Nyquist Criterion Calculator
The formula
What the nyquist criterion tells you
The scaling law behind nyquist criterion executed with its exponent printed: a·x^n, plus the sensitivity that makes power laws unforgiving.
Calculation: Nyquist Criterion = a × x^3.5 (empirical power law). Enter your inputs and every substitution is shown below the result.
Reading the result
The elasticity line is the point: with exponent 3.5 a 10 % measurement error costs 40 % of the answer.
Limitations and best practice
Power laws hold within a fitted range — extrapolating far outside it silently misleads.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Where does the exponent come from?
Why log scales?
Source & methodology
Published empirical scaling relation.
Nyquist Criterion: the number, the method and the caveats
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Searchers land on a Nyquist Criterion page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
There is a habit that separates people who get useful answers from Physics Laboratory numbers: they decide what question the figure answers before they compute it. Nyquist Criterion answers “Nyquist Criterion?” — and nothing else, which is precisely why the result is trustworthy.
In Science & Research the same quantity is often quoted under two or three different conventions. The formula printed above fixes one convention and applies it consistently, which is what makes results from this page comparable with each other.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here nyquist criterion = 11.314, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Input quantity first, at ≈39.6 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Every input in Nyquist Criterion, and what it does to the answer
The engine implements a single stated model: Nyquist Criterion = a × x^3.5 (empirical power law). There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Input quantity (example value 2) is a quantity rather than a category — precision here is cheap and worth having. Quantities scale everything downstream — a one-unit error here is multiplied across the whole result.
Scaling constant a (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Reference/output unit scale (example value 1) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Quantities scale everything downstream — a one-unit error here is multiplied across the whole result.
Nyquist Criterion with real numbers, step by step
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Input quantity, Scaling constant a, Reference/output unit scale. Run to the end, the nyquist criterion resolves to 11.314 — Steep exponent — small input errors blow up the output; measure x carefully on the bands this tool uses.
- x^3.5 = 11.3137
- Result = 1.00 × 11.3137 = 11.3137
- Elasticity: +1 % in x moves the result 3.5 %
Log₁₀ result — 1.05. Compare it against the main result of 11.314 before drawing conclusions.
Sensitivity (Δ% per +1 % x) — 3.5 %. This is the number experienced users quote when the headline alone would mislead.
Double x gives — 128.000. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
How far Nyquist Criterion can reasonably move
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Input quantity setting | Nyquist Criterion |
|---|---|
| 80 % of the example value | 5.181 |
| 90 % of the example value | 7.824 |
| example inputs | 11.314 |
| 110 % of the example value | 15.794 |
| 120 % of the example value | 21.416 |
Across 5 settings of Input quantity, the result spans 5.181 to 21.416. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Input quantity alone; the substitution steps will follow your figures exactly.
What actually moves your Nyquist Criterion
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the nyquist criterion was recalculated from scratch. Read it as a map of where Nyquist Criterion is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Input quantity +10 % → Nyquist Criterion = 15.794 · −10 % → 7.824 (the nyquist criterion shifts ≈39.6 %)
- Scaling constant a +10 % → Nyquist Criterion = 12.445 · −10 % → 10.182 (the nyquist criterion shifts ≈10.0 %)
- Reference/output unit scale: ten percent up gives 12.445, ten percent down gives 10.182 — ≈10.0 % of the nyquist criterion either way
Input quantity is the dominant lever here: ten percent either way moves the result by about 39.6 %, from 7.824 to 15.794. That is where a careless figure does the most damage, so check it against a source, and treat Scaling constant a as the second priority (≈10.0 % per ten percent). The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
Reading the result: bands, zones and thresholds
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “Steep exponent — small input errors blow up the output; measure x carefully” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Input quantity already spans 7.824 to 15.794. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Where Nyquist Criterion sits next to similar measures: this tool answers “how much is the Nyquist Criterion”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
Common mistakes with Nyquist Criterion (and the fix)
Power laws hold within a fitted range — extrapolating far outside it silently misleads. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Reusing a Nyquist Criterion from last season. In Science & Research the inputs are the thing that drifts; the formula does not.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Input quantity dominating — a careful figure there beats false precision everywhere else.
The subtlest error is answering the wrong question precisely. Confirm that nyquist criterion is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.
Six things to confirm before acting on Nyquist Criterion
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Note the date and the inputs beside the number so the figure can be audited later.
- Re-verify Input quantity against a source document — ten percent of error there moves the headline by ≈39.6 %.
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Five steps from raw inputs to a figure you can defend
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Nyquist Criterion takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Nyquist Criterion are input quantity, scaling constant a, reference/output unit scale. Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. When two sources disagree, it is almost never the arithmetic that differs.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Nyquist Criterion (11.314 for the example values), and note the verdict band. Note the assumption you are least sure about; that is where the real risk lives.
Step 3 — isolate your variables. Change one field, observe, revert. The live sensitivity list does the ranking for the default inputs; verify it against your own, because dominance shifts when the starting point shifts. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Nyquist Criterion from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 11.314 output. Six months from now the context is what turns this figure into a trend. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
From calculation to decision: where Nyquist Criterion earns its keep
Most Physics Laboratory disagreements are arithmetic disagreements in disguise. When Nyquist Criterion of 11.314 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Rounding early is the quietest way to introduce a permanent error.
Professionals in Physics Laboratory use this style of calculation as a screening filter before spending real money or effort: a quick Nyquist Criterion check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Nothing here is stored or transmitted, so the habit of checking is free: open the page, re-enter current figures, compare with the number you saved last time. A result worth acting on survives having its two shakiest inputs halved.
Nyquist Criterion — frequently asked questions
What affects Nyquist Criterion the most?
Nyquist Criterion is driven above all by Input quantity. Perturbing only that field by ten percent either way produced 15.794 against the 11.314 baseline — a ≈39.6 % response, while Scaling constant a manages ≈10.0 %.
Which matters more: scaling constant a or input quantity?
Input quantity, by a factor of about 4.0. Concretely: ten percent on Input quantity is worth ≈39.6 % of Nyquist Criterion, the same nudge on Scaling constant an only ≈10.0 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Nyquist Criterion?
With the example inputs on this page the result is 11.314, labelled “Steep exponent — small input errors blow up the output; measure x carefully”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Nyquist Criterion by hand?
Three steps: write the formula (Nyquist Criterion = a × x^3.5 (empirical power law)), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Nyquist Criterion than any number of calculator runs.
What happens to Nyquist Criterion if input quantity changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 7.824 to 15.794 across the ten-percent probe, i.e. ≈39.6 % sensitivity on the nyquist criterion.
Is the Nyquist Criterion result of 11.314 good or bad?
The tool answers “what”, not “whether”: 11.314 carries the verdict “Steep exponent — small input errors blow up the output; measure x carefully” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Can Nyquist Criterion be negative or empty?
Yes, and that is informative rather than broken: a negative Nyquist Criterion usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
How many significant figures are reliable in Nyquist Criterion?
About as many as your least precise input. The tool computes at full precision and displays rounded output; report 11.314 to a decimal place your inputs can actually support.
Where does the exponent come from?
Empirical fits to observations or physics (homology relations); cite the range of validity when reporting.
Why log scales?
Quantities spanning many orders of magnitude compare as straight lines on log axes.
Does this Nyquist Criterion tool store my numbers?
No. The entire calculation runs in your browser session; nothing entered above is transmitted or saved, which is the correct behaviour for sensitive Science & Research figures and the reason you can re-run this page as often as you like.
Key terms on this page
- Log₁₀ result
- 1.05 on the example inputs — a companion figure printed beside the headline of Nyquist Criterion so that no result is read in isolation.
- Sensitivity (Δ% per +1 % x)
- 3.5 % on the example inputs — a companion figure printed beside the headline of Nyquist Criterion so that no result is read in isolation.
- Double x gives
- 128.000 on the example inputs — a companion figure printed beside the headline of Nyquist Criterion so that no result is read in isolation.
- Nyquist Criterion
- The primary output of this tool: 11.314 for the default inputs, computed exactly from Nyquist Criterion = a × x^3.5 (empirical power law).
- Worked example
- The calculation written out in full so that nothing on this page has to be taken on trust.
- Verdict band
- The interpretation attached to a result (“Steep exponent — small input errors blow up the output; measure x carefully” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Nyquist Criterion moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
There is no black box on this page — the engine evaluates Nyquist Criterion = a × x^3.5 (empirical power law). Source of record: Published empirical scaling relation. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The promise to the reader is narrow and testable: same inputs, same output, no silent rounding, and no figure presented without the formula that produced it.
After the number: what to do with it
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.