QRD Acoustic Diffuser Calculator (1D)
Use this tool to generate well depths for a one-dimensional Quadratic Residue Diffuser (QRD). Enter a prime number of wells, target design frequency, and well width.
What this acoustic diffuser calculator does
This page calculates the well pattern for a classic 1D QRD acoustic diffuser. A diffuser scatters reflected sound so your room sounds more open and natural without making it dead like heavy absorption can. Instead of removing energy, diffusion redistributes reflections across time and angle.
For home studios, listening rooms, podcast spaces, and small project rooms, a QRD panel can improve imaging and reduce harsh flutter echoes when placed correctly. The calculator gives you both the depth sequence and practical build metrics (panel width and estimated effective range).
How the QRD formula works
A QRD uses mathematical residues from a prime number sequence. Each well depth is set according to:
- Residue: rn = n² mod N
- Depth: dn = rn × λ / (2N)
- Wavelength: λ = c / f
Where N is the prime number of wells, c is speed of sound, and f is the target design frequency. The result is a repeating pattern that spreads reflected sound energy over different phases.
Choosing good input values
1) Design frequency
Lower design frequency means deeper wells and more low-frequency diffusion potential. Higher design frequency gives shallower wells that are easier to build but act on higher frequencies.
2) Prime number of wells
The number of wells must be prime for standard QRD math. Common values:
- 7 wells: compact starter build
- 11 wells: balanced size and performance
- 13 or 17 wells: smoother scattering at the cost of width
3) Well width
Narrower wells increase the upper frequency limit but are harder to construct accurately. Wider wells are easier to build and sturdier, but they reduce high-frequency diffusion.
Interpreting calculator results
After calculation, you will see:
- Wavelength at your design frequency
- Maximum well depth required for the panel
- Panel width based on well count and width
- Estimated operating range from low to high diffusion limits
- Full cut-depth schedule for each well
The frequency range is an engineering approximation to guide design decisions. Real performance depends on mounting location, room dimensions, boundaries, and construction precision.
Build tips for better real-world performance
- Use rigid material (MDF, plywood, hardwood, or dense composite).
- Keep partitions straight and consistent to avoid phase errors.
- Measure depth from the same reference plane for every well.
- Seal joints to reduce rattles and unintended resonances.
- Install at first reflection points, rear wall, or behind listening position depending on room goals.
When to use diffusion vs absorption
If a room is bright and chaotic, start with broadband absorption at first reflection points and bass trapping in corners. Once decay is under control, add diffusion to preserve energy and spaciousness. In many rooms, the best outcome is a hybrid of both approaches.
Quick FAQ
Can I use a non-prime well count?
For classic QRD math, prime values are strongly preferred. Non-prime values can create repeated patterns that reduce diffusion quality.
Can I scale the panel?
Yes. Changing design frequency proportionally changes well depths. Changing well width affects the panel width and high-frequency behavior.
Is one panel enough?
Usually, one panel helps but multiple panels placed strategically provide much more audible improvement, especially on rear and side boundaries.