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Physics

Thermal Expansion

ΔL = α L ΔT. Free online Thermal Expansion. Calculate thermal expansion online — fast, accurate, mobile-friendly, no signup needed.

ΔL (m)
0.0006

Derivation

  1. ├── 01Givenalpha = 1.2000e-5, L = 1, dT = 50
  2. ├── 02Formulae.alpha × e.L × e.dT
  3. ├── 03Substitutee.1.2000e-5 × e.1 × e.50
  4. └── 04Compute ΔL (m)6.0000e-4
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§01What is

Understanding the Thermal Expansion

The Thermal Expansion computes ΔL (m) from 3 inputs: α (1/k), length (m), δt (k). ΔL = α L ΔT.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Thermal Expansion sits in that toolkit — it ΔL = α L ΔT. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

e.alpha × e.L × e.dT

Where

alpha
α (1/K)
L
Length (m)
dT
ΔT (K)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: α (1/K) = 0.000012, Length (m) = 1, ΔT (K) = 50.

  1. 01Start by noting the input — α (1/K): 0.000012.
  2. 02Start by noting the input — Length (m): 1.
  3. 03Start by noting the input — ΔT (K): 50.
  4. 04Substitute these values into the formula: e.alpha × e.L × e.dT
  5. 05Compute ΔL (m): the calculator returns 0.0006.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Thermal Expansion Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

α (1/K) halved

alpha = 6.00000e-6 (from 1.20000e-5)

Keep every other input at its default and halve the α (1/k). See how δl (m) responds.

  1. 01New α (1/K): 6.00000e-6
  2. 02Baseline ΔL (m): 0.0006
  3. 03New ΔL (m): 0.0003
  4. 04ΔL (m) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

α (1/K) doubled

alpha = 2.40000e-5 (from 1.20000e-5)

Keep every other input at its default and double the α (1/k). See how δl (m) responds.

  1. 01New α (1/K): 2.40000e-5
  2. 02Baseline ΔL (m): 0.0006
  3. 03New ΔL (m): 0.0012
  4. 04ΔL (m) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Length (m) halved

L = 0.5 (from 1)

Keep every other input at its default and halve the length (m). See how δl (m) responds.

  1. 01New Length (m): 0.5
  2. 02Baseline ΔL (m): 0.0006
  3. 03New ΔL (m): 0.0003
  4. 04ΔL (m) decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Length (m) doubled

L = 2 (from 1)

Keep every other input at its default and double the length (m). See how δl (m) responds.

  1. 01New Length (m): 2
  2. 02Baseline ΔL (m): 0.0006
  3. 03New ΔL (m): 0.0012
  4. 04ΔL (m) increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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