FIRE Calculator

Key formulas used in the FIRE calculation

The calculator is built around a few core concepts: your target portfolio size, the compounding of your investments, and the effect of ongoing contributions. The main steps are:

1. Compute the target portfolio required to support your desired retirement spending at your chosen withdrawal rate.
2. Grow your current portfolio by the expected annual return.
3. Add your annual contributions.
4. Repeat the growth and contribution steps each year until you reach (or exceed) the target portfolio, or until a maximum number of years has passed.

The target portfolio is calculated from your desired annual spending in retirement and your withdrawal rate. In basic form:

Target portfolio = Desired annual spending ÷ (Withdrawal rate ÷ 100)

For example, if you want to spend $40,000 per year and you choose a 4% withdrawal rate, the target portfolio is $40,000 ÷ 0.04 = $1,000,000.

Year by year, the calculator applies compound growth and contributions. If we let:

• P₀ be your initial savings (current portfolio),
• r be your expected annual return (as a decimal, so 5% becomes 0.05),
• C be your annual contribution, and
• P_t be your portfolio value after t years,

then, in simplified closed-form terms, ignoring the stopping rule when you hit the target:

Pt = P0 × (1 + r)t + C × [((1 + r)t − 1) ÷ r]

The calculator instead iterates year by year, which is easier to implement in code and helps handle edge cases such as zero or very small returns. In algorithm form:

balance = current_savings
for each year t:
  balance = balance × (1 + r)
  balance = balance + annual_contribution
  if balance ≥ target_portfolio:
      stop and report t years to FIRE
  stop after a maximum number of years if FIRE is not reached

To express the target portfolio formula more formally, here is a MathML representation:

How to interpret your FIRE results

Once you click the calculate button, the tool returns two main outputs:

• Estimated years to FIRE – the number of years it may take to reach your target portfolio size given your current savings, annual contributions, and expected return.
• Target portfolio size – the total portfolio value that, at your chosen withdrawal rate, would be expected to support your desired annual spending.

If the estimated years to FIRE is a relatively small number, it suggests that, under your assumptions, you are on a faster path to financial independence. If the number is very large, or the calculator indicates that FIRE is not reached within the projection horizon, it may be a sign that your current savings rate, expected returns, or spending goals need adjustment.

Consider the following when interpreting your results:

• Sensitivity to return assumptions: Small changes in the expected annual return (for example, 5% versus 7%) can meaningfully change your years to FIRE. Historical averages do not guarantee future performance, so it can be helpful to test both optimistic and conservative scenarios.
• Impact of savings rate: Increasing your annual contributions typically has a powerful effect on your timeline, especially in the early and middle years of your plan. This is because a higher savings rate both raises contributions and often reduces desired retirement spending if it reflects a more frugal lifestyle.
• Role of spending goals: Lowering your desired annual spending in retirement reduces the target portfolio, which can substantially shorten your path to FIRE. Many people find that revisiting housing, transportation, and lifestyle choices can change their long-term numbers more than trying to chase higher investment returns.
• Withdrawal rate trade-offs: A lower withdrawal rate (for example, 3% instead of 4%) is more conservative, but requires a larger portfolio and therefore typically leads to more years to FIRE. A higher withdrawal rate means you can reach your goal with a smaller portfolio, but increases the risk that your money may not last in all market conditions.

Worked example: estimating a FIRE timeline

To see how the calculator works in practice, imagine the following situation:

• Current savings: $10,000
• Annual contribution: $12,000
• Expected annual return: 5%
• Desired annual spending in retirement: $40,000
• Withdrawal rate: 4%

Step 1: Calculate the target portfolio. Using the withdrawal rate formula:

Target portfolio = 40,000 ÷ 0.04 = 1,000,000

So you are aiming for a $1,000,000 portfolio.

Step 2: Project year-by-year growth. In the first year:

• Start with $10,000.
• Apply 5% growth: $10,000 × 1.05 = $10,500.
• Add $12,000 contribution: $10,500 + $12,000 = $22,500.

At the end of year one, your projected balance is $22,500.

In the second year:

• Apply 5% growth: $22,500 × 1.05 = $23,625.
• Add $12,000 contribution: $23,625 + $12,000 = $35,625.

The calculator continues this process each year, checking whether your balance has reached $1,000,000. With these assumptions, you would typically reach the target portfolio in a few decades. The exact year may differ slightly from hand calculations due to rounding and the specific implementation, but the order of magnitude will be similar.

You can then experiment with different inputs. For example, raising your annual contribution from $12,000 to $18,000, or reducing your desired retirement spending from $40,000 to $35,000, will generally shorten the time to FIRE. Conversely, lowering your expected return or choosing a more conservative withdrawal rate will lengthen the estimated timeline.

Comparing different FIRE scenarios

One of the main benefits of this calculator is the ability to compare how changes in savings, returns, and withdrawal rates affect your path to financial independence. The table below summarizes some qualitative differences between more aggressive and more conservative assumptions.

Use the calculator to create your own scenarios by adjusting one input at a time. For instance, hold your expected return constant and test different savings levels, or keep your spending target fixed and explore how different withdrawal rates change the target portfolio.

Assumptions and limitations of this FIRE calculator

Because FIRE planning involves the future, any projection is necessarily uncertain. This tool uses a simplified model that can be very helpful for education and planning, but it does not capture every real-world factor. Some important assumptions and limitations include:

• Constant annual return: The calculator assumes a fixed average annual return on your investments. Real markets are volatile, and the sequence of returns (the order in which good and bad years occur) can strongly affect outcomes, especially around the time you retire.
• Regular contributions: Contributions are assumed to be the same every year. In reality, your income and savings rate may rise or fall, you might pause contributions, or you might front-load savings in certain years.
• Spending is not adjusted for inflation: Unless explicitly stated otherwise, the desired annual spending you enter is treated as a constant figure in today’s money. The model does not automatically adjust for inflation or changes in lifestyle over time.
• No explicit taxes or fees: The projections typically ignore the impact of taxes, account types (taxable versus tax-advantaged), investment management fees, trading costs, and other frictions that can reduce realized returns.
• Withdrawal rate is a simple rule of thumb: The withdrawal rate you choose is not a guarantee that your portfolio will last for a particular number of years. It is only a planning guideline based on past research and common rules of thumb. Future conditions may be better or worse than the historical periods used in those studies.
• Fixed lifestyle and goals: The calculator does not model changes in your spending needs, such as children, healthcare events, housing changes, or new income sources that may appear later (for example, pensions or social benefits).
• Projection horizon: To avoid unrealistically long calculations, the tool typically caps the projection at a maximum number of years. If your inputs would require more time than that to reach FIRE, the calculator may state that the goal is not reached within the modeled period.

Because of these limitations, the results should be interpreted as rough estimates rather than precise forecasts. The calculator is best used to explore how different saving, spending, and return assumptions influence your path to financial independence, not as a definitive retirement plan.

This tool is intended for general educational and informational purposes only and does not provide personalized financial, investment, tax, or legal advice. Your specific situation may differ significantly from the simplified scenarios modeled here. Consider consulting a qualified financial professional before making major decisions based on FIRE projections.

Using the results to refine your FIRE plan

After running several scenarios, you may notice patterns. For many people, the most powerful levers are savings rate and desired spending, rather than chasing higher investment returns. You might use the calculator to answer questions such as:

• How many additional years would it take to reach FIRE if I increased my retirement spending goal?
• What happens if I lower my expected investment return to reflect more conservative assumptions?
• How much faster could I reach financial independence if I temporarily increase my savings rate for the next decade?

Experimenting with these variables can help you set realistic expectations, identify trade-offs, and design a path to financial independence that matches your risk tolerance and lifestyle preferences. By revisiting your plan regularly and updating your inputs as your situation changes, you can keep your FIRE journey aligned with your evolving goals.