pressure readings, e.g., using data from a weather station psychrometer.
- Solve for Actual Vapor Pressure — when you know RH and saturated vapor pressure, e.g., calculating moisture content for HVAC load analysis.
- Solve for Saturated Vapor Pressure — when you know RH and actual vapor pressure, e.g., verifying a sensor calibration against known conditions.
- Solve for RH from Dewpoint — when you have temperature and dewpoint readings, e.g., converting weather report dewpoint data to relative humidity.
- Solve for Dewpoint Temperature — when you know temperature and RH and need the dewpoint, e.g., predicting condensation on cold surfaces.
- Solve for Temperature — when you know dewpoint and RH and need the air temperature, e.g., back-calculating conditions from logged humidity data.
Key Concepts
Relative humidity expresses how close the air is to saturation as a percentage. At 100% RH, the air cannot hold more moisture and condensation begins. The saturation vapor pressure increases exponentially with temperature, which is why warm air can hold much more moisture than cold air. The Magnus formula provides an accurate approximation for the temperature-vapor pressure relationship.
Applications
- HVAC engineering: controlling indoor humidity for occupant comfort and preventing condensation on cold surfaces
- Meteorology: forecasting fog, dew, and precipitation based on temperature and dewpoint measurements
- Agriculture: monitoring greenhouse humidity to prevent plant diseases like mildew and botrytis
- Museum conservation: maintaining stable humidity to protect artwork, documents, and artifacts from moisture damage
- Electronics manufacturing: controlling humidity in clean rooms to prevent static discharge and corrosion
Common Mistakes
- Comparing RH values at different temperatures — 50% RH at 30°C contains far more moisture than 50% RH at 10°C because warm air holds more water vapor
- Confusing relative humidity with absolute humidity — RH is a percentage of capacity, not a measure of actual moisture content; use dewpoint or mixing ratio for absolute comparisons
- Assuming constant RH means constant comfort — a room at 50% RH and 20°C feels comfortable, but 50% RH at 35°C feels oppressively muggy because the absolute moisture content is much higher
Frequently Asked Questions
What is a comfortable indoor humidity level?
Most people find 30–50% RH comfortable. Below 30% can dry out skin, eyes, and mucous membranes and raise the risk of respiratory infection; above 60% encourages mold growth, dust mites, and condensation on cold surfaces. ASHRAE Standard 55 recommends 30–60% RH for general occupied spaces.
What is the difference between dewpoint and relative humidity?
Dewpoint is the temperature at which the air becomes fully saturated and condensation begins, an absolute measure of moisture. RH expresses how close the air currently is to that saturation point as a percentage. A dewpoint of 20 °C with an air temperature of 25 °C gives about 73% RH; warm the same air to 35 °C and RH falls to about 43% without losing any moisture.
Why does relative humidity change throughout the day?
RH rises as temperature drops (the air's saturation capacity falls) and falls as temperature climbs. That is why mornings often feel damp and afternoons feel dry even though the actual moisture content of the air may not change much. Use dewpoint, mixing ratio, or absolute humidity for moisture comparisons across temperatures.
What is the formula for relative humidity?
The vapor-pressure form is RH = (e / eₛ) × 100, where e is actual vapor pressure and eₛ is saturation vapor pressure at the air temperature. The Magnus formula provides eₛ(T) ≈ 6.1078 × exp(17.271 × T / (237.7 + T)) hPa for T in °C, which the dewpoint card on this calculator uses to relate temperature, dewpoint, and RH.
How do you calculate dewpoint from temperature and RH?
Using the Magnus approximation: γ = 17.271 × T / (237.7 + T) + ln(RH / 100); then Tᴅ = 237.7 × γ / (17.271 − γ), with T and Tᴅ in °C. For T = 25 °C and RH = 60%, γ ≈ 1.133, giving Tᴅ ≈ 16.7 °C. Any surface cooler than the dewpoint will collect condensation.
What is the saturation vapor pressure of water?
Saturation vapor pressure is the partial pressure of water vapor in equilibrium with liquid water at a given temperature. It roughly doubles every 10 °C: ≈ 0.61 kPa at 0 °C, ≈ 1.23 kPa at 10 °C, ≈ 2.34 kPa at 20 °C, and ≈ 4.24 kPa at 30 °C. This exponential growth is why warm air can hold so much more moisture than cold air.
How does humidity affect human comfort?
High humidity slows evaporative cooling from the skin, making warm air feel hotter (the heat index quantifies this). Low humidity in cold weather accelerates evaporation and feels colder. Indoor comfort ranges typically fall between 30–60% RH at 20–24 °C; outside that band, occupants report discomfort, dry-eye symptoms, or condensation problems.
Worked Examples
HVAC Design
At 24 °C supply air and 55% RH, what dewpoint does the AC need to hit to dehumidify?
An office HVAC engineer is sizing a chilled-water coil. Return-air sensors read 24 °C dry-bulb and 55% RH. To pull moisture out, the coil surface has to sit below the air's dewpoint — use the Magnus equation to find it.
- T = 24 °C, RH = 55%
- γ = 17.271 × T / (237.7 + T) + ln(RH / 100)
- γ = 17.271 × 24 / (237.7 + 24) + ln(0.55)
- γ = 414.50 / 261.70 + (−0.5978)
- γ = 1.5839 − 0.5978 = 0.9861
- Tᵈ = 237.7 × γ / (17.271 − γ) = 237.7 × 0.9861 / 16.285
Dewpoint Tᵈ ≈ 14.4 °C
A coil leaving-air temperature of about 12 °C (a few degrees below dewpoint) is the standard rule of thumb for sensible-plus-latent cooling. The deeper the coil sits below dewpoint, the more moisture it condenses out.
Archive Preservation
A museum reads 21 °C and a dewpoint of 12 °C — what's the relative humidity?
A rare-book vault is climate-controlled to 21 °C with a dewpoint sensor showing 12 °C. Conservation standards (ASHRAE Chapter 24) target 45–55% RH year-round for paper and parchment. Check whether the room is in spec.
- T = 21 °C, Tᵈ = 12 °C
- γ_T = 17.271 × 21 / (237.7 + 21) = 1.4020
- γ_Tᵈ = 17.271 × 12 / (237.7 + 12) = 0.8300
- RH = 100 × exp(γ_Tᵈ − γ_T)
- RH = 100 × exp(0.8300 − 1.4020) = 100 × exp(−0.5720)
RH ≈ 56.4% (just above the 45–55% target)
An RH of 56% is a touch high but acceptable. Above ~65% RH, mold-growth risk on cellulose materials rises sharply; below 30% RH, paper becomes brittle. Many archives accept a wider 30–60% band as long as daily swing stays under ±5%.
Greenhouse Agronomy
Greenhouse air is 82% RH against a saturated vapor pressure of 2.34 kPa — what's the actual vapor pressure?
A tomato greenhouse logs SVP = 2.34 kPa (matching about 20 °C leaf temperature) and 82% RH from the controller. The grower needs the actual vapor pressure (AVP) to compute vapor-pressure deficit (VPD = SVP − AVP), the variable that actually drives stomatal transpiration.
- RH = 82%, eₛ = 2.34 kPa
- e = (RH / 100) × eₛ
- e = 0.82 × 2.34 kPa
Actual vapor pressure e ≈ 1.92 kPa
VPD = 2.34 − 1.92 ≈ 0.42 kPa — on the low end of the 0.4–1.2 kPa sweet spot for tomatoes. Below 0.4 kPa, transpiration stalls and calcium-deficiency symptoms like blossom-end rot increase; above 1.2 kPa plants close stomata and yield falls.
Relative Humidity Formulas
Two formulations describe the same moisture state. The vapor-pressure ratio is algebraic and exact for known partial pressures; the Magnus / dewpoint pair is the working approximation used in meteorology and HVAC when temperature and dewpoint are the measured inputs:
Vapor-Pressure Form
RH = (e / es) × 100Relative humidity from actual and saturation vapor pressure
Magnus / Dewpoint Form
γ = 17.271 × T / (237.7 + T) + ln(RH / 100)Magnus auxiliary γ for the dewpoint solve
Td = 237.7 × γ / (17.271 − γ)Dewpoint temperature from T and RH
RH = 100 × exp(γTd − γT)Relative humidity from temperature and dewpoint
Where:
- RH — relative humidity (percent of saturation, 0–100%)
- e — actual partial pressure of water vapor (Pa, kPa, mbar)
- es — saturation vapor pressure at temperature T (same units as e)
- T — air (dry-bulb) temperature in degrees Celsius
- Td — dewpoint temperature in degrees Celsius
- γ — dimensionless Magnus auxiliary used in the dewpoint solve
The Magnus constants (17.271 and 237.7 °C) are the most common fit for the 0–60 °C range used in HVAC and meteorology; alternative coefficient sets (Tetens, Alduchov & Eskridge) exist for sub-zero or high-temperature regimes. The exponential growth of es(T) — roughly doubling every 10 °C — is why warm air can hold so much more moisture than cold air, and why a falling temperature at sunset drives RH up overnight.
Saturation Vapor Pressure of Water vs Temperature
Saturation vapor pressure es is the water-vapor pressure at equilibrium over liquid water — the denominator in relative humidity (RH = e / es × 100). It rises steeply with temperature, roughly doubling every 10 °C. Click a row to load that saturation vapor pressure (in kPa) into the calculator above, keeping your other inputs; the SVP-solve mode switches to the RH solve since that row supplies es as an input rather than an output.
| Temperature (°C) | es (kPa) | es (mmHg) |
|---|---|---|
| 0 | 0.6113 | 4.585 |
| 5 | 0.8726 | 6.545 |
| 10 | 1.228 | 9.212 |
| 15 | 1.706 | 12.79 |
| 20 | 2.339 | 17.54 |
| 25 | 3.169 | 23.77 |
| 30 | 4.245 | 31.84 |
| 35 | 5.627 | 42.2 |
| 40 | 7.381 | 55.37 |
| 50 | 12.34 | 92.59 |
| 60 | 19.93 | 149.5 |
| 80 | 47.37 | 355.3 |
| 100 | 101.3 | 760 |
Standard steam-table values for saturation vapor pressure over liquid water; the kPa column is authoritative and the mmHg column is derived (1 kPa = 7.5006 mmHg). Saturation vapor pressure is the denominator in relative humidity (RH = e / es × 100). Cross-check against standard references such as ASHRAE Fundamentals psychrometric data or NIST/ASME steam tables.
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