Mathematical decision tools for growth engineers and founders. Instant, un-gated, and engineered with open formulas.
Calculate exact Target ROAS, break-even thresholds, and required profit margins across Google & Meta campaigns.
ROAS = Gross Revenue / Ad Spend
Convert seamlessly between gross profit margin percentage and markup on cost. Avoid dangerous pricing errors.
Margin % = (Price - Cost) / Price
Itemize cost of goods, warehouse rent, software tools, taxes, and ad spend to model net operating profit (EBITDA).
Operating Profit = (Rev - COGS) - Fixed OPEX
Model customer acquisition backward from LTV to calculate maximum allowable CAC, CPL, and max PPC click bids.
Max CPC = (Net LTV / 3) × (CR₁ × CR₂)
Evaluate margin-adjusted Customer Lifetime Value, benchmark your LTV:CAC ratio health, and track CAC recovery speed.
Payback Mo = CAC / (ARPU × Gross Margin %)
Model token consumption COGS, Inference Efficiency Ratio (IER), true gross margins, Net LTV:CAC, and safe hybrid token quotas.
IER = Revenue / Direct Inference COGS (GPUs + Token APIs)
Model customer acquisition cohorts from inbound traffic down to net contribution profit using ARPU, ARPPU, and ROMI.
Profit = UA × (ARPU - CPA_visitor)
Cross-calculate acquisition costs, expected CTR, and conversion rates to stress-test your paid media budget.
CPA = CPC / Conversion Rate
Estimate the number of referring domains required to rank in the Top 10 based on keyword difficulty and target DR.
Link Gap = Competitor Med. Ref. Domains - Current
Forecast monthly Google Search ad spend from keyword demand and compute margin-based break-even CPC bids.
Max CPC = (AOV × Margin %) × CR %
Simulate 25 real-time scenarios analyzing Net Profit and ROAS across fluctuating CPC bids and conversion rates.
Net Margin = (Clicks × CR × AOV × Margin %) - Budget
Calculate statistical significance, two-tailed Z-scores, p-values, confidence intervals, and required sample size per variant.
Z = (p_B - p_A) / SE_pool
Forecast broadcast campaign revenue, benchmark Revenue Per Subscriber (RPS), calculate ESP ROI, and model list decay.
ROI = ((Email Revenue - ESP Cost) / ESP Cost) × 100
Model compounding competitor link growth, portfolio decay (link rot), required monthly velocity, and capital budgets to rank in Top 10.
V_mo = [RD_target(1+g)^T - RD_curr(1-δ)^T] · δ / [1 - (1-δ)^T]
Simulate passage extraction probability, exponential positional decay (t½ ≈ 350 tokens), and multi-engine viability across Google AI Overviews, Perplexity, and ChatGPT Search.
S_cit = 0.15·S_len + 0.25·S_pos + 0.20·S_fd + 0.15·S_edr + 0.10·S_dr + 0.15·S_fmt
Model total annual software expenditure across Ahrefs, SE Ranking, and Semrush. Quantify seat fees, credit overages, net migration savings, and reallocated link budgets.
ΔTCO = [S₁ + U₁·C_seat + O_credits] - [S₂ + U₂·C_seat + A_pack]