Use this calculator to generate well depths for a 1D Quadratic Residue Diffuser (QRD). Enter your target design frequency, well count, and dimensions to get a build-ready depth table.
Tip: choose prime N values (7, 11, 13, 17...) for classic QRD behavior. Non-prime values can be calculated but typically produce weaker diffusion patterns.
What is a QRD diffuser?
A Quadratic Residue Diffuser is an acoustic surface that scatters reflected sound energy in time and direction. Instead of absorbing sound like a foam panel, a QRD keeps energy in the room while reducing harsh specular reflections and flutter echo. This helps a space feel clearer and more natural, especially in studios, listening rooms, and home theaters.
How this QRD diffuser calculator works
This tool uses the classic 1D QRD sequence based on quadratic residues. For each well index n, a residue value is computed and converted into physical depth. The depth formula used is:
- Residue: R(n) = n² mod N
- Depth step: dstep = c / (2 × N × f0)
- Well depth: d(n) = R(n) × dstep
Where N is well count, f0 is design frequency, and c is speed of sound. The result table lists each well depth in millimeters and inches for easy workshop use.
Frequency range estimates
The calculator also provides a practical operating range estimate:
- Low-end estimate: tied to maximum well depth (deeper wells scatter lower frequencies).
- High-end estimate: tied to well width (narrow wells support higher-frequency diffusion).
These are first-order estimates and should be treated as design guidance rather than exact room predictions.
Choosing your inputs
1) Prime number of wells (N)
Prime values are preferred because they generate more uniform residue distributions. Common sizes include 7, 11, 13, and 17 wells. Higher N gives finer phase steps and broader patterns, but construction becomes more complex.
2) Design frequency (f0)
Lower f0 means deeper wells, larger panels, and heavier builds. Higher f0 makes shallower, easier panels that focus on mid/high diffusion. For many small rooms, f0 between 600 and 1000 Hz is a practical starting point.
3) Well width
Well width strongly influences the upper working limit. Wide wells are easier to build but diffuse less effectively at high frequencies. Very narrow wells improve high-frequency behavior but increase cutting and assembly precision demands.
Build tips for real projects
- Keep partition walls straight and equal thickness to preserve sequence accuracy.
- Cut depths consistently; millimeter-level errors are worth avoiding.
- Use rigid materials (plywood, MDF, hardwood) to reduce panel resonance.
- Seal and finish surfaces to prevent humidity drift and warping.
- Mount at first reflection points, rear wall, or ceiling clouds based on room goals.
Practical limitations
This calculator models an idealized 1D QRD. Real performance also depends on edge effects, panel mounting, finite size, spacing from boundaries, and room modal behavior. For mission-critical rooms, combine this tool with measurement software and professional acoustic design.
Quick example
If you choose N = 7, f0 = 700 Hz, c = 343 m/s, and 70 mm wells, the calculator will produce a single-period sequence of 7 depth values. Repeat that period across multiple blocks to build a wider diffuser. The sequence repeats physically, but directional scattering improves as total panel area grows.