Glass Transition Temperature Estimate Calculator
The Fox equation estimates the glass transition temperature (Tg) of a miscible binary polymer blend from the Tg values and weight fractions of the two components: 1/Tg_blend = w1/Tg1 + w2/Tg2 (all temperatures in Kelvin). This is widely used in polymer blend design, copolymer characterization, and plasticization calculations. Enter the Tg of each component in degrees Celsius and the weight fraction of component 1 (w2 = 1 - w1 is calculated automatically). The result is returned in both Celsius and Kelvin.
Fox equation
1 / Tg_blend = w1 / Tg1 + w2 / Tg2
(Tg in Kelvin = T in C + 273.15)
Where w1 and w2 are the weight fractions of the two components (w1 + w2 = 1), and Tg1 and Tg2 are the glass transition temperatures of the pure components in Kelvin. This empirical relationship, proposed by Fox in 1956, assumes ideal mixing and applies to fully miscible blends.
Limitations of the Fox equation
The Fox equation works well for many miscible polymer blends and plasticizer-polymer systems, but has several limitations. It assumes no specific interactions between components (hydrogen bonding or other strong interactions can cause positive or negative deviations). It does not apply to immiscible blends, which retain separate Tg values. For copolymers with very different monomer Tg, the Gordon-Taylor equation (which includes an interaction parameter k) provides better accuracy.
Glass transition temperature: frequently asked questions
What is the glass transition temperature?
The glass transition temperature (Tg) is the temperature range over which an amorphous polymer changes from a hard, glassy state to a softer, rubbery state. Below Tg, chain segment mobility is frozen; above Tg, segments can move. Tg profoundly affects mechanical properties, dimensional stability, and processing behavior.
What is the Fox equation?
The Fox equation estimates Tg for a miscible blend of two polymers: 1/Tg_blend = w1/Tg1 + w2/Tg2, where w1 and w2 are weight fractions and Tg1 and Tg2 are glass transition temperatures in Kelvin. It is an empirical relationship that works well for many compatible polymer pairs.
What are Tg values for common polymers?
Polystyrene (PS): 100 C. Polymethylmethacrylate (PMMA): 105 C. Polycarbonate (PC): 147 C. Polyethylene (PE): -120 C. Polypropylene (PP): -10 C. Natural rubber (NR): -70 C. Polyvinyl chloride (PVC, unplasticized): 82 C. These values shift with molecular weight and plasticizer content.
Does the Fox equation work for all polymer blends?
The Fox equation applies only to fully miscible (single-phase) polymer blends. Immiscible blends (most common) retain separate Tg values for each phase. For copolymers and plasticized systems, the Fox equation also provides a reasonable estimate, substituting the Tg of the plasticizer (often well below room temperature) for one component.
How does plasticizer affect Tg?
Adding a plasticizer (small molecule with low Tg) to a polymer reduces the blend Tg. The Fox equation predicts this: adding 10 weight percent of a plasticizer with Tg = -60 C (213 K) to PVC (Tg = 82 C = 355 K) gives: 1/Tg = 0.10/213 + 0.90/355 = 0.000470 + 0.002535 = 0.003005; Tg = 333 K = 60 C. This is why plasticized PVC (flexible) feels very different from rigid PVC.
Official sources
- ASTM E1356, "Standard Test Method for Assignment of the Glass Transition Temperature by Differential Scanning Calorimetry": astm.org.
- NIST, Polymer Properties Data: nist.gov.
- ASM International, "ASM Handbook Vol. 11: Failure Analysis and Prevention (Polymers section)": asminternational.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.