QRD Diffuser Design Calculator

A quadratic-residue diffuser — also known as a Schroeder diffuser — is a row of wells of different depths, separated by thin fins, invented by Manfred Schroeder. The depths follow a number sequence that gives the reflected sound an almost-flat scattering pattern across a wide range of angles, so instead of a hard specular echo you get even, diffuse reflection. For a prime number of wells N, well n gets the depth dₙ = (n² mod N) · λₗₒₓ / (2N), where λₗₒₓ = c / fₗₒₓ is the wavelength at your chosen design frequency. The deepest well sets how low the diffuser still works; the well width sets the top limit, fₕₒₕₕ = c / (2·width), because once the wavelength gets close to a well’s width the wells stop behaving as designed. A 2D Skyline diffuser extends the idea to a grid of square blocks whose heights come from a 2D residue array ((x²+y²) mod N), scattering in both directions instead of just one. The scattering coefficient — a standardised measure (ISO 17497-1) of how evenly energy is scattered across angles — is what separates a true diffuser from a merely irregular surface; an ideal QRD approaches a scattering coefficient of 1.0 across its design bandwidth. To identify the frequency range where room modes are dominant and diffusion is most valuable, use the Room Mode Calculator before sizing your diffuser panels.

The equations are exact, but a built acoustic diffuser is an approximation of the ideal. A panel of finite size loses low-frequency diffusion (you need enough periods), and tiling identical periods side by side creates lobing — concentrations of energy at certain angles — which modulated or optimised sequences (such as primitive-root diffusers or number-theoretic designs) are designed to avoid. For a DIY diffuser, fin thickness, accurate well depths, and a rigid build with dense material all affect real-world performance. The Schroeder frequency of a room (roughly 2000√(RT60/V), where RT60 is reverberation time and V is volume) marks the boundary below which room modes dominate — diffusers are most effective above this frequency, while bass traps and broadband absorbers handle below it. Most importantly, a diffuser scatters energy rather than removing it: use it to keep a space sounding live and spacious (classically on the rear wall behind the listener), and reach for absorption when you actually need to reduce energy. For calibrating how much total absorption a room needs alongside diffusion, the Reverb Time Designer lets you model the balance between absorptive and diffusive treatment.

The Schroeder frequency (also called the crossover frequency) divides a room's acoustic behaviour into two regimes. Below it, the room behaves modally: a small number of discrete standing waves (room modes) dominate the response, producing strong peaks and nulls at specific frequencies that move around the room. Above it, modes overlap so densely that the response becomes statistical and diffuse — the reverberant field where Sabine's equation and RT60 apply. The formula is: fₛ ≈ 2000 × √(RT60 / V), where RT60 is the reverberation time in seconds and V is the room volume in cubic metres. A 30 m³ room with an RT60 of 0.4 s, for example, has a Schroeder frequency around 230 Hz.

This boundary matters for diffuser placement: a QRD panel works in the statistical (above-Schroeder) region, where its designed scattering pattern is meaningful. Below the Schroeder frequency, room modes require modal treatment — bass traps, broadband absorbers, or room geometry changes — not diffusion. Use the Room Mode Calculator to map the specific standing waves in your space, and the RT60 Calculator to measure the reverberation time you need to plug into the formula above.