Deterministic engineering solvers: biquad filter design, room eigenmodes, LLM VRAM fit.
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Design one RBJ-cookbook biquad and report its numerical behaviour. The identical function behind the /lab/biquad coefficient tables. Returns coefficients at the requested sample rate, coefficients at every other rate whose Nyquist limit clears the corner, pole/zero geometry, the −3 dB points solved by bisection, a Q sweep, a gain sweep where the type uses gain, and the quantised forms. The 240-point response curve is omitted unless include=curve is passed. Non-finite values (a notch is −∞ at f0; a low-pass is −∞ at Nyquist) are encoded as the strings "Infinity", "-Infinity" and "NaN" — JSON has no other honest option, and null would be a different answer. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
Corner (or centre) frequency f0 in Hz. Must be below Nyquist.
Filter type.
Filter Q. Defaults to the type’s own default. Shelves ignore it (S is fixed at 1, matching Web Audio).
Sample rate in Hz. Defaults to 48000.
Peak/shelf gain in dB. Ignored by types that do not use gain.
Optional heavy block to include, omitted by default. "curve": The 240-point log-spaced magnitude response, and one per sweep row.
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Design one RBJ-cookbook biquad and report its numerical behaviour. The identical function behind the /lab/biquad coefficient tables. Returns coefficients at the requested sample rate, coefficients at every other rate whose Nyquist limit clears the corner, pole/zero geometry, the −3 dB points solved by bisection, a Q sweep, a gain sweep where the type uses gain, and the quantised forms. The 240-point response curve is omitted unless include=curve is passed. Non-finite values (a notch is −∞ at f0; a low-pass is −∞ at Nyquist) are encoded as the strings "Infinity", "-Infinity" and "NaN" — JSON has no other honest option, and null would be a different answer. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| q | number | Filter Q. Defaults to the type’s own default. Shelves ignore it (S is fixed at 1, matching Web Audio). |
| fs | number | Sample rate in Hz. Defaults to 48000. |
| freq* | number | Corner (or centre) frequency f0 in Hz. Must be below Nyquist. |
| gain | number | Peak/shelf gain in dB. Ignored by types that do not use gain. |
| type* | string | Filter type. |
| include | string | Optional heavy block to include, omitted by default. "curve": The 240-point log-spaced magnitude response, and one per sweep row. |
{
"type": "object",
"required": [
"type",
"freq"
],
"properties": {
"q": {
"type": "number",
"maximum": 100,
"minimum": 0.01,
"description": "Filter Q. Defaults to the type’s own default. Shelves ignore it (S is fixed at 1, matching Web Audio)."
},
"fs": {
"type": "number",
"default": 48000,
"maximum": 768000,
"minimum": 1000,
"description": "Sample rate in Hz. Defaults to 48000."
},
"freq": {
"type": "number",
"maximum": 1000000,
"minimum": 0.1,
"description": "Corner (or centre) frequency f0 in Hz. Must be below Nyquist."
},
"gain": {
"type": "number",
"maximum": 40,
"minimum": -40,
"description": "Peak/shelf gain in dB. Ignored by types that do not use gain."
},
"type": {
"enum": [
"lowpass",
"highpass",
"bandpass",
"notch",
"allpass",
"peaking",
"lowshelf",
"highshelf"
],
"type": "string",
"description": "Filter type."
},
"include": {
"enum": [
"curve"
],
"type": "string",
"description": "Optional heavy block to include, omitted by default. \"curve\": The 240-point log-spaced magnitude response, and one per sweep row."
}
},
"additionalProperties": false
}Solve an ideal Gaussian laser beam: Rayleigh range, divergence, radius at a distance, and the waist behind a focusing lens. The identical function behind the worked examples on /lab/gaussian-beam-calculator, built from the same q-propagation the calculator runs. Give a wavelength and a 1/e^2 waist radius to get the Rayleigh range, the far-field half-angle divergence and the depth of focus. Add `distance` (metres from the waist) for the beam radius and phase-front curvature there. Add `focal` (millimetres) to put a thin lens at the waist and get the focused waist radius, its distance behind the lens and its Rayleigh range. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| focal | number | Focal length in millimetres of a thin lens placed at the waist. When given, the result includes the focused waist. |
| waist* | number | 1/e^2 waist RADIUS in millimetres (not the diameter). At least one wavelength: the model is paraxial. |
| distance | number | Distance in metres, from the waist (or, when `focal` is given, from the lens, after it). Negative is upstream. When given, the result includes the beam radius and phase-front curvature there. |
| wavelength* | number | Vacuum wavelength in nanometres (632.8 for HeNe, 1064 for Nd:YAG). |
{
"type": "object",
"required": [
"wavelength",
"waist"
],
"properties": {
"focal": {
"type": "number",
"maximum": 1000000,
"minimum": 0.001,
"description": "Focal length in millimetres of a thin lens placed at the waist. When given, the result includes the focused waist."
},
"waist": {
"type": "number",
"maximum": 1000,
"minimum": 0.0001,
"description": "1/e^2 waist RADIUS in millimetres (not the diameter). At least one wavelength: the model is paraxial."
},
"distance": {
"type": "number",
"maximum": 1000000,
"minimum": -1000000,
"description": "Distance in metres, from the waist (or, when `focal` is given, from the lens, after it). Negative is upstream. When given, the result includes the beam radius and phase-front curvature there."
},
"wavelength": {
"type": "number",
"maximum": 20000,
"minimum": 100,
"description": "Vacuum wavelength in nanometres (632.8 for HeNe, 1064 for Nd:YAG)."
}
},
"additionalProperties": false
}Decide whether one LLM fits one accelerator, at every quantization. The identical function behind the /lab/llm-vram instrument. Returns one row per quantization (FP16 through Q3_K_M) with weight bytes and their basis, headroom, the largest context that fits, and the bandwidth-limited decode ceiling; plus the chosen best-fitting quant, the full-precision row, and a five-state verdict. Model geometry comes from each repo’s own config.json and tensor-shape index; accelerator capacity and bandwidth come from the site’s device table. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| gpu* | string | Accelerator slug. |
| batch | integer | Concurrent sequences sharing the cache. Omit it for the published page's 1. |
| model* | string | Model slug. |
| context | integer | Context length in tokens used for the headline verdict. Omit it and the solver takes its own default of 8192, which is what the published page states. |
| kvBytes | integer | Bytes per KV cache element: 2 for FP16/BF16 cache, 1 for an 8-bit cache. Omit it for the published page's 2. |
{
"type": "object",
"required": [
"model",
"gpu"
],
"properties": {
"gpu": {
"enum": [
"rtx-5090",
"rtx-5080",
"rtx-5070-ti",
"rtx-4090",
"rtx-4080-super",
"rtx-4070-ti-super",
"rtx-4060-ti-16gb",
"rtx-3090",
"rtx-3060-12gb",
"rtx-6000-ada",
"l40s",
"a100-40gb",
"a100-80gb",
"h100-sxm",
"h200-sxm",
"rx-7900-xtx",
"apple-m4-24gb",
"apple-m4-pro-48gb",
"apple-m4-max-128gb",
"apple-m3-ultra-512gb",
"jetson-orin-nano-super-8gb",
"jetson-agx-orin-64gb"
],
"type": "string",
"description": "Accelerator slug."
},
"batch": {
"type": "integer",
"default": 1,
"maximum": 1024,
"minimum": 1,
"description": "Concurrent sequences sharing the cache. Omit it for the published page's 1."
},
"model": {
"enum": [
"deepseek-r1-distill-llama-70b",
"deepseek-r1-distill-llama-8b",
"deepseek-r1-distill-qwen-1-5b",
"deepseek-r1-distill-qwen-14b",
"deepseek-r1-distill-qwen-32b",
"deepseek-r1-distill-qwen-7b",
"dolphin-mistral-24b-venice-edition",
"falcon3-7b-instruct",
"gemma-2-27b-it",
"gemma-2-9b-it",
"gemma-3-12b-it",
"gemma-3-1b-it",
"gemma-3-27b-it",
"gemma-3-4b-it",
"gpt-oss-120b",
"gpt-oss-20b",
"granite-3-3-8b-instruct",
"hermes-4-3-36b",
"hy3",
"k2-horizon-7b",
"kat-coder-v2-5-dev",
"laguna-s-2-1",
"laguna-xs-2-1",
"llama-3-1-70b-instruct",
"llama-3-1-8b-instruct",
"llama-3-1-nemotron-70b-instruct",
"llama-3-2-1b-instruct",
"llama-3-2-3b-instruct",
"llama-3-3-70b-instruct",
"minicpm5-1b",
"minicpm5-2b",
"mistral-7b-instruct-v0-3",
"mistral-nemo-instruct-2407",
"mistral-small-24b-instruct-2501",
"mixtral-8x7b-instruct-v0-1",
"nanbeige4-2-3b",
"nex-n2-5-pro",
"olmo-2-1124-13b-instruct",
"ornith-1-5-35b-a3b",
"ornith-1-5-9b",
"phi-3-5-mini-instruct",
"phi-4",
"phi-4-mini-instruct",
"qwen-agentworld-35b-a3b",
"qwen2-5-0-5b-instruct",
"qwen2-5-1-5b-instruct",
"qwen2-5-14b-instruct",
"qwen2-5-32b-instruct",
"qwen2-5-3b-instruct",
"qwen2-5-72b-instruct",
"qwen2-5-7b-instruct",
"qwen2-5-coder-32b-instruct",
"qwen2-5-coder-7b-instruct",
"qwen3-0-6b",
"qwen3-1-7b",
"qwen3-14b",
"qwen3-30b-a3b",
"qwen3-32b",
"qwen3-4b",
"qwen3-8b",
"qwq-32b",
"qwythos-9b-claude-mythos-5-1m",
"smollm2-1-7b-instruct",
"smollm2-135m-instruct",
"smollm2-360m-instruct",
"spark-x2-5-4b",
"tinyllama-1-1b-chat-v1-0",
"yi-1-5-34b-chat"
],
"type": "string",
"description": "Model slug."
},
"context": {
"type": "integer",
"default": 8192,
"maximum": 10000000,
"minimum": 1,
"description": "Context length in tokens used for the headline verdict. Omit it and the solver takes its own default of 8192, which is what the published page states."
},
"kvBytes": {
"type": "integer",
"default": 2,
"maximum": 4,
"minimum": 1,
"description": "Bytes per KV cache element: 2 for FP16/BF16 cache, 1 for an 8-bit cache. Omit it for the published page's 2."
}
},
"additionalProperties": false
}Solve a two-mirror laser cavity: g-parameters, stability, and the TEM00 waist and mirror spot sizes. The identical function behind the worked examples on /lab/optics-bench, built from the resonator code the bench runs. Give the mirror spacing `l` (cm), each mirror radius `r1`, `r2` (cm; positive is concave toward the cavity, negative convex, omitted means flat) and the wavelength `w` (nm). Returns g1, g2, their product, the round-trip half-trace and whether the cavity is stable; when it is, `mode` holds the waist radius (um), its distance from mirror 1 (cm) and the spot radius on each mirror (mm). `mode` is null for an unstable cavity or one on the g1*g2 = 0 or 1 boundary. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| l* | number | Mirror spacing (cavity length), centimetres. |
| w* | number | Wavelength, nanometres. |
| r1 | number | Radius of curvature of mirror 1, cm. Positive = concave toward the cavity, negative = convex. Omit for a flat mirror. |
| r2 | number | Radius of curvature of mirror 2, cm, same convention. Omit for a flat mirror. |
{
"type": "object",
"required": [
"l",
"w"
],
"properties": {
"l": {
"type": "number",
"maximum": 10000,
"minimum": 0.1,
"description": "Mirror spacing (cavity length), centimetres."
},
"w": {
"type": "number",
"maximum": 20000,
"minimum": 100,
"description": "Wavelength, nanometres."
},
"r1": {
"type": "number",
"maximum": 100000,
"minimum": -100000,
"description": "Radius of curvature of mirror 1, cm. Positive = concave toward the cavity, negative = convex. Omit for a flat mirror."
},
"r2": {
"type": "number",
"maximum": 100000,
"minimum": -100000,
"description": "Radius of curvature of mirror 2, cm, same convention. Omit for a flat mirror."
}
},
"additionalProperties": false
}Solve a vented loudspeaker box for the length of round port to cut, with both end corrections, the smallest workable diameter and the peak port air speed. The identical function behind the worked examples on /lab/port-length-calculator and the calculator itself. Give the net box volume `vol` (litres), the port inside diameter `dia` (cm) and the tuning `fb` (Hz); `temp` (deg C, default 20) sets the speed of sound. Returns the length to cut (cm), the acoustic length and the end correction it contains, the port area, length/diameter, the air volume the port displaces, and the smallest diameter that can reach the tuning. When the port is too narrow, `tooNarrow` is true and `cutLengthCm` is negative: the end corrections alone already exceed the acoustic length the tuning needs. Add `sd` (cone area, cm^2) and `xmax` (peak excursion, mm) together for the peak port air speed. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| fb* | number | Box tuning frequency, hertz. |
| sd | number | Driver effective cone area Sd, cm^2. Give with `xmax` for the peak port air speed. |
| dia* | number | Inside diameter of a round port, centimetres. For a slot, the diameter of the round port of equal area, 2*sqrt(w*h/pi). |
| vol* | number | Net internal box volume, litres (after the driver, bracing and port are subtracted). |
| temp | number | Air temperature, deg C. Default 20. |
Solve the eigenmodes of a rectangular room. The identical function behind the /lab/room-modes instrument. Dimensions are in feet and are converted at 0.3048 m/ft. Returns every mode below maxFreq, the three axial fundamentals, mode pile-ups (three or more modes within 5 Hz, capped at 200 Hz because dense modes above the Schroeder crossover are desirable rather than a defect), the widest axial gap below 200 Hz, and Schroeder frequencies at RT60 = 0.3 s and 0.6 s. The full mode list is omitted unless include=modes is passed; counts are always present. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| width* | number | Room width in feet. |
| height* | number | Ceiling height in feet. |
| length* | number | Room length in feet. |
| include | string | Optional heavy block to include, omitted by default. "modes": Every solved mode and the axial subset, with their (nx, ny, nz) orders. |
| maxFreq | number | Highest mode frequency to solve for, in Hz. Defaults to 300. Mode count scales with volume × frequency³, so a large room and a high maxFreq together are refused with a 400 once the enumeration would exceed 100,000 modes; the error names the maxFreq that would have worked. |
{
"type": "object",
"required": [
"width",
"length",
"height"
],
"properties": {
"width": {
"type": "number",
"maximum": 100,
"minimum": 3,
"description": "Room width in feet."
},
"height": {
"type": "number",
"maximum": 40,
"minimum": 3,
"description": "Ceiling height in feet."
},
"length": {
"type": "number",
"maximum": 100,
"minimum": 3,
"description": "Room length in feet."
},
"include": {
"enum": [
"modes"
],
"type": "string",
"description": "Optional heavy block to include, omitted by default. \"modes\": Every solved mode and the axial subset, with their (nx, ny, nz) orders."
},
"maxFreq": {
"type": "number",
"default": 300,
"maximum": 1000,
"minimum": 20,
"description": "Highest mode frequency to solve for, in Hz. Defaults to 300. Mode count scales with volume × frequency³, so a large room and a high maxFreq together are refused with a 400 once the enumeration would exceed 100,000 modes; the error names the maxFreq that would have worked."
}
},
"additionalProperties": false
}Solve the best rectangular room proportions for a given volume. The identical function that renders /lab/room-shape/{lo}-{hi}. Give a room volume in cubic feet and get the proportions to build: the length and width as multiples of the ceiling height, the exact dimensions at your volume, the widest axial gap they leave, and how far those proportions sit from a full solve at your exact volume. Also returns the band the volume falls in, that band's guarantee across its whole range, and which Bolt constraints are active at the answer. Five bands cover 800-5,000 cubic feet; a volume outside that range is refused rather than served from the nearest band. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| volume* | number | Room volume in cubic feet. Five bands cover 800–5000 ft³; anything outside that is a 400 naming the range, never an answer from the nearest band. |
{
"type": "object",
"required": [
"volume"
],
"properties": {
"volume": {
"type": "number",
"maximum": 1000000,
"minimum": 1,
"description": "Room volume in cubic feet. Five bands cover 800–5000 ft³; anything outside that is a 400 naming the range, never an answer from the nearest band."
}
},
"additionalProperties": false
}Solve the on-axis magnetic field of an air-core solenoid. The identical function behind the /lab/solenoid table. Returns the centre field per amp-turn and at the requested turns and current, the on-axis profile out to three half-lengths, the span over which the field holds to within 1% and 5% of its centre value, the field at the coil mouth as a fraction of the centre, how far the infinite-solenoid shortcut mu0*n*I overstates the answer, and the turn count below which the closed form should not be used on this geometry. Dimensions are in millimetres. The field is exactly linear in turns x current, so only that product changes the answer. Every result carries provenance.canonicalUrl — the published page for these exact inputs, or the lane hub when they are off the published grid.
| Argument | Type | Description |
|---|---|---|
| turns | integer | Number of turns. Defaults to 1, which is what the published pages state (their figures are per amp-turn). The field is exactly linear in turns x current. |
| length* | number | Winding length along the axis, in millimetres. |
| current | number | Winding current in amperes. Defaults to 1. Only the product of turns and current changes the answer. |
| diameter* | number | Mean winding diameter in millimetres. |
{
"type": "object",
"required": [
"diameter",
"length"
],
"properties": {
"turns": {
"type": "integer",
"default": 1,
"maximum": 1000000,
"minimum": 1,
"description": "Number of turns. Defaults to 1, which is what the published pages state (their figures are per amp-turn). The field is exactly linear in turns x current."
},
"length": {
"type": "number",
"maximum": 5000,
"minimum": 0.1,
"description": "Winding length along the axis, in millimetres."
},
"current": {
"type": "number",
"default": 1,
"maximum": 10000,
"minimum": 0.000001,
"description": "Winding current in amperes. Defaults to 1. Only the product of turns and current changes the answer."
},
"diameter": {
"type": "number",
"maximum": 2000,
"minimum": 0.1,
"description": "Mean winding diameter in millimetres."
}
},
"additionalProperties": false
}| xmax |
| number |
| Driver peak one-way excursion, mm. Give with `sd`. |
{
"type": "object",
"required": [
"vol",
"dia",
"fb"
],
"properties": {
"fb": {
"type": "number",
"maximum": 500,
"minimum": 1,
"description": "Box tuning frequency, hertz."
},
"sd": {
"type": "number",
"maximum": 20000,
"minimum": 1,
"description": "Driver effective cone area Sd, cm^2. Give with `xmax` for the peak port air speed."
},
"dia": {
"type": "number",
"maximum": 200,
"minimum": 0.1,
"description": "Inside diameter of a round port, centimetres. For a slot, the diameter of the round port of equal area, 2*sqrt(w*h/pi)."
},
"vol": {
"type": "number",
"maximum": 100000,
"minimum": 0.1,
"description": "Net internal box volume, litres (after the driver, bracing and port are subtracted)."
},
"temp": {
"type": "number",
"maximum": 60,
"minimum": -50,
"description": "Air temperature, deg C. Default 20."
},
"xmax": {
"type": "number",
"maximum": 100,
"minimum": 0.1,
"description": "Driver peak one-way excursion, mm. Give with `sd`."
}
},
"additionalProperties": false
}