Calculator Formula Directory
Every formula behind all 63 TorchFI calculators
Core FIRE Formulas
FIRE Number
Formula: FIRE Number = Annual Expenses ÷ Withdrawal Rate
At the standard 4% withdrawal rate: FIRE Number = Annual Expenses × 25. This is the foundational FIRE calculation derived from the Trinity Study.
Coast FIRE Age
Formula: Coast Age = Current Age + ln(Target / Current Savings) ÷ ln(1 + Return Rate)
The age at which your existing savings will grow to your FIRE number through compound interest alone — no additional contributions needed.
Lean / Fat FIRE Number
Formula: Annual Expenses ÷ Withdrawal Rate
Same core formula as FIRE Number, but with different expense inputs. Lean FIRE uses minimal expenses ($20K-40K), Fat FIRE uses luxury-level expenses ($100K+).
Barista FIRE Number
Formula: (Expenses − Side Income) ÷ Withdrawal Rate
Your portfolio only needs to cover the shortfall between your expenses and part-time/side income.
Flamingo FIRE Number
Formula: Flamingo Number = Full FIRE Number ÷ 2; Doubling Time ≈ 72 ÷ Return Rate
Save half your FIRE number, then semi-retire while your portfolio doubles through compound interest (Rule of 72).
Savings & Investing Formulas
Compound Interest
Formula: A = P(1 + r)^t + C × ((1 + r)^t − 1) / r
Where P = principal, r = annual return rate, t = years, C = annual contribution. The most important formula in personal finance.
Savings Rate
Formula: Savings Rate = (Income − Expenses) ÷ Income × 100
Your single most important FIRE metric. A 50% savings rate means every year worked buys one year of freedom.
Dividend FIRE Number
Formula: Expenses ÷ Dividend Yield
How much you need invested to cover expenses entirely from dividends, without selling shares.
Investment Fee Impact
Formula: Fee Cost = P × ((1 + r − f)^t − (1 + r)^t)
Shows how a small annual fee percentage compounds into massive lost returns over decades.
Mortgage Payoff vs Invest
Formula: Compare: Mortgage Interest Saved vs. Market Return on Invested Lump Sum
Withdrawal Strategy Formulas
Safe Withdrawal Rate
Formula: Annual Income = Portfolio Balance × Withdrawal Rate
The 4% rule: withdraw 4% of your initial portfolio in year 1, then adjust for inflation annually.
Withdrawal Strategy Comparator
Formula: Compares 4% Rule, Guyton-Klinger Guardrails, VPW, and CAPE-based dynamic withdrawals across historical market scenarios.
Tax-Efficient Withdrawal
Formula: Optimizes withdrawal order across taxable brokerage, traditional accounts, and Roth accounts to minimize lifetime tax burden.
Sequence of Returns Risk
Formula: Monte Carlo simulation generating randomized market return sequences to measure portfolio failure probability.
Monte Carlo Simulation
Formula: Returns ~ N(μ, σ²) with μ = 10% (nominal), σ = 15%; runs thousands of randomized scenarios.
72(t) SEPP
Formula: RMD Method = Balance ÷ IRS Life Expectancy; Amortization = PMT(rate, life, balance); Annuitization = Balance × Annuity Factor
Three IRS-approved methods for penalty-free early IRA withdrawals before 59½.
Tax & Retirement Account Formulas
Roth vs Traditional 401(k)
Formula: Compare: (Contribution × (1 − Tax_now) × (1 + r)^t) vs. (Contribution × (1 + r)^t × (1 − Tax_retirement))
401(k) Early Withdrawal Penalty
Formula: Net = Withdrawal − 10% Penalty (if < 59½) − Federal Tax − State Tax
Social Security Break-Even
Formula: SSA benefit reduction = 5/9% per month (first 36 months before FRA) + 5/12% beyond; Delayed retirement credits = 8% per year past FRA
Life & Planning Formulas
Net Worth
Formula: Net Worth = Sum(Assets) − Sum(Liabilities)
FIRE Age / Years to FIRE
Formula: Years = ln((Target × r + Annual Savings) / (Current Savings × r + Annual Savings)) / ln(1 + r)
Inflation-Adjusted FIRE
Formula: Real Value = Nominal Value ÷ (1 + Inflation Rate)^Years; FIRE Number adjusts upward with expected inflation.
Couple FIRE
Formula: Combined Expenses ÷ Withdrawal Rate; two income streams, two Social Security benefits, shared expenses.
FIRE With Kids
Formula: (Expenses + Child Costs × Number of Children) ÷ Withdrawal Rate
Cost of Living Comparison
Formula: City FIRE Number = City Monthly Expenses × 12 ÷ Withdrawal Rate
Lifestyle Inflation Impact
Formula: Additional FIRE Number = Annual Lifestyle Increase ÷ Withdrawal Rate
One More Year Formula
Formula: One more year of working = +1 year of savings − 1 year of portfolio withdrawals = net impact on portfolio survival probability