# Crop Factor Calculator

> Computes a sensor's crop factor (43.27 mm full-frame diagonal ÷ sensor diagonal), its area relative to full frame, and the full-frame equivalent focal length and depth-of-field-equivalent aperture for a given lens.

- Calculator id: `crop-factor` · Category: Photography & Optics (`photography`) · Tool name: `calculate_crop_factor`
- Canonical page: https://tttkmbb.com/photography/crop-factor · This document: https://tttkmbb.com/photography/crop-factor.md · JSON definition: https://tttkmbb.com/photography/crop-factor.json

## Purpose

Computes a sensor's crop factor (43.27 mm full-frame diagonal ÷ sensor diagonal), its area relative to full frame, and the full-frame equivalent focal length and depth-of-field-equivalent aperture for a given lens.

**Use when:** You want to compare lenses across sensor formats, convert a focal length to its full-frame equivalent, or quantify how much smaller a sensor is than full frame.

**Do not use when:** You need the actual angle of view in degrees (use field-of-view) or the depth of field at a focus distance (use depth-of-field).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `sensor` | enum: full_frame \| aps_c \| aps_c_canon \| micro_four_thirds \| one_inch \| medium_format_44x33 \| smartphone_1_over_2_3 |  | optional, default "full_frame" | Sensor format preset providing the sensor width and height. |
| `sensor_width_mm` | number | mm | optional | Optional sensor width in mm; overrides the sensor preset. (> 0, max 200) |
| `sensor_height_mm` | number | mm | optional | Optional sensor height in mm; overrides the sensor preset. (> 0, max 200) |
| `focal_length_mm` | number | mm | optional | Optional actual focal length; returns its full-frame equivalent focal length. (min 1, max 5000) |
| `aperture_f` | number |  | optional | Optional f-number; returns the full-frame aperture giving the same depth of field. (min 0.5, max 128) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `crop_factor` | number |  | Full-frame diagonal (43.27 mm) divided by the sensor diagonal. |
| `sensor_diagonal_mm` | number | mm | √(width² + height²). |
| `sensor_area_mm2` | number | mm² | width × height. |
| `area_ratio_to_full_frame` | number |  | Sensor area divided by the full-frame area of 864 mm². |
| `light_gathering_stops_vs_full_frame` | number | stops | log2(area ratio): stops of total light the sensor collects relative to full frame at the same exposure settings (negative = less). |
| `equivalent_focal_length_mm` | number | mm | focal_length_mm × crop factor: full-frame focal length with the same diagonal angle of view (only when focal_length_mm is given). |
| `equivalent_aperture_f` | number |  | aperture_f × crop factor: full-frame f-number with the same depth of field and diffraction; exposure is unchanged (only when aperture_f is given). |

## Formula

`crop_factor = √(36² + 24²) / √(width² + height²); equivalent_focal_length_mm = focal_length_mm × crop_factor; equivalent_aperture_f = aperture_f × crop_factor; area_ratio = width × height / 864`

Diagonal-based crop factor as used by camera makers; sensors with a different aspect ratio (4:3 Micro Four Thirds) have a slightly different horizontal factor. Equivalent aperture describes depth of field and total light, not exposure.

## Data Sources

- Wikipedia – Crop factor — https://en.wikipedia.org/wiki/Crop_factor (reference, retrieved 2026-09-24)
- Cambridge in Colour – Digital camera sensor sizes — https://www.cambridgeincolour.com/tutorials/digital-camera-sensor-size.htm (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/crop-factor?`
- `POST https://tttkmbb.com/api/v1/calculate/crop-factor` 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/crop-factor · OpenAPI operationId `calculate_crop_factor` 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": "crop-factor", "inputs": {…}}`

## Example

- APS-C 23.5 × 15.6 mm with a 35 mm f/2 lens: inputs `{"sensor":"aps_c","focal_length_mm":35,"aperture_f":2}` → `{"crop_factor":1.534,"sensor_diagonal_mm":28.21,"equivalent_focal_length_mm":53.7,"equivalent_aperture_f":3.07,"area_ratio_to_full_frame":0.424}`
- Micro Four Thirds with a 25 mm lens: inputs `{"sensor":"micro_four_thirds","focal_length_mm":25}` → `{"crop_factor":1.999,"sensor_diagonal_mm":21.64,"equivalent_focal_length_mm":50,"sensor_area_mm2":224.9}`

```
GET https://tttkmbb.com/api/v1/calculate/crop-factor?sensor=aps_c&focal_length_mm=35&aperture_f=2
```

## Limitations

You need the actual angle of view in degrees (use field-of-view) or the depth of field at a focus distance (use depth-of-field). Diagonal-based crop factor as used by camera makers; sensors with a different aspect ratio (4:3 Micro Four Thirds) have a slightly different horizontal factor. Equivalent aperture describes depth of field and total light, not exposure. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Does a crop sensor change the lens' focal length?**

No. A 35 mm lens stays 35 mm; the smaller sensor records a central crop of the image, so the framing matches a 53.7 mm lens on full frame (35 × 1.534).

**Why is there an 'equivalent aperture' if exposure does not change?**

f/2 gives the same exposure on any sensor. But for the same framing, a crop sensor at f/2 has the depth of field, diffraction and total light of f/3.1 on full frame; the equivalent aperture expresses that.

## Related

- [Field of View Calculator](https://tttkmbb.com/photography/field-of-view.md) — Actual angle of view for the lens on this sensor.
- [Depth of Field Calculator](https://tttkmbb.com/photography/depth-of-field.md) — Depth of field with the sensor's circle of confusion.
- [Hyperfocal Distance Calculator](https://tttkmbb.com/photography/hyperfocal-distance.md) — Hyperfocal distance for the same sensor and lens.