2d qrd diffuser calculator - Aaron Graves, PhDude Replica

2D QRD / Skyline Diffuser Calculator

Enter your design values to generate a full depth matrix, build dimensions, and a quick cut list.

Prime Number (N) Common choices: 7, 11, 13, 17. Prime values give cleaner residue sequences.

Design Frequency f₀ (Hz) Lower f₀ means deeper wells and better low-frequency diffusion.

Well Width (mm) Used to estimate upper effective frequency.

Speed of Sound c (m/s) Use 343 m/s at room temperature (~20°C).

Tiles X (horizontal repeats)

Tiles Y (vertical repeats)

Fill inputs and click calculate.

What this 2D QRD diffuser calculator does

A 2D QRD diffuser (often called a skyline diffuser) scatters reflected sound in both horizontal and vertical directions. This calculator builds a quadratic residue pattern and converts it into well depths in millimeters so you can move directly into CAD, cutting, or CNC production.

How the math works

1) Residue sequence

For a prime number N, each index value is generated by:

r(n) = n² mod N

for n = 0 to N-1.

2) Base depth step

The base depth step is tied to your design frequency f₀:

d_step = c / (2 × N × f₀)

where c is speed of sound in m/s.

3) 2D depth index

A 2D skyline-style cell at position (x, y) uses:

index(x,y) = (r(x) + r(y)) mod N

and its physical depth is:

depth(x,y) = index(x,y) × d_step

Practical design notes

Lower frequency performance tracks with deeper maximum wells.
Upper useful range is constrained by well width: approximately c/(2 × well width).
Prime N is strongly recommended for proper residue distribution.
Construction tolerance matters: keep depth errors small and consistent.

Build workflow (recommended)

Choose N and f₀ from your acoustic goal and available depth.
Generate matrix and cut list.
Group blocks by depth index to simplify production.
Dry-fit first, then glue with a square reference jig.
Install at first-reflection zones or rear wall as required by your room strategy.

Common mistakes to avoid

Choosing a very low f₀ without enough physical depth.
Using non-prime N and expecting textbook QRD behavior.
Ignoring finish thickness (paint/veneer can alter shallow steps).
Mixing units during fabrication (mm vs inches).

Final tip

This calculator is excellent for planning, prototyping, and material estimation. For critical studio rooms, combine it with measurements (REW, ETC, and polar checks) so your diffuser placement and target band match the full treatment plan.