# FIRE Number Calculator

> Computes the portfolio needed to fund annual expenses at a safe withdrawal rate (the FIRE number, 25× expenses at 4 %), your progress towards it, and the years until current savings plus annual saving reach it at an assumed return.

- Calculator id: `fire-number` · Category: Finance (`finance`) · Tool name: `calculate_fire_number`
- Canonical page: https://tttkmbb.com/finance/fire-number · This document: https://tttkmbb.com/finance/fire-number.md · JSON definition: https://tttkmbb.com/finance/fire-number.json

## Purpose

Computes the portfolio needed to fund annual expenses at a safe withdrawal rate (the FIRE number, 25× expenses at 4 %), your progress towards it, and the years until current savings plus annual saving reach it at an assumed return.

**Use when:** You want to know how much you need to retire early or become financially independent, and how many years of saving at your current rate it will take.

**Do not use when:** You want to project a balance to a fixed retirement age (use retirement-savings) or test how long a balance lasts (use savings-withdrawal).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `annual_expenses` | number |  | required | Yearly spending the portfolio must cover, in today's money. (> 0, max 1000000000) |
| `withdrawal_rate_percent` | number | % | optional, default 4 | Percent of the portfolio withdrawn in the first year; 4 % is the Trinity-study rule, 3–3.5 % is more conservative for long retirements. (> 0, max 20) |
| `current_savings` | number |  | optional, default 0 | Amount already invested towards the goal. (min 0, max 1000000000000) |
| `annual_savings` | number |  | optional | Amount saved and invested per year; takes precedence over annual_income × savings_rate_percent. (min 0, max 1000000000) |
| `annual_income` | number |  | optional | Yearly income, used with savings_rate_percent when annual_savings is omitted. (min 0, max 1000000000) |
| `savings_rate_percent` | number | % | optional | Percent of annual_income saved each year. (min 0, max 100) |
| `annual_return_percent` | number | % | optional, default 7 | Expected annual return in percent; use a real (after-inflation) return since expenses are in today's money. (min -50, max 50) |
| `current_age` | number | years | optional | Optional; enables the projected FI age. (min 0, max 100) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `fire_number` | number |  | annual_expenses / (withdrawal_rate_percent / 100). |
| `fire_multiple` | number |  | 100 / withdrawal_rate_percent (25 at 4 %). |
| `progress_percent` | number | % | current_savings / fire_number × 100. |
| `remaining_to_save` | number |  | max(0, fire_number − current_savings), before any growth. |
| `annual_savings_used` | number |  | annual_savings, or annual_income × savings_rate_percent / 100. |
| `years_to_fi` | number | years | Years until savings plus growth reach the FIRE number (0 if already reached). |
| `fi_age` | number | years | current_age + years_to_fi (only when current_age is given). |

## Formula

`fire_number = annual_expenses / (withdrawal_rate_percent/100); with r = annual_return_percent/100, S = annual_savings (end of year) and C = current_savings: years_to_fi = ln((fire_number + S/r) / (C + S/r)) / ln(1 + r) (r ≠ 0), or (fire_number − C) / S when r = 0`

Annual compounding with savings added at the end of each year and constant returns. The 4 % rule comes from the Trinity study (Cooley, Hubbard & Walz 1998) for 30-year horizons with a 50–75 % stock allocation; longer retirements argue for a lower rate.

## Data Sources

- Wikipedia – Trinity study (safe withdrawal rates) — https://en.wikipedia.org/wiki/Trinity_study (reference, retrieved 2026-09-24)
- Wikipedia – FIRE movement — https://en.wikipedia.org/wiki/FIRE_movement (reference, retrieved 2026-09-24)
- Investopedia – What Is the 4% Rule for Withdrawals in Retirement? — https://www.investopedia.com/terms/f/four-percent-rule.asp (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/fire-number?annual_expenses=…`
- `POST https://tttkmbb.com/api/v1/calculate/fire-number` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/fire-number · OpenAPI operationId `calculate_fire_number` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "fire-number", "inputs": {…}}`

## Example

- 40,000 expenses at 4 %, 100,000 saved, 30 % of 100,000 income, 7 %, age 30: inputs `{"annual_expenses":40000,"withdrawal_rate_percent":4,"current_savings":100000,"annual_income":100000,"savings_rate_percent":30,"annual_return_percent":7,"current_age":30}` → `{"fire_number":1000000,"fire_multiple":25,"progress_percent":10,"remaining_to_save":900000,"annual_savings_used":30000,"years_to_fi":14.7,"fi_age":44.7}`
- 60,000 expenses at 3.5 %: inputs `{"annual_expenses":60000,"withdrawal_rate_percent":3.5}` → `{"fire_number":1714285.71,"fire_multiple":28.57,"progress_percent":0}`

```
GET https://tttkmbb.com/api/v1/calculate/fire-number?annual_expenses=40000&withdrawal_rate_percent=4&current_savings=100000&annual_income=100000&savings_rate_percent=30&annual_return_percent=7&current_age=30
```

## Limitations

You want to project a balance to a fixed retirement age (use retirement-savings) or test how long a balance lasts (use savings-withdrawal). Annual compounding with savings added at the end of each year and constant returns. The 4 % rule comes from the Trinity study (Cooley, Hubbard & Walz 1998) for 30-year horizons with a 50–75 % stock allocation; longer retirements argue for a lower rate. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why 25 times expenses?**

Withdrawing 4 % of a portfolio each year means the portfolio must be 1 / 0.04 = 25 times the annual withdrawal. At 3.5 % it is 28.6×, at 3 % it is 33.3×.

**Should expenses include taxes?**

Yes. Withdrawals from pre-tax accounts are taxable, so annual_expenses should be the gross amount needed including income tax and health insurance.

## Related

- [Retirement Savings Calculator](https://tttkmbb.com/finance/retirement-savings.md) — Project the balance to a specific retirement age.
- [Savings Withdrawal Calculator](https://tttkmbb.com/finance/savings-withdrawal.md) — How long the portfolio lasts at a given withdrawal.
- [Rule of 72 Calculator](https://tttkmbb.com/finance/rule-of-72.md) — Doubling time at the assumed return.