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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.

When to use

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).

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.

Inputs

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		default full_frame	Sensor format preset providing the sensor width and height.
`sensor_width_mm`	number	mm	no	Optional sensor width in mm; overrides the sensor preset. Range: > 0, ≤ 200
`sensor_height_mm`	number	mm	no	Optional sensor height in mm; overrides the sensor preset. Range: > 0, ≤ 200
`focal_length_mm`	number	mm	no	Optional actual focal length; returns its full-frame equivalent focal length. Range: ≥ 1, ≤ 5000
`aperture_f`	number		no	Optional f-number; returns the full-frame aperture giving the same depth of field. Range: ≥ 0.5, ≤ 128

Outputs

Output	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).

Example

APS-C 23.5 × 15.6 mm with a 35 mm f/2 lens: {"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: {"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

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/crop-factor (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/crop-factor · Markdown: https://tttkmbb.com/photography/crop-factor.md · JSON definition: https://tttkmbb.com/photography/crop-factor.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="crop-factor"
OpenAPI operationId: calculate_crop_factor
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Crop factor (reference)
Cambridge in Colour – Digital camera sensor sizes (reference)

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 calculators

Field of View Calculator — Actual angle of view for the lens on this sensor.
Depth of Field Calculator — Depth of field with the sensor's circle of confusion.
Hyperfocal Distance Calculator — Hyperfocal distance for the same sensor and lens.