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Relative Humidity Calculator

Computes relative humidity from air temperature and dew point as the ratio of Magnus-formula vapour pressures, and the absolute humidity (grams of water vapour per cubic metre) from the ideal-gas law for water vapour.

When to use

A weather report gives temperature and dew point and you need the relative humidity, or you need the water-vapour content of air in g/m³ (e.g. for drying, greenhouses or HVAC).

Do not use when: You have relative humidity and need the dew point (use dew-point), or you need humidity ratio in g/kg of dry air, which also requires the air pressure.

Formula

es(T) = 6.1094·exp(17.625·T/(243.04 + T)) hPa (T in °C); RH = 100·es(Td)/es(T); absolute humidity = 100·es(Td) / (461.5 · (T + 273.15)) kg/m³ × 1000

Magnus formula with Alduchov & Eskridge (1996) coefficients; water vapour treated as an ideal gas with Rv = 461.5 J/(kg·K). Accurate to about 0.5 % RH for −40 to +50 °C.

Inputs

Parameter	Type	Required	Description
`temperature`	number	yes	Air (dry-bulb) temperature in temperature_unit. Range: ≥ -60, ≤ 140
`dew_point`	number	yes	Dew point temperature in temperature_unit; cannot exceed the air temperature. Range: ≥ -80, ≤ 140
`temperature_unit`	enum: c \| f	default c	Unit of the temperature input(s).

Outputs

Output	Type	Unit	Description
`relative_humidity_percent`	number	%	RH = 100 × es(Td) / es(T).
`absolute_humidity_g_m3`	number	g/m³	Mass of water vapour per cubic metre of air, e / (Rv × T_K).
`vapor_pressure_hpa`	number	hPa	Partial pressure of water vapour, es(Td).
`saturation_vapor_pressure_hpa`	number	hPa	es(T) at the air temperature.
`saturation_absolute_humidity_g_m3`	number	g/m³	Water vapour content the air could hold at 100 % RH and this temperature.
`dew_point_depression_c`	number	°C	T − Td in Celsius.
`comfort`	string		NWS dew-point comfort band.

Example

25 °C, dew point 19.15 °C: {"temperature":25,"dew_point":19.15,"temperature_unit":"c"} → {"relative_humidity_percent":70,"absolute_humidity_g_m3":16.09,"vapor_pressure_hpa":22.13,"saturation_vapor_pressure_hpa":31.62,"dew_point_depression_c":5.9}

30 °C, dew point 10 °C: {"temperature":30,"dew_point":10,"temperature_unit":"c"} → {"relative_humidity_percent":28.9,"absolute_humidity_g_m3":8.76,"saturation_absolute_humidity_g_m3":30.28}

GET https://tttkmbb.com/api/v1/calculate/relative-humidity?temperature=25&dew_point=19.15&temperature_unit=c

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/relative-humidity (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/relative-humidity · Markdown: https://tttkmbb.com/weather/relative-humidity.md · JSON definition: https://tttkmbb.com/weather/relative-humidity.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="relative-humidity"
OpenAPI operationId: calculate_relative_humidity
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Alduchov OA, Eskridge RE (1996) Improved Magnus form approximation of saturation vapor pressure, J Appl Meteorol 35:601-609 (peer_reviewed)
Wikipedia – Dew point (reference)

FAQ

Can relative humidity exceed 100 %?

Not in this calculator: a dew point above the air temperature is physically impossible for saturated equilibrium and returns an error.

What is the difference between absolute humidity and humidity ratio?

Absolute humidity is grams of vapour per cubic metre of moist air; the humidity ratio (mixing ratio) is grams of vapour per kilogram of dry air and needs the total air pressure.

Related calculators

Dew Point Calculator — Inverse: dew point from temperature and relative humidity.
Air Density Calculator — Density of moist air from temperature, pressure and humidity.
Heat Index Calculator — Apparent temperature from temperature and humidity.