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Tool // Diffusion science / Proof that can’t be faked

Bass diffusion model calculator: how fast will your launch reach its market?

The Bass model forecasts how many people adopt a new product over time, using an innovation rate p for people who adopt on their own and an imitation rate q for people influenced by earlier adopters. Enter the market size and both rates to see the adoption curve and its peak.

Adopters after 12 periods
90,869
Share of market
91%
Peak adoption period
6.2
PeakPeriodCumulative adopters
Adopters

How does the adoption forecaster work?

Borrowed from Diffusion science: Bass model (p, q)

F(t)=1−e−(p+q)t1+qpe−(p+q)tt∗=ln⁡(q/p)p+qF(t) = \frac{1 - e^{-(p+q)t}}{1 + \frac{q}{p}e^{-(p+q)t}} \qquad t^* = \frac{\ln(q/p)}{p+q}

Frank Bass built the model to explain how durable goods spread. Early adopters start the curve, and word of mouth speeds it up until the market fills.

A high q relative to p gives an S-shaped curve with a clear peak. A high p relative to q gives a fast start that then slows.

Worked example

A US software launch targets 100,000 buyers with p = 0.03 and q = 0.38 per quarter. Adoption reaches about 43,900 after 6 quarters and 90,900 after 12, with peak sales near quarter 6.2.

How should I read my result?

q below p

Adoption is driven by marketing, not word of mouth. Expect a fast start and a long tail.

q of 2 to 10 times p

A typical S-curve. Invest early in seeding and referrals to pull the peak forward.

q more than 10 times p

Word of mouth dominates and the start is slow. Seed a first group deliberately.

Embed this calculator

Add this calculator to your own page. The snippet includes a link back to the source.

Questions about adoption forecaster

How do I choose p and q?

Fit them to early sales data, or borrow values from a similar past launch.

Does the model include price?

No. The basic model covers timing of adoption, not the effect of price changes.

Is market size fixed?

In this version yes. Update it as the addressable market changes.

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