Methodology & Formulas

Core Assumptions

All TorchFI calculators are built on well-established financial principles and peer-reviewed research. Below are the key formulas, their sources, and links to the calculators that use them.

The 4% Rule & FIRE Number

Based on the Trinity Study (Cooley, Hubbard, and Walz, 1998) and subsequent analyses by Wade Pfau and Michael Kitces. The 4% rule finds that withdrawing 4% of a balanced portfolio (60% stocks / 40% bonds) in year one, then adjusting for inflation annually, has historically sustained a 30-year retirement with high probability.

Formula: FIRE Number = Annual Expenses × 25

Used by: FIRE Number Calculator, Lean FIRE Calculator, Fat FIRE Calculator, Can I FIRE?

Source: Cooley, Hubbard & Walz (1998). AAII Journal

Coast FIRE

Calculates how much you need today so that your investments grow to your FIRE number by a target retirement age without additional contributions. Uses the compound interest formula solved for present value.

Formula: Coast Number = FIRE Number / (1 + r)^t

Used by: Coast FIRE Calculator

Barista FIRE

Calculates the portfolio needed when you plan to work part-time and cover a portion of your expenses. The calculator subtracts projected part-time income from expenses before applying the 4% rule.

Formula: Portfolio Needed = (Annual Expenses − Part-Time Income) × 25

Used by: Barista FIRE Calculator

Compound Interest

Standard compound interest formula: A = P(1 + r)^t where P is principal, r is annual return rate, and t is years. Our calculators use annual compounding by default.

Used by: Compound Interest Calculator, Investment Fee Impact Calculator, FIRE Timeline

Investment Returns

Default expected return is 7% annually (nominal), which approximates the S&P 500's historical average after inflation (~10% nominal minus ~3% inflation = ~7% real). Users can adjust this to model different scenarios.

Source: Damodaran, A. Historical Returns on Stocks, Bonds and Bills — NYU Stern

Inflation

Default inflation assumption is 3% annually, based on the Federal Reserve's long-term target.

Source: U.S. Bureau of Labor Statistics — CPI-U

Safe Withdrawal Rate

Our withdrawal calculators start with the 4% rule and offer comparisons against Guyton-Klinger guardrails, Variable Percentage Withdrawal (VPW), and CAPE-based dynamic withdrawals.

Sources: Guyton & Klinger (2006) — Journal of Financial Planning · Bogleheads VPW · Kitces & Pfau (2014) rising equity glide path research

Used by: Safe Withdrawal Rate Calculator, Withdrawal Strategy Comparator

Monte Carlo Simulation

Runs thousands of randomized market scenarios using historical S&P 500 return (mean ~10%, σ ~15%) and volatility data. Results show probability distributions rather than single-point estimates.

Reference: Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. Springer.

Used by: Monte Carlo Calculator, FIRE Timeline

Tax Calculations

Tax-related calculators use current US federal tax brackets from the IRS. Country-specific calculators use each nation's official tax authority data.

Sources: IRS Publication 590-B · IRS Revenue Procedure (annual) · ATO (Australia) · HMRC (UK) · CRA (Canada) · NPS (Korea) · Belastingdienst (Netherlands) · BFS (Switzerland) · SAT (Mexico) · SARS (South Africa) · Receita Federal (Brazil)

Sequence of Return Risk

Models the impact of experiencing negative returns early in retirement. Our FIRE Bridge calculator and Sequence Risk calculator allow stress-testing against historical worst-case sequences (1973 Oil Crisis, 2000 Dot-com crash, 2008 GFC).

Used by: FIRE Bridge Calculator, Sequence of Return Risk Calculator

Data Sources

Every default value in our calculators is sourced from official government publications:

• US: IRS Revenue Procedure (annual), SSA COLA notices, Bureau of Labor Statistics
• UK: HMRC tax tables, UK State Pension rates, ONS cost of living data
• Australia: ATO superannuation rates, Centrelink pension thresholds
• Canada: CRA TFSA/RRSP limits, CPP/OAS amounts
• EU/EEA: National tax authorities' published rates
• Asia: NPS (Korea), Japan Pension Service, CPF (Singapore)
• Other: SARS (South Africa), SAT (Mexico), Receita Federal (Brazil)

All data is reviewed and updated annually in October–November after government budget announcements. See our Review Policy for the correction log and update schedule, or References for the full list of academic papers.

Open Source

All formulas are public and anyone can verify the math. See our Methodology page for formulas and References for research sources.

Limitations

• All calculators produce estimates, not guarantees. Markets are unpredictable.
• Historical returns do not guarantee future results.
• Calculators do not account for all possible scenarios (job loss, disability, inheritance, etc.).
• Our tools are for educational purposes, not financial advice. Consult a qualified professional for personalized advice.