About & Quantitative Methodology

The Calculatorium (https://thecalculatorium.com) is an open-formula financial, statistical, e-commerce, and SaaS modeling reference developed and maintained by the The Calculatorium Quantitative Research & Engineering Desk.

01 // Open-Formula Transparency & Pre-Rendered Accuracy

Many online calculator directories hide their underlying equations or rely on generic one-size-fits-all templates. On The Calculatorium, every tool displays its exact algebraic or statistical equation directly below the results, pre-computes baseline outputs and 5-tier sensitivity tables at build time, and provides a step-by-step worked numerical derivation using real numbers.

02 // 34 Specialized Mathematical Engines

Our 205 calculators are powered by 34 domain-specific mathematical kernels:

• Payment & FX Fee Gross-Up (payment_fee): Models combined domestic base rates, cross-border/FX surcharges, fixed per-transaction fees, and B2B reverse invoice gross-up: ReverseGross = (TargetNet + Fixed) / (1 - BaseRate - IntlRate).
• E-Commerce & Paid Ad ROAS (ecom_profit): Models landed COGS, payment processing drag, unit contribution margin, and minimum Break-Even ROAS.
• LLM API Token Pricing (llm_token_cost): Separates input prompt tokens from higher-cost output completion tokens per 1M tokens, including 50% prefix prompt-caching discounts.
• SaaS Unit Economics & Valuation (saas_ltv_cac, rule_of_40, saas_ndr, ai_saas, saas_valuation): Models gross-margin-adjusted LTV:CAC, CAC payback months, Brad Feld's Rule of 40 (YoY ARR Growth % + EBITDA/FCF Margin %), Cohort Net Dollar Retention (NDR / GDR), and ARR exit multiples.
• Quantitative Risk, Sharpe & Kelly Sizing (kelly_criterion, sharpe_ratio, futures_liquidation, impermanent_loss, crypto_mining): Implements J. L. Kelly Jr.'s (1956) allocation equation f* = ((p * b - q) / b) * Fraction, William F. Sharpe's (1966) risk-adjusted ratio (Rp - Rf) / σp, perpetual futures isolated liquidation price, Uniswap AMM impermanent loss, and ASIC kWh tariff breakeven.
• Statistical Inference & Power Analysis (stats_significance, sample_size_mde, std_deviation, z_score_outlier, binomial_prob): Computes two-proportion Z-tests, Lehr's 80%-power sample size per variant N = 2·p_bar·(1-p_bar)·(Z_α/2 + Z_β)² / (p2 - p1)², 3-sigma outlier bounds, and exact discrete binomial cumulative probabilities P(X >= k).
• Corporate Finance, Venture SAFE, Real Estate & Operations (burn_runway, safe_dilution, house_flip_70, w2_to_1099, tax_reserve, employee_turnover, sla_downtime, eoq_inventory): Models startup net burn & cash runway, Y Combinator Post-Money SAFE dilution, the 70% ARV rule for house flipping, W-2 to 1099 contractor rate conversion, SHRM attrition replacement cost, SRE 99.99% uptime error budgets, and Ford W. Harris's (1913) Economic Order Quantity EOQ = sqrt(2DS/H).

03 // Primary Data Sources & Benchmark Citations

Industry quartile benchmarks and default rate parameters are compiled from publicly verifiable primary sources, including:

• Official merchant fee schedules published by Stripe, PayPal, Adyen, Square, Apple App Store, and Amazon FBA.
• Official API token pricing documentation from Anthropic (Claude Sonnet & Opus), OpenAI (GPT series), and Google DeepMind (Gemini).
• KeyBanc Capital Markets Private SaaS Survey, Bessemer Venture Partners Cloud Index, and U.S. Bureau of Labor Statistics (BLS) compensation data.
• Peer-reviewed statistical and quantitative literature (Fisher 1925, Neyman & Pearson 1933, Kelly 1956, Thorp 1969, Uniswap v2/v3 Core Whitepapers).

04 // Editorial Contact & Corrections Policy

If you identify a rate schedule update or wish to request a new domain formula, contact our editorial engineering team at editorial@thecalculatorium.com.