# Hemocytometer Cell Count Calculator

> Converts a hemocytometer count into cell concentration with cells/mL = (cells counted ÷ large squares counted) × dilution factor × 10⁴, and optionally the total cells in a sample, trypan-blue viability and the volume that contains a target number of cells.

- Calculator id: `hemocytometer-count` · Category: Biology, Earth & Space (`science`) · Tool name: `calculate_hemocytometer_cell_count`
- Canonical page: https://tttkmbb.com/science/hemocytometer-count · This document: https://tttkmbb.com/science/hemocytometer-count.md · JSON definition: https://tttkmbb.com/science/hemocytometer-count.json

## Purpose

Converts a hemocytometer count into cell concentration with cells/mL = (cells counted ÷ large squares counted) × dilution factor × 10⁴, and optionally the total cells in a sample, trypan-blue viability and the volume that contains a target number of cells.

**Use when:** You counted cells in the large 1 mm² squares of a Neubauer hemocytometer and need the concentration, the number of cells in your flask or the volume to seed a given number of cells.

**Do not use when:** You counted in the small central squares or used a different chamber depth (adjust the volume per square), used an automated counter, or need cell growth rates (use cell-doubling-time).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `cells_counted` | integer |  | required | Number of (live, unstained) cells counted in all the squares together. (min 0, max 10000000) |
| `squares_counted` | integer |  | optional, default 4 | Number of large 1 mm × 1 mm squares counted (each holds 0.1 µL at the standard 0.1 mm depth); typically the 4 corner squares. (min 1, max 18) |
| `dilution_factor` | number |  | optional, default 1 | Dilution of the sample before loading (2 for a 1:1 mix with trypan blue, 10 for 1:9). (min 1, max 1000000) |
| `sample_volume_ml` | number | mL | optional | Volume of the original cell suspension; gives the total cell number. (> 0, max 1000000) |
| `dead_cells_counted` | integer |  | optional | Stained (dead) cells counted in the same squares; gives the viability. (min 0, max 10000000) |
| `target_cells` | number |  | optional | Number of cells you want to take; gives the suspension volume needed. (> 0, max 1000000000000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `cells_per_ml` | number | cells/mL | (cells_counted / squares_counted) × dilution_factor × 10⁴. |
| `cells_per_ml_text` | string |  | The concentration in scientific notation. |
| `cells_per_square` | number |  | cells_counted / squares_counted. |
| `poisson_counting_error_percent` | number | % | Relative standard error of the count, 100 / √cells_counted. |
| `total_cells` | number |  | cells_per_ml × sample_volume_ml (when the volume is given). |
| `viability_percent` | number | % | 100 × live / (live + dead) (when dead_cells_counted is given). |
| `total_cells_per_ml` | number | cells/mL | Concentration including dead cells (when dead_cells_counted is given). |
| `volume_for_target_ml` | number | mL | target_cells / cells_per_ml (when target_cells is given). |

## Formula

`cells/mL = (cells_counted / squares_counted) × dilution_factor × 10⁴; total = cells/mL × sample_volume_ml; viability % = 100 × live / (live + dead); volume_for_target = target_cells / cells/mL`

Standard Neubauer geometry: each large square is 1 mm × 1 mm × 0.1 mm = 0.1 µL, so cells per square × 10⁴ = cells per mL. Counting error follows Poisson statistics (≈ 10 % for 100 cells, 7 % for 200), which is why at least 100 cells should be counted.

## Data Sources

- Wikipedia – Hemocytometer — https://en.wikipedia.org/wiki/Hemocytometer (reference, retrieved 2026-09-24)
- Wikipedia – Trypan blue — https://en.wikipedia.org/wiki/Trypan_blue (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/hemocytometer-count?cells_counted=…`
- `POST https://tttkmbb.com/api/v1/calculate/hemocytometer-count` 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/hemocytometer-count · OpenAPI operationId `calculate_hemocytometer_cell_count` 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": "hemocytometer-count", "inputs": {…}}`

## Example

- 200 cells in 4 squares, 1:1 trypan blue, 10 mL flask: inputs `{"cells_counted":200,"squares_counted":4,"dilution_factor":2,"sample_volume_ml":10,"dead_cells_counted":20,"target_cells":1000000}` → `{"cells_per_ml":1000000,"cells_per_ml_text":"1.00 × 10^6 cells/mL","cells_per_square":50,"total_cells":10000000,"viability_percent":90.91,"volume_for_target_ml":1,"poisson_counting_error_percent":7.07}`
- 120 cells in 4 squares, undiluted: inputs `{"cells_counted":120,"squares_counted":4,"dilution_factor":1}` → `{"cells_per_ml":300000,"cells_per_ml_text":"3.00 × 10^5 cells/mL","cells_per_square":30}`

```
GET https://tttkmbb.com/api/v1/calculate/hemocytometer-count?cells_counted=200&squares_counted=4&dilution_factor=2&sample_volume_ml=10&dead_cells_counted=20&target_cells=1000000
```

## Limitations

You counted in the small central squares or used a different chamber depth (adjust the volume per square), used an automated counter, or need cell growth rates (use cell-doubling-time). Standard Neubauer geometry: each large square is 1 mm × 1 mm × 0.1 mm = 0.1 µL, so cells per square × 10⁴ = cells per mL. Counting error follows Poisson statistics (≈ 10 % for 100 cells, 7 % for 200), which is why at least 100 cells should be counted. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Do I enter live cells only?**

Enter the unstained (live) cells as cells_counted and the blue (dead) cells as dead_cells_counted; the main concentration is then viable cells per mL and viability is live / (live + dead).

**Which dilution factor for trypan blue?**

Mixing equal volumes of cells and 0.4 % trypan blue is a 1:1 dilution, so the factor is 2; 10 µL cells + 90 µL stain is a factor of 10.

**How many cells should I count?**

At least 100 in total (ideally 100–200 per large square set); dilute if squares are overcrowded (> 200 per square) and count more squares if there are fewer than about 20 per square.

## Related

- [Cell Doubling Time Calculator](https://tttkmbb.com/science/cell-doubling-time.md) — Doubling time from two counts taken at different times.
- [Dilution Calculator](https://tttkmbb.com/chemistry/dilution.md) — Dilute the suspension to a target concentration (C1V1 = C2V2).
- [Centrifuge RCF / RPM Converter](https://tttkmbb.com/science/centrifuge-rcf-rpm.md) — Convert the ×g of the pelleting step to rpm.