Linear thermal expansion calculator
A 10 m steel beam with α of 0.000012 per kelvin heated by 50 K grows 0.006 m, ending at 10.006 m. Enter the original length, the expansion coefficient and the temperature change to get both the change and the new length. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Original length
- 10
- Expansion coefficient
- 0.000012
- Temperature change
- 50
- Length change
- 0.006
- Final length
- 10.006
Linear thermal expansion describes how the length of a solid changes when its temperature rises or falls while the material stays in one phase and is free to expand. In textbooks and design handbooks the first-order model is a single product: the change in length ΔL equals the original length L₀ times the coefficient of linear expansion α times the temperature change ΔT. Typical α values for metals sit near ten to the minus five per kelvin; polymers and ceramics span a wider range. This calculator accepts those three numbers, rejects a negative original length because a negative geometric length is not a physical starting point for the model, then returns both the length change and the final length after the temperature shift. Positive ΔT models heating and growth for ordinary positive α; negative ΔT models cooling and contraction.
How linear thermal expansion is defined from L₀, α, and ΔT
Start from the engineering idealization used in secondary school and first-year materials courses: when a free solid rod or beam of initial length L₀ experiences a uniform temperature change ΔT and the material has a constant coefficient of linear expansion α over that interval, the change in length is ΔL equals L₀ times α times ΔT.
Length may be expressed in metres, millimetres, or inches as long as L₀ and ΔL share the same unit; α is inverse temperature, usually per kelvin or per degree Celsius, which are numerically identical for a temperature interval. Positive α with positive ΔT describes ordinary metals that grow when heated; negative ΔT describes cooling that shortens the same rod; unusual materials with negative α contract on heating and simply reverse the sign of ΔL.
The calculator does not integrate a temperature-dependent α of T curve, does not convert free expansion into constrained thermal stress, does not apply the two- or three-dimensional factors for area and volume expansion, and does not look up handbook tables by alloy name. It answers only the algebraic definition that homework sets call linear thermal expansion. Negative original length is the critical validation edge: a geometric length below zero is rejected with invalid input instead of returning a meaningless negative L₀ times α times ΔT product.
Zero length is allowed and yields zero change.
Where linear thermal expansion calculations show up in real work
Secondary-school and college physics courses constantly assign problems that give L₀, α, and ΔT and ask for ΔL or the final length, often for steel bridges, aluminum rails, or glass rods. University engineering labs use the same three-number reduction before they introduce constrained expansion, thermal stress, or finite-element temperature loads. Civil and mechanical designers sanity-check expansion joints, pipe runs, and precision machine frames when only free expansion is needed as a first bound.
If you later need area or volume expansion factors, temperature-dependent coefficient tables, unit conversion between metres and feet, or thermal stress under fixed ends, treat those as separate search intents and landings rather than overloading this linear thermal expansion calculator page.
What you can do with it
Homework and lab answer keys
Compute ΔL = L₀·α·ΔT for textbook free-expansion sets so teachers and auto-graders share one ground truth including the negative-length rejection.
Expansion-joint and rail checks
Estimate free length change of beams, rails, and pipe runs from design L₀, material α, and seasonal temperature swing.
FAQ
What happens if the original length is negative?
A negative geometric length is not valid for the linear thermal expansion model.
What units should I use?
Convert before calling if your sheet uses mixed units.
What does it cost?
The browser tool is free and runs locally.
Can I calculate how much a part shrinks when it cools?
Yes. Enter the temperature change as a negative number and the length change comes out negative, showing the contraction. The final length is then shorter than the original one.
Does it calculate thermal stress when the part cannot expand?
No. It assumes nothing stops the object from expanding. If the part is clamped or fixed at both ends, the stress that builds up needs a separate calculation that this tool does not perform.
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/thermo/linear-expansion \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"original_length":10,"expansion_coefficient":0.000012,"temperature_change":50}'const res = await fetch("https://api.kit.forhosting.com/thermo/linear-expansion", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"original_length": 10,
"expansion_coefficient": 0.000012,
"temperature_change": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/thermo/linear-expansion",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"original_length": 10,
"expansion_coefficient": 0.000012,
"temperature_change": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/thermo/linear-expansion", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"original_length":10,"expansion_coefficient":0.000012,"temperature_change":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"original_length":10,"expansion_coefficient":0.000012,"temperature_change":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/thermo/linear-expansion", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"original_length": 10,
"expansion_coefficient": 0.000012,
"temperature_change": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "thermo.linear_expansion",
"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
What you send and what you get back
Classic textbook checks include a ten-metre steel beam with α near twelve times ten to the minus six per kelvin heated by fifty degrees, which recovers a sub-millimetre growth of about six millimetres; a copper wire cooled by twenty degrees; and a zero-coefficient check that returns zero change. Send three finite numbers under the fields original_length, expansion_coefficient, and temperature_change. original_length is L₀ in any consistent length unit and must be greater than or equal to zero. expansion_coefficient is α in inverse kelvin or inverse Celsius and may be positive, zero, or negative. temperature_change is ΔT in kelvin or Celsius degrees and may be positive for heating or negative for cooling. Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. When original_length is negative the error message states that length must be non-negative for the linear thermal expansion formula, so clients can fix the record rather than guessing. On success the response echoes cleaned inputs, length_change as ΔL, final_length as L₀ plus ΔL, the formula string, and method linear_expansion. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where linear thermal expansion calculations show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Precision-assembly temperature bounds
Turn workshop temperature drift into expected dimensional growth for fixtures and machine frames before measuring scrap.
Technical questions
What formula does this linear thermal expansion calculator use?
ΔL = L₀ · α · ΔT, where L₀ is original_length, α is expansion_coefficient, and ΔT is temperature_change. The response also returns final_length = L₀ + ΔL.
Can temperature_change or the expansion coefficient be negative?
Yes. Negative ΔT models cooling; negative α models materials that contract on heating. Both simply reverse the sign of ΔL when the other factors are positive.