Thermal Expansion in 3D Printing
How thermal expansion affects 3D printed part dimensions.
The delta-L = alpha x L0 x delta-T formula for FDM, resin, and metal printing with worked examples.
The Formula
ΔL is the dimensional change in mm, α is the coefficient of linear thermal expansion (CTE) in 1/K or 1/°C, L₀ is the original length in mm, and ΔT is the temperature change in Kelvin (equivalent to Celsius change).
Variables
| Symbol | Meaning |
|---|---|
| ΔL | Change in length (mm) |
| α | Linear coefficient of thermal expansion (1/K) |
| L₀ | Original length at reference temperature (mm) |
| ΔT | Temperature change (K or °C) |
CTE Values for Common 3D Printing Materials
| Material | CTE (10&sup6; /K) | Notes |
|---|---|---|
| PLA | 41–68 | Low warping tendency |
| PETG | 60–80 | Moderate |
| ABS | 70–90 | High warping risk |
| ASA | 70–80 | Similar to ABS |
| Nylon PA12 | 55–100 | High, absorbs moisture |
| TPU 95A | 100–150 | Very high, flexible |
| Aluminum | 23 | Reference for metal beds |
Example 1 — ABS warping
200mm ABS print cooling from 240C (print temp) to 25C (room temp)
ΔL = 80 × 10&sup6; × 200 × (240 - 25) = 80 × 10&sup6; × 200 × 215
ΔL = 3.44 mm contraction — 1.7% of total length
This is why ABS warps so aggressively. A 200mm part contracts 3.4mm as it cools. The base layers are already stuck to the bed while upper layers are still hot and trying to contract, creating internal stress that lifts the corners.
Example 2 — Aluminum bed vs PLA part mismatch
PLA part on 60C aluminum bed, cooling to 25C after print. 100mm part.
PLA contraction: 55e-6 × 100 × 35 = 0.19 mm
Aluminum contraction: 23e-6 × 100 × 35 = 0.08 mm
Mismatch: 0.11 mm per 100mm — why PLA sometimes pops off the bed automatically when cool
Key Notes
- CTE values for FDM materials are highly anisotropic. The Z-axis (layer-to-layer) typically expands 2-4x more than X/Y because inter-layer bonding is weaker than within-layer crystalline structure. Published bulk CTE values usually apply to injection-molded material, not FDM.
- Enclosures reduce warping by keeping parts at elevated temperature during printing, reducing the total ΔT until the print is fully complete. The part cools uniformly rather than cooling top-down, which distributes thermal stress more evenly.
- For resin printing, CTE matters less during printing (UV cure is near-isothermal) but affects long-term dimensional stability. Standard resins typically have CTE of 60-110 × 10&sup6; /K.