WBGT estimate from temperature and humidity calculator
At 32 °C and 65% relative humidity in the shade, the estimated wet bulb globe temperature is just over twenty-eight degrees Celsius. A quick heat-stress screen from basic weather readings, not a replacement for a WBGT meter. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Temperature c
- 32
- Relative humidity percent
- 65
- Estimated wet bulb c
- 26.636942
- Estimated wbgt c
- 28.245859
- Approximation
- shade_no_solar_load
This calculator estimates wet bulb globe temperature from Celsius air temperature and relative humidity when conditions are shaded and direct solar load is not represented. It first approximates natural wet-bulb temperature, then combines that result with air temperature to produce a simplified WBGT value. The calculation is quick, repeatable, and useful for screening environmental heat conditions when only basic weather observations are available. It is an estimate rather than a substitute for a properly positioned WBGT instrument, especially in sun, near radiant heat, or where wind differs from ordinary outdoor conditions.
What this shade WBGT estimate represents
Wet bulb globe temperature is designed to summarize several environmental contributors to heat stress, but a complete field measurement normally uses separate wet-bulb, globe, and dry-bulb sensors. This calculator addresses a narrower situation: you have shade air temperature and relative humidity, but no globe thermometer or direct wet-bulb reading. It estimates wet-bulb temperature with an empirical formula and treats air temperature as the globe-temperature stand-in for a simplified no-solar-load result.
That makes the output suitable for an initial screen, a consistent comparison between records, or a lightweight automated workflow. It does not measure a person’s core temperature, account for clothing, workload, acclimatization, hydration, medical conditions, or local radiant sources. It also cannot reconstruct direct sunlight from humidity and air temperature alone.
Read the value as an environmental approximation under shade assumptions. If a policy, sporting event, industrial procedure, or health decision requires an official WBGT, use a calibrated instrument and the thresholds specified by the responsible authority rather than relying on this estimate by itself.
How temperature and humidity become an estimate
The calculation uses the Stull empirical approximation for wet-bulb temperature. That expression combines Celsius air temperature and relative humidity through square-root, power, and arctangent terms, and is commonly useful because it needs no iterative psychrometric solver or pressure observation. After obtaining the estimated wet-bulb temperature, the calculator applies a shade approximation: seventy percent wet-bulb temperature plus thirty percent air temperature.
The accepted domain is deliberately explicit. Temperature must be from minus twenty through fifty degrees Celsius, and relative humidity must be from five through ninety-nine percent, inclusive. Those limits keep the inputs within the practical validity region used for the wet-bulb approximation.
Humidity outside that percentage interval returns an invalid-input error instead of extrapolating a plausible-looking but unsupported answer.
Using the result responsibly
Provide an air temperature observed in shade and a relative-humidity percentage measured for the same place and time. The response repeats both inputs, reports the estimated wet-bulb temperature, reports the estimated WBGT, and labels the approximation as shade with no solar load. Keeping the intermediate wet-bulb estimate visible makes the result easier to audit and reproduce in a spreadsheet or another implementation.
For comparisons, use measurements collected with consistent sensor exposure and timing; mixing a sun-heated temperature sensor with shaded humidity data can create a misleading result. Outdoor sun, hot machinery, furnaces, warm walls, unusual wind, and protective clothing can all make experienced heat strain differ substantially from this number. A sensible workflow uses the estimate to flag records for attention, then applies the organization’s current heat-safety procedure and obtains instrument readings where consequences are meaningful.
No weather service is contacted, so the caller remains responsible for supplying representative observations.
What you can do with it
Screen shaded work conditions
Turn a nearby shaded temperature and humidity observation into a preliminary WBGT estimate before deciding whether an instrument reading is needed.
Add a consistent field to weather records
Calculate the same simplified shade indicator for each observation in an environmental dataset without calling an external weather service.
Check sensor dashboards
Display an approximate WBGT beside temperature and humidity while clearly identifying it as a no-solar-load estimate rather than a measured value.
FAQ
Is this a measured WBGT value?
No. It is a simplified shade estimate derived only from air temperature and relative humidity.
Does it account for direct sunlight?
No. Direct solar load and other radiant heat require globe-temperature information that these two inputs do not provide.
What temperature range is accepted?
The calculator accepts finite Celsius temperatures from -20 through 50, inclusive.
How is WBGT estimated from temperature and humidity?
First the wet-bulb temperature is approximated with Stull’s formula from air temperature and humidity. The shade WBGT is then seventy percent of that wet-bulb value plus thirty percent of the air temperature.
What humidity range is accepted?
Relative humidity from 5 through 99 percent, inclusive. Readings outside that span are rejected instead of being stretched into a plausible-looking answer the approximation does not support.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/earth/wbgt-estimate \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"temperature_c":32,"relative_humidity_percent":65}'const res = await fetch("https://api.kit.forhosting.com/earth/wbgt-estimate", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"temperature_c": 32,
"relative_humidity_percent": 65
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/earth/wbgt-estimate",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"temperature_c": 32,
"relative_humidity_percent": 65
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/earth/wbgt-estimate", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"temperature_c":32,"relative_humidity_percent":65}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"temperature_c":32,"relative_humidity_percent":65}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/earth/wbgt-estimate", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"temperature_c": 32,
"relative_humidity_percent": 65
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "earth.wbgt_estimate",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How temperature and humidity become an estimate
Values must be actual finite JSON numbers; numeric strings, missing fields, infinities, and not-a-number values are rejected rather than silently converted.
Using the result responsibly
The API costs $0.002 per request, while the browser version can run the same deterministic arithmetic locally.
Technical questions
Why is humidity limited to 5 through 99 percent?
That is the supported relative-humidity interval for this implementation of the empirical wet-bulb approximation; values outside it return invalid_input.
What does the API request cost?
Each API request costs $0.002. The same deterministic calculation is also available in the browser experience.