# Depth of Field, Field of View & Exposure Calculator

> Near and far sharpness limits, hyperfocal distance, angle of view, crop factor and ND filters. Enter the sensor, focal length, aperture and focus distance to get the near and far limits of acceptable sharpness, the total depth of field and the hyperfocal distance, with the circle of confusion taken from the sensor size, from a print and viewing distance or from your own value. The same input gives the horizontal, vertical and diagonal angle of view, the scene width covered, the full-frame equivalent focal length and aperture, the magnification, the exposure value, ND filter conversions (stops, optical density, filter factor) and the 500 and NPF rules for sharp stars. Part of the Lumina photo studio.

Part of usefulweb.site (https://usefulweb.site/). Part of [Lumina](https://lumina.usefulweb.site/) (ownerApp: lumina). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://luminadepthoffield.usefulweb.site/ (interactive tool at https://luminadepthoffield.usefulweb.site/tool)
- JSON API: POST https://luminadepthoffield.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://luminadepthoffield.usefulweb.site/api/v1/tool)
- OpenAPI: https://luminadepthoffield.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://luminadepthoffield.usefulweb.site/mcp - tool `lumina_depth_of_field`

## Inputs
- sensor (select): Sensor size - Typical dimensions from the manufacturers; “inch” types are a historical naming, not a measurement.
- sensorWidth (number): Custom sensor width - Only with “Custom size”.
- sensorHeight (number): Custom sensor height - Only with “Custom size”.
- focalLength (number, required): Focal length - The real focal length printed on the lens (not the 35 mm equivalent).
- fNumber (number, required): Aperture (f-number)
- focusDistance (number, required): Focus distance - Distance from the lens to the subject in focus.
- cocMode (select): Sharpness criterion
- cocDivisor (integer): Diagonal divisor - Classic standard only: 1500 gives 0.029 mm on full frame; Zeiss uses 1730, stricter users 3000.
- printWidth (number): Print width
- printHeight (number): Print height
- viewingDistance (number): Viewing distance
- acuity (number): Visual acuity at 25 cm - 5 line pairs per millimetre at 25 cm is the usual assumption for normal eyesight.
- cocCustom (number): Circle of confusion - Only with “My own circle of confusion”.
- imageWidthPx (integer): Image width - Optional: long side of the full-resolution photo in pixels, for the pixel pitch (NPF rule).
- shutter (text): Shutter time - For the exposure value and the ND filter: 1/125, 0.5 or 30 (seconds). Leave empty to skip that part.
- iso (number): ISO
- ndValue (number): ND filter strength
- ndUnit (select): ND filter given as
- declination (number): Star declination - For the full NPF rule: 0° at the celestial equator (fastest trails), near ±90° at the celestial poles.

## Method
- Thin-lens depth of field: hyperfocal distance H = f²/(N·c) + f; near limit s(H − f)/(H + s − 2f); far limit s(H − f)/(H − s), or infinity once the focus distance s reaches H. Distances are measured from the lens.
- Circle of confusion c: the sensor diagonal divided by 1500 (or your divisor); or, from a print, the smallest blur the eye resolves on the print (1/acuity at 25 cm, scaled with the viewing distance) divided by the enlargement from the sensor diagonal to the print diagonal; or your own value.
- Angle of view 2·atan(d/2f) for the sensor width, height and diagonal at infinity focus, and with the image distance fs/(s − f) at the focus distance. Magnification f/(s − f); the scene covered is the sensor size divided by it.
- Crop factor = 43.27 mm (full-frame diagonal) ÷ sensor diagonal. The same field of view needs f × crop on full frame; the same depth of field and total light needs N × crop (and ISO × crop² for the same noise from total light).
- Exposure value EV = log₂(N²/t), EV₁₀₀ = EV − log₂(ISO/100). ND filters: stops = log₂(factor), optical density = log₁₀(factor) = 0.301 × stops; the shutter time grows by the filter factor.
- Star trails: 500 rule = 500/(f × crop) seconds; NPF rule (Michaud) simple (35N + 30p)/f and full (16.856N + 0.0997f + 13.713p)/(f·cos δ) with the pixel pitch p in µm. These are rules of thumb, not guarantees.

## Limits
- Depth of field is a convention, not a physical edge: sharpness falls off gradually, and the result depends on the chosen circle of confusion. Lens distance scales measure from the sensor plane; close-ups, zoom lenses that breathe, and very wide or fisheye lenses deviate from the thin-lens model.