Show HN: Unsure Calculator – back-of-a-napkin probabilistic calculator

How it works & notation

• Calculator interprets expressions with uncertain numbers, sampling them via Monte Carlo (≈250k evaluations) and reporting quantiles (esp. 95% ranges).
• a~b denotes a range; in some versions this is a normal distribution with a and b at ±2σ, in newer code it’s a uniform distribution, causing confusion because the deployed web app lags behind the changelog.
• Other syntaxes discussed: x +- d for a normal with mean x and 95% bounds x±d; function-like distributions (G(µ,σ), U(a,b), etc.) were proposed.
• The tool treats the whole expression as a single random variable, not doing formal error propagation.

Statistical limitations & edge cases

• Multiple comments probe behavior on divisions with ranges including 0 (e.g. 1/(-1~1)); users expected something like ±∞, but the tool reports a finite 95% interval. Some argue this is correct for a 95% CI; others find it unintuitive given heavy-tailed reciprocal distributions.
• Negative outputs from all-positive “ranges” arise because those ranges are 95% intervals of an underlying normal, which extends below zero; some find this reasonable, others would prefer hard-bounded intervals.
• Independence assumptions are highlighted as a major caveat: real-world quantities (rent vs. food, tasks sharing a person, macroeconomic shocks) are often correlated, which the tool doesn’t model.
• Several commenters note people systematically underestimate 90–95% intervals; the tool can help expose that overconfidence.

Feature ideas and UX feedback

• Requests: explicit choice of distribution (normal, uniform, log-normal, triangular), correlation modeling, constraints (e.g. B = 4 − A, B>0), a “confidence” operator, non-scalar multiplication (e.g. sum of dice instead of scaling a single draw), better mobile UX, and graphical plots beyond ASCII histograms.
• Some find web latency high; others use or propose faster CLI / Python / NumPy variants.

Alternative approaches and related tools

• Mentioned alternatives: probabilistic spreadsheets (Guesstimate, Carlo), Squiggle language, Android “distribution calculator”, command-line tools (fermi, Precel), qalc, NIST uncertainty calculator, interval/affine arithmetic, fuzzy numbers, Prolog interval constraint libraries, Emacs calculator modes.
• Debate over Monte Carlo vs. interval/fuzzy methods: Monte Carlo is more flexible in distributions; interval approaches give hard bounds and can be faster but don’t produce full PDFs.

Perceived uses and educational value

• Widely praised as a way to build intuition for uncertainty, Fermi estimation, and back-of-the-envelope reasoning.
• Example use cases: software/project estimation, personal finance, LLM or cloud cost estimation, marketing campaign planning, rough market sizing, geometry/engineering back-calculations.