Wien peak wavelength calculator
Turn a blackbody temperature in kelvins into the wavelength where its glow peaks: 5778 K gives about half a micrometre. Doubling the temperature halves the peak, so hot stars and warm surfaces are easy to compare. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Creativity
- 5,778
- Temperature k
- 5,778
- Peak wavelength m
- 0.0000005015
- Wien displacement constant m k
- 0.002897772
This Wien peak wavelength calculator converts an absolute blackbody temperature in kelvins into the wavelength where its spectral radiance per unit wavelength reaches its maximum. It applies Wien's displacement law with the SI displacement constant and returns the result in metres, along with the temperature, constant, and formula used. The calculation is deterministic and runs without network access. Temperatures must be finite and strictly greater than zero because zero or negative absolute temperatures are outside the formula's valid input domain.
What Wien's displacement law tells you
A blackbody emits a continuous spectrum whose shape depends on temperature. As the object becomes hotter, the maximum of the wavelength-based spectrum moves toward shorter wavelengths; as it becomes cooler, that maximum moves toward longer wavelengths. Wien's displacement law summarizes this inverse relationship as lambda max equals b divided by T.
Here, T is absolute temperature in kelvins and b is the Wien displacement constant, 2.897771955 times ten to the minus three metre kelvins. Because the constant combines metres and kelvins, dividing it by kelvins leaves a wavelength in metres. This result is the peak of spectral radiance expressed per unit wavelength, not a claim that the blackbody emits only at that wavelength.
Real blackbodies radiate across a broad spectrum on both sides of the maximum. The result is useful for quickly locating that maximum and comparing objects with different temperatures. For example, a stellar photosphere produces a much shorter peak wavelength than a room-temperature surface.
The inverse proportionality also makes comparisons simple: doubling the absolute temperature halves the calculated peak wavelength.
How to enter temperature and interpret the result
Provide one field named temperature as a finite number measured in kelvins. Do not enter degrees Celsius or Fahrenheit directly, because Wien's law requires an absolute thermodynamic temperature. Convert those scales to kelvins before calling the calculator.
To express it in micrometres, multiply by one million. Keeping metres as the canonical response avoids ambiguity and makes the output directly compatible with SI-based calculations.
Physical scope, conventions, and practical checks
Use this calculator when the source can reasonably be modeled as an ideal blackbody or when a blackbody approximation is sufficient for an estimate. Stars, heated laboratory emitters, planets, and thermal surfaces are common teaching examples, but real materials can contain absorption lines, emission lines, atmospheric effects, or wavelength-dependent emissivity that move or reshape an observed maximum. There is also an important convention behind the answer: the location of a spectrum's peak depends on whether radiance is expressed per unit wavelength or per unit frequency.
This capability uses the wavelength form of Wien's law and returns the wavelength-domain maximum. Converting that wavelength to a frequency does not produce the independently calculated peak of the frequency-domain spectrum, because the two spectral densities use different interval measures. For a quick reasonableness check, confirm that every result is positive and that a higher temperature produces a smaller wavelength.
What you can do with it
Estimate a star's spectral peak
Convert an effective photosphere temperature into a wavelength-domain blackbody peak for astronomy exercises and first-pass comparisons.
Check thermal emitter calculations
Verify the expected peak wavelength of a heated ideal emitter before selecting detectors, filters, or classroom measurement ranges.
Validate scientific software
Generate deterministic reference values and explicit invalid-temperature cases for tests of blackbody and radiative-transfer code.
FAQ
What formula does the calculator use?
It uses the wavelength form of Wien's displacement law: lambda max equals b divided by T, with b equal to 2.897771955 × 10^-3 metre kelvins.
What unit should the temperature use?
Enter absolute temperature in kelvins. Celsius and Fahrenheit values must be converted to kelvins first.
What unit is the peak wavelength returned in?
Multiply it by 10^9 for nanometres or 10^6 for micrometres.
Why are zero and negative temperatures rejected?
Wien's formula divides by absolute temperature, and its blackbody domain requires a temperature greater than zero kelvins. Zero would cause division by zero and negative values would produce a nonphysical wavelength.
Does this give the frequency-spectrum peak too?
No. It gives the maximum when spectral radiance is expressed per unit wavelength. The per-frequency spectrum has a different maximum and must be calculated with its own form.
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/astro/wien-peak-wavelength \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"temperature":5778}'const res = await fetch("https://api.kit.forhosting.com/astro/wien-peak-wavelength", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"temperature": 5778
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/wien-peak-wavelength",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"temperature": 5778
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/wien-peak-wavelength", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"temperature":5778}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"temperature":5778}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/wien-peak-wavelength", 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": 5778
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.wien_peak_wavelength",
"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 to enter temperature and interpret the result
A successful response includes temperature_k, which repeats the validated input; peak_wavelength_m, which is the calculated maximum in metres; wien_displacement_constant_m_k, which records the constant used; and formula, which identifies the relationship. To express the result in nanometres, multiply peak_wavelength_m by one billion. The endpoint rejects missing, nonnumeric, infinite, zero, and negative temperatures with an invalid_input error. That strict behavior matters in automated pipelines: an invalid absolute temperature should stop a calculation instead of producing infinity, a negative wavelength, or a plausible-looking fallback. API calls use $0.002 per request, while the browser version can run the same pure calculation locally.
Physical scope, conventions, and practical checks
You can also multiply the returned peak_wavelength_m by temperature_k; apart from floating-point representation, the product should reproduce the stated displacement constant. The calculation uses no clock, random source, stored state, or external service, so identical valid inputs yield identical JSON values.
Technical questions
How much does an API calculation cost?
Each API request costs $0.002. The browser calculator can run the same deterministic formula locally for free.