# Dilution Calculator

> Applies the dilution equation C1·V1 = C2·V2 to find the missing one of stock concentration, stock volume, final concentration or final volume, plus the solvent to add and the dilution factor.

- Calculator id: `dilution` · Category: Chemistry (`chemistry`) · Tool name: `calculate_dilution`
- Canonical page: https://tttkmbb.com/chemistry/dilution · This document: https://tttkmbb.com/chemistry/dilution.md · JSON definition: https://tttkmbb.com/chemistry/dilution.json

## Purpose

Applies the dilution equation C1·V1 = C2·V2 to find the missing one of stock concentration, stock volume, final concentration or final volume, plus the solvent to add and the dilution factor.

**Use when:** You are diluting a stock solution and need how much stock to take, the final volume to make up, or the concentration that results.

**Do not use when:** You are preparing a solution from solid solute (use molarity) or the concentrations are in mass percent with very different densities (C1V1 = C2V2 assumes volumes are additive and the unit is amount per volume).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `stock_concentration` | number |  | optional | Concentration of the stock solution in any unit (M, mM, mg/mL, %, X); all concentrations share the unit. (> 0) |
| `stock_volume` | number |  | optional | Volume of stock solution taken, in any unit shared with final_volume (mL, L, µL). (> 0) |
| `final_concentration` | number |  | optional | Concentration after dilution, same unit as stock_concentration. (> 0) |
| `final_volume` | number |  | optional | Total volume after dilution, same unit as stock_volume. Leave empty to solve for it. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `stock_concentration` | number |  | C1, given or solved. |
| `stock_volume` | number |  | V1, given or solved. |
| `final_concentration` | number |  | C2, given or solved. |
| `final_volume` | number |  | V2, given or solved. |
| `solvent_volume_to_add` | number |  | V2 − V1: diluent (water, buffer) to add to the stock volume. |
| `dilution_factor` | number |  | C1 / C2 = V2 / V1, e.g. 4 means a 1:4 (4×) dilution. |
| `solved_for` | string |  | Name of the quantity that was left empty and computed. |

## Formula

`C1 × V1 = C2 × V2; solvent_volume_to_add = V2 − V1; dilution_factor = C1 / C2`

Exactly three of the four quantities must be given. The relation assumes the amount of solute is conserved and volumes are additive, which holds well for dilute aqueous solutions.

## Data Sources

- OpenStax Chemistry 2e – 3.3 Molarity – Dilution of Solutions — https://openstax.org/books/chemistry-2e/pages/3-3-molarity (textbook, retrieved 2026-09-23)
- Wikipedia – Dilution — https://en.wikipedia.org/wiki/Dilution (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/dilution?`
- `POST https://tttkmbb.com/api/v1/calculate/dilution` 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/dilution · OpenAPI operationId `calculate_dilution` 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": "dilution", "inputs": {…}}`

## Example

- 2 M stock, 25 mL, to 0.5 M: inputs `{"stock_concentration":2,"stock_volume":25,"final_concentration":0.5}` → `{"final_volume":100,"solvent_volume_to_add":75,"dilution_factor":4,"solved_for":"final_volume"}`
- 10 mL of 0.1 M made up to 250 mL: inputs `{"stock_concentration":0.1,"stock_volume":10,"final_volume":250}` → `{"final_concentration":0.004,"solvent_volume_to_add":240,"dilution_factor":25,"solved_for":"final_concentration"}`

```
GET https://tttkmbb.com/api/v1/calculate/dilution?stock_concentration=2&stock_volume=25&final_concentration=0.5
```

## Limitations

You are preparing a solution from solid solute (use molarity) or the concentrations are in mass percent with very different densities (C1V1 = C2V2 assumes volumes are additive and the unit is amount per volume). Exactly three of the four quantities must be given. The relation assumes the amount of solute is conserved and volumes are additive, which holds well for dilute aqueous solutions. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Which units can I use?**

Any, as long as both concentrations share one unit and both volumes share one unit; the result comes out in the same units (e.g. mM and µL).

**What is the difference between a 1:4 dilution and a 1-in-4 dilution?**

Both conventions exist; here dilution_factor = 4 means 1 part stock brought to 4 parts total (3 parts solvent added), which is the C1V1 = C2V2 interpretation.

## Related

- [Molarity Calculator](https://tttkmbb.com/chemistry/molarity.md) — Prepare the stock solution from solid solute first.
- [Mass Percent Calculator](https://tttkmbb.com/chemistry/mass-percent.md) — Mass-based concentration units (%, ppm, ppb).