Formula & Calculator
Depth of Field (Simplified)
Estimates the range of distances that appear acceptably sharp in a photograph, based on aperture, focal length, and focus distance.
Interpretation
DOF ≈ 2·N·c·s² / f². Approximate depth of field. N is f‑number, c is circle of confusion, s is focus distance, f is focal length. Used in photography.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| DOF | Depth of field | m |
| N | f-number | |
| c | Circle of confusion | mm |
| s | Subject distance | m |
| f | Focal length | mm |
What it means
Depth of field is the range of distances over which objects appear acceptably sharp. This simplified formula shows that DOF increases with smaller aperture (larger N), larger acceptable blur circle (c), and shorter focal length. It is used by photographers to control focus and to achieve creative effects. Understanding this helps in selecting aperture and focusing distance for desired sharpness. The formula is an approximation valid for small apertures and moderate distances.
Worked example
Depth of Field – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| N (f‑number) | 2.8 |
| s (focus distance, m) | 5 |
| f (mm) | 50 |
| Parameter | Value |
|---|---|
| N | 16 |
| s | 10 |
| f | 35 |
Common mistakes
- Depth of field (simplified): DOF ≈ 2·N·c·s² / f² – for distant objects (hyperfocal approximation).
- N: f‑number (focal ratio).
- c: Circle of confusion diameter – often taken as the sensor’s pixel pitch or a standard value (e.g., 0.03 mm for 35mm).
- s: Subject distance – in the same units as f.
- f: Focal length – in the same units as s.
- Assumptions: Small apertures, not macro distances – for macro, use more complex formulas.
Applications
Depth of field (simplified), DOF ≈ 2·N·c·s²/f², estimates the range of distances that appear acceptably sharp in an image, depending on aperture (N), circle of confusion (c), object distance (s), and focal length (f). Photographers and cinematographers use this to control which parts of the scene are in focus. Engineers designing camera systems use it to set specifications. A small aperture gives large depth of field, while a large aperture gives shallow depth of field for subject isolation. This concept is also applied in machine vision to ensure proper focus of objects. Understanding depth of field is essential for creative and technical photography.
- Photography and cinematography – creative focus control
- Camera system design and specification
- Machine vision – ensuring object focus in production lines
- Optical simulation and ray tracing
- Education on aperture and focus effects
Frequently Asked Questions
It estimates the range of distances that appear acceptably sharp in a photograph: DOF ≈ 2·N·c·s² / f².
N = f‑number.
c = circle of confusion (acceptable blur diameter).
s = focus distance.
f = focal length.
It is the largest blur spot that is still perceived as sharp. It is often set to about 1/1500 of the image diagonal for a given sensor size.
DOF is proportional to N; a smaller aperture (larger N) gives deeper DOF. A larger aperture (smaller N) gives shallower DOF.
DOF is inversely proportional to f² and proportional to s². Longer focal lengths and closer focus distances give shallower DOF.
For a 50mm lens (f=0.05 m) at f/2.8 (N=2.8), focusing at s=2 m, with c=0.03 mm (0.00003 m): DOF ≈ 2×2.8×0.00003×4 / (0.05²) = 2×2.8×0.00012 / 0.0025 = 0.000672 / 0.0025 ≈ 0.269 m = 27 cm.
- Assuming depth of field depends only on aperture; focal length and distance have a stronger effect.
- Using the wrong circle of confusion for the sensor size.
- Not converting units consistently.
Smaller sensors require shorter focal lengths for the same field of view, which increases DOF for the same f‑number.
The focus distance beyond which everything is acceptably sharp. It is given by H = f²/(N·c) + f.
Portrait photographers use wide apertures (small N) to achieve shallow DOF, blurring the background while keeping the subject sharp.