# CAGR Calculator

> Computes the compound annual growth rate that turns a beginning value into an ending value over a number of years, together with the total return and growth multiple.

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

## Purpose

Computes the compound annual growth rate that turns a beginning value into an ending value over a number of years, together with the total return and growth multiple.

**Use when:** You need a smoothed per-year growth rate for revenue, a portfolio, a population or any quantity measured at two points in time.

**Do not use when:** You need to account for interim deposits or withdrawals (CAGR ignores cash flows; use a money-weighted return), or the period is under a year.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `beginning_value` | number |  | required | Value at the start of the period. (> 0, max 1000000000000000) |
| `ending_value` | number |  | required | Value at the end of the period. (> 0, max 1000000000000000) |
| `years` | number | years | required | Length of the period in years; fractional values allowed (18 months = 1.5). (> 0, max 200) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `cagr_percent` | number | % | ((ending / beginning)^(1/years) − 1) × 100. |
| `total_return_percent` | number | % | (ending / beginning − 1) × 100 over the whole period. |
| `growth_multiple` | number |  | ending_value / beginning_value. |
| `simple_average_annual_return_percent` | number | % | total_return_percent / years, the arithmetic (non-compounded) average for comparison. |

## Formula

`CAGR = ((ending_value / beginning_value)^(1 / years) − 1) × 100`

CAGR is the constant annual rate that would produce the same end value with annual compounding; it smooths out volatility and says nothing about the path in between.

## Data Sources

- Investopedia – Compound Annual Growth Rate (CAGR) Formula and Calculation — https://www.investopedia.com/terms/c/cagr.asp (reference, retrieved 2026-09-23)
- Wikipedia – Compound annual growth rate — https://en.wikipedia.org/wiki/Compound_annual_growth_rate (reference, retrieved 2026-09-23)

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/cagr?beginning_value=…&ending_value=…&years=…`
- `POST https://tttkmbb.com/api/v1/calculate/cagr` 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/cagr · OpenAPI operationId `calculate_cagr` 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": "cagr", "inputs": {…}}`

## Example

- 10,000 to 19,000 over 3 years: inputs `{"beginning_value":10000,"ending_value":19000,"years":3}` → `{"cagr_percent":23.86,"total_return_percent":90,"growth_multiple":1.9,"simple_average_annual_return_percent":30}`
- 100 to 50 over 2 years: inputs `{"beginning_value":100,"ending_value":50,"years":2}` → `{"cagr_percent":-29.29,"total_return_percent":-50,"growth_multiple":0.5}`

```
GET https://tttkmbb.com/api/v1/calculate/cagr?beginning_value=10000&ending_value=19000&years=3
```

## Limitations

You need to account for interim deposits or withdrawals (CAGR ignores cash flows; use a money-weighted return), or the period is under a year. CAGR is the constant annual rate that would produce the same end value with annual compounding; it smooths out volatility and says nothing about the path in between. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How is CAGR different from average annual return?**

The arithmetic average ignores compounding. Growing 10,000 to 19,000 in 3 years is 30 % per year on average but only 23.86 % CAGR, because each year's growth builds on the previous one.

**How do I count the years?**

Use the elapsed time between the two measurements, not the number of data points: values at the ends of 2020 and 2023 span 3 years.

## Related

- [ROI Calculator](https://tttkmbb.com/finance/roi.md) — Total and annualized return on an investment.
- [Rule of 72 Calculator](https://tttkmbb.com/finance/rule-of-72.md) — How long this growth rate takes to double the value.