# Toolstacks — Complete Machine & LLM Reference Manual (llms-full.txt) > Comprehensive mathematical documentation, variable specifications, equations, and worked examples for all calculators on Toolstacks (https://toolstacks.xyz). --- ## 1. AI Cost Calculator - **URL**: https://toolstacks.xyz/tools/ai-cost-calculator/ - **Category**: AI & Automation - **Summary**: Forecasts API token expenses for major foundation models (GPT-4o, Claude 3.5 Sonnet, Gemini 1.5 Flash / Pro, DeepSeek V3, etc.) based on token inputs, token outputs, prompt cache rates, and request volumes. - **Formula**: `Total Request Cost = (Input Tokens / 1,000,000 × Input Rate) + (Output Tokens / 1,000,000 × Output Rate) + (Cached Tokens / 1,000,000 × Cached Rate)` `Monthly Cost = Total Request Cost × Daily Requests × 30.4167` - **Variables**: - `Input Tokens`: Number of prompt tokens submitted per API request. - `Output Tokens`: Number of generation tokens produced per API request. - `Cached Tokens`: Number of prompt tokens retrieved from provider KV cache. - `Request Volume`: Daily or monthly count of total requests. - **Assumptions**: 1 token ≈ 0.75 English words (approx. 4 characters). Excludes hosting egress, network transit, and custom fine-tuning charges. --- ## 2. AI ROI Calculator - **URL**: https://toolstacks.xyz/tools/ai-roi-calculator/ - **Category**: AI & Automation - **Summary**: Computes net annual benefit, break-even period in months, and return on investment (ROI %) for enterprise or departmental AI tooling implementations. - **Formula**: `Gross Annual Savings = (Hours Saved / Month × Average Hourly Wage × 12) + Incremental Annual Revenue` `Total 1st Year Cost = Implementation Fee + (Monthly Software & API Costs × 12)` `Net Benefit = Gross Annual Savings - Total 1st Year Cost` `ROI (%) = (Net Benefit / Total 1st Year Cost) × 100` `Payback Period (Months) = (Total 1st Year Cost / (Gross Annual Savings / 12))` - **Variables**: - `Hours Saved / Month`: Total productive labor hours reclaimed by the team. - `Average Hourly Wage`: Fully burdened hourly compensation rate ($/hr). - `Implementation Fee`: One-time setup, onboarding, and engineering cost. - `Monthly Platform Cost`: Recurring SaaS license or API subscription fees. --- ## 3. AI Automation Savings Calculator - **URL**: https://toolstacks.xyz/tools/ai-automation-savings-calculator/ - **Category**: AI & Automation - **Summary**: Quantifies operational cost savings and reclaimed capacity when automating manual business processes with AI or algorithmic automation. - **Formula**: `Annual Labor Cost Before = (Hours Spent per Week × 52) × Fully Burdened Hourly Rate` `Annual Labor Cost After = Annual Labor Cost Before × (1 - Automation Percentage / 100)` `Annual Net Savings = (Annual Labor Cost Before - Annual Labor Cost After) - Annual Tooling Cost` - **Variables**: - `Weekly Hours`: Manual employee hours dedicated to the repetitive workflow. - `Burdened Hourly Rate`: Employee hourly compensation including benefits. - `Automation Percentage`: Estimated proportion of the workflow handled autonomously. - `Annual Tooling Cost`: Annual software licensing fee for the automation system. --- ## 4. Subscription Cost Calculator - **URL**: https://toolstacks.xyz/tools/subscription-cost-calculator/ - **Category**: Subscriptions - **Summary**: Audits recurring services across streaming, software, productivity, and fitness to calculate total monthly, annual, 5-year, and 10-year cumulative spending. - **Formula**: `Monthly Total = Sum of Monthly Equivalent Fees across all subscriptions` `Annual Total = Monthly Total × 12` `5-Year Total = Annual Total × 5` `10-Year Total = Annual Total × 10` - **Assumptions**: Assumes subscription prices remain constant; does not factor in potential future price increases or currency fluctuations. --- ## 5. Subscription Savings & Wealth Calculator - **URL**: https://toolstacks.xyz/tools/subscription-savings-calculator/ - **Category**: Subscriptions - **Summary**: Models the compound future wealth generated by canceling or downgrading recurring subscriptions and redirecting those savings into an investment fund. - **Formula**: `Future Value (FV) = Monthly Savings × [((1 + r/12)^(12×t) - 1) / (r/12)]` where: - `r` = Annual expected investment rate of return (e.g., 0.08 for 8%). - `t` = Time horizon in years. - **Key Insight**: A modest $60/month subscription reduction compounding at an 8% average return yields over $35,000 in 20 years. --- ## 6. Coast FIRE Calculator - **URL**: https://toolstacks.xyz/tools/coast-fire-calculator/ - **Category**: Financial Planning - **Summary**: Calculates the exact investment balance needed at your current age so compound growth alone will fund your desired retirement nest egg without further contributions. - **Formula**: `Target Nest Egg = Desired Annual Retirement Spending / Safe Withdrawal Rate (typically 4%)` `Coast FIRE Required Number = Target Nest Egg / (1 + Real Return Rate)^(Retirement Age - Current Age)` `Real Return Rate = Nominal Annual Return Rate - Annual Inflation Rate` - **Variables**: - `Current Age`: Age today. - `Retirement Age`: Target age when retirement withdrawals begin. - `Desired Annual Spending`: Target annual living expenses in retirement (in today's dollars). - `Nominal Return Rate`: Expected average investment return before inflation (e.g., 8-10%). - `Inflation Rate`: Long-term expected inflation (typically 2.5-3%). --- ## 7. Mortgage Recast Calculator - **URL**: https://toolstacks.xyz/tools/mortgage-recast-calculator/ - **Category**: Financial Planning - **Summary**: Determines new reduced monthly payments and lifetime interest savings when making a lump-sum principal prepayment and recasting an existing fixed-rate mortgage. - **Formula**: `New Principal Balance = Current Principal - Lump Sum Prepayment` `New Monthly Payment (P&I) = New Principal × [c(1 + c)^n] / [(1 + c)^n - 1]` where: - `c` = Monthly interest rate (Annual Interest Rate / 12) - `n` = Remaining term in months (Remaining Years × 12) - **Key Distinction**: Recasting preserves your existing interest rate, loan servicer, and remaining payoff date, whereas refinancing creates a new loan with underwriting fees and a new term. --- ## 8. Lottery Payout & Windfall Calculator - **URL**: https://toolstacks.xyz/tools/lottery-payout-calculator/ - **Category**: Money & Savings - **Summary**: Compares lump-sum cash option versus 30-year graduated annuity option for major lottery prizes, calculating mandatory federal withholding (24%), top federal tax bracket (37%), and state income tax liabilities. - **Formula**: `Cash Option = Advertised Jackpot × Cash Option Ratio (typically ~48-52%)` `Federal Mandatory Withholding = Cash Option × 24%` `Estimated Federal Top Bracket Liability = Cash Option × 37%` `State Tax Liability = Cash Option × State Tax Rate` `Net Lump Sum Payout = Cash Option - (Federal Top Tax Liability + State Tax Liability)` - **Key Consideration**: Annuities typically pay 30 graduated payments increasing at 5% annually, protecting winners against impulsive spending, whereas lump sums allow immediate investment deployment. --- ## Data Privacy & Technology Architecture All Toolstacks calculators run entirely in the browser using client-side JavaScript. No inputs or financial figures are sent to any remote server or persistent database. All tools are free, requiring no user account or login. For general inquiries or formula questions, visit https://toolstacks.xyz/about/ or contact team@toolstacks.xyz.