Polymer Polydispersity Index (PDI) Calculator

What Is the Polydispersity Index (PDI)?

The polydispersity index, usually written as PDI or given the symbol Đ (said 'đjay' or just 'dispersity'), is the number polymer chemists use to describe how uniform or how mixed a polymer sample's chain lengths are. Unlike a small molecule such as water or glucose, where every single molecule has exactly the same mass, a polymer sample is really a mixture of chains of many different lengths, all built from the same repeating unit but stopped at different points during the reaction.

Because of that, a polymer doesn't have one single molecular weight — it has a molecular weight distribution. PDI is simply a way of squeezing that whole distribution into one easy-to-compare number. A PDI close to 1.0 means the chains are almost all the same length. A high PDI, like 5 or 10, means the sample contains a wide mix of short and long chains sitting together.

This calculator lets you find PDI three different ways: directly from known Mn and Mw values, from a raw list of chain lengths and how many of each you have, or by solving backward for Mn or Mw when you already know the PDI. It also works out the degree of polymerization when you give it the repeat unit's molar mass.

The PDI Formula (Mw / Mn)

The polydispersity index is defined as the ratio of two different kinds of 'average' molecular weight — the weight-average molecular weight (Mw) divided by the number-average molecular weight (Mn):

• PDI (Đ) = Mw / Mn
• Mn = (Σ Ni·Mi) / (Σ Ni) — number-average molar mass
• Mw = (Σ Ni·Mi²) / (Σ Ni·Mi) — weight-average molar mass

Why Mn and Mw Are Different Averages

Mn, the number-average molecular weight, treats every chain equally, no matter how big or small it is — it's the total mass of the sample divided by the total number of chains, which is exactly how a simple average works. If you had ten chains and added up their weights and divided by ten, you'd get Mn.

Mw, the weight-average molecular weight, is calculated differently: it gives more influence to the bigger, heavier chains, because it weighs each chain's contribution by its own mass as well as its count. In practice, this means that a handful of very long chains can pull Mw noticeably higher than Mn, even if those long chains are a small fraction of the total number of chains present.

Because Mw is always pulled upward by the heavier chains while Mn treats every chain the same, Mw is always greater than or equal to Mn for any real polymer sample. That's exactly why their ratio, PDI = Mw/Mn, can never fall below 1.0 — and the further apart Mw and Mn are, the wider and more spread out the true chain-length distribution actually is.

How to Calculate PDI from a Chain-Length Distribution

If you already know Mn and Mw — say, from a gel permeation chromatography (GPC) or size-exclusion chromatography (SEC) report — the 'PDI from Mn & Mw' mode above gives you the answer instantly: just type both numbers in and the ratio is calculated for you.

But sometimes you're starting from raw data instead: a list of chain lengths (or molar masses) and how many chains exist at each one, maybe from a simulation, a theoretical distribution, or a manually counted sample. The 'PDI from Chain Distribution Table' mode handles that case directly. Add a row for every distinct molar mass Mi in your sample along with the count or relative frequency Ni at that mass, and the calculator sums everything using the Mn and Mw formulas above — no spreadsheet or manual summation required.

This mode also reports the z-average molecular weight, Mz, a third, even more heavily weighted average that some polymer characterization reports quote alongside Mn and Mw, along with the total chain count and total sample mass so you can double-check your entered data.

Solving the Mn / Mw / PDI Triangle

Because PDI is just Mw divided by Mn, if you know any two of the three values — Mn, Mw, or PDI — you automatically know the third one. This comes up constantly in coursework and lab reports: a problem might give you the number-average molecular weight and the polydispersity index and ask you to find the weight-average molecular weight, or the other way around.

The 'Solve for Mn or Mw' mode does exactly that. Choose whether you want to solve for Mw or for Mn, enter the value you already know along with the PDI, and the calculator rearranges the formula for you: Mw = Mn × PDI, or Mn = Mw / PDI.

Degree of Polymerization (DPn and DPw)

The degree of polymerization tells you, on average, how many repeat units are strung together in a single polymer chain — essentially the chain length measured in monomer units rather than in grams per mole. It's found by dividing a molecular weight average by the molar mass of the single repeat unit (M0), which is usually just the monomer's molar mass, minus any small molecule lost during polymerization (like water in a condensation reaction).

This calculator can compute both DPn (from Mn) and DPw (from Mw) automatically — just tick the 'degree of polymerization' checkbox in the Mn & Mw mode or the distribution mode and enter the repeat unit's molar mass. For example, polystyrene's repeat unit (styrene) has a molar mass of about 104.15 g/mol, so a polystyrene chain with Mn = 42,000 g/mol has a DPn of roughly 403 repeat units.

How to Read a PDI Value: Narrow vs Broad Distribution

A PDI value on its own doesn't mean much until you know what range it falls in. As a general guide across the polymer chemistry field:

• PDI = 1.0: perfectly monodisperse — every chain is exactly the same length. This is essentially never achieved by synthetic polymers, though it's approached by proteins and other precisely templated biomolecules.
• PDI 1.0-1.2: narrow distribution — typical of living or controlled polymerizations such as anionic polymerization, ATRP, or RAFT, where chain growth is tightly regulated.
• PDI 1.2-2.0: moderate distribution — a fairly uniform sample. Many step-growth (condensation) polymers approach the theoretical Flory 'most probable distribution' limit of exactly 2.0 at very high conversion.
• PDI 2.0-5.0: broad distribution — common in conventional free-radical polymerization, where chains start and stop at random points throughout the reaction.
• PDI above 5.0: very broad, often multimodal distribution — typical of branched or crosslinked industrial polymers such as low-density polyethylene (LDPE), which can show PDI values well into the double digits.

Why Polydispersity Matters in the Real World

PDI isn't just an academic number — it has a direct, practical effect on how a polymer behaves. A material with a narrow, low PDI tends to have more consistent, predictable mechanical properties, melting behavior, and processing characteristics, because nearly all of its chains behave the same way under stress or heat. That consistency is exactly why pharmaceutical polymers, precision coatings, and high-performance engineering plastics are often synthesized under tightly controlled 'living' polymerization conditions specifically to keep PDI low.

A broader PDI, on the other hand, usually means a mix of short chains (which can act almost like a plasticizer, lowering strength and melting point) and very long chains (which increase viscosity and toughness) sitting in the same material. Manufacturers sometimes deliberately target a broader distribution because it can improve processability — for example, making a plastic easier to extrude or mold — even though it sacrifices some property consistency. Quality control labs routinely run GPC/SEC analysis and report PDI alongside Mn and Mw specifically to catch batch-to-batch drift in a polymerization process before it reaches production.

Who Uses a Polydispersity Index Calculator

Polymer chemistry students use PDI calculations constantly in coursework covering step-growth and chain-growth polymerization, since it's one of the standard ways professors test whether a student understands the difference between number-average and weight-average statistics. Graduate researchers working with GPC/SEC instruments use PDI to characterize every new polymer they synthesize, whether it's for a materials science thesis or a new drug-delivery polymer.

Quality control and process engineers in plastics, rubber, adhesives, and coatings manufacturing track PDI batch to batch to make sure a polymerization reactor is behaving consistently. Materials scientists designing new formulations use PDI, alongside Mn and Mw, to predict how a candidate polymer will process and perform before committing to full-scale production.

A Quick Note on Accuracy

The formulas used in this calculator — Mn = ΣNiMi/ΣNi, Mw = ΣNiMi²/ΣNiMi, Mz = ΣNiMi³/ΣNiMi², and PDI = Mw/Mn — are the standard statistical definitions used throughout polymer science and taught in every introductory polymer chemistry course. They make this calculator reliable for coursework, lab report calculations, quick research estimates, and general reference use.

For a certified, instrument-reported PDI value used in a publication or a regulatory filing, always rely on the calibrated output from your GPC/SEC instrument's own software, since real-world chromatography results depend on column calibration, the reference standards used, and detector response in ways a simple hand calculation like this one cannot fully capture.