Bokeh & Background Blur Calculator: How Much Will the Background Blur?
Work out how blurred the background will be: blur disc size on the sensor, as a percentage of the frame and in pixels, from focal length, aperture, subject distance or framing, background distance and sensor size. Includes depth of field on the subject, a blur-versus-distance chart and a same-framing lens comparison (50 mm f/1.4 vs 85 mm f/1.8 vs 135 mm f/2 vs a phone).
How it works
m = f ÷ (s − f) · entrance pupil D = f ÷ N · blur disc on the sensor b = D × m × (s_b − s) ÷ s_b (background at infinity: b = D × m) · blur % of frame = b ÷ sensor width · pixels = b ÷ sensor width × horizontal pixels · from framing: s = f + f × scene width ÷ sensor width · hyperfocal H = f² ÷ (N × c) + f, near = s(H − f) ÷ (H + s − 2f), far = s(H − f) ÷ (H − s)
A point of light behind the subject is out of focus, so it spreads into a disc on the sensor. The disc size depends on three things: the entrance pupil (focal length divided by f-number, the size of the opening seen from the front of the lens), the magnification at which the subject is focused, and how far behind the subject the background sits compared with its distance from the camera. Dividing the disc by the sensor width turns it into a share of the frame, which is what you see in the photo and lets you compare a phone, an APS-C body and full frame fairly. You can set the shot by subject distance or by how much of the scene you want across the frame (head and shoulders, half body, full body); the calculator then finds the camera distance. The background can be measured from the camera or from the subject, or set to 0 for a distant horizon. The results add depth of field on the subject (circle of confusion = sensor diagonal ÷ 1442 unless you enter your own), a table of blur against background distance, a chart showing how the blur grows as the background moves back and what stopping down two stops does, and a same-framing comparison that moves the camera for each lens while the subject and background stay where they are. The main lessons: for a fixed framing the pupil diameter decides the blur, so an 85 mm f/1.8 (47 mm pupil) beats a 50 mm f/1.4 (36 mm pupil); a background several times farther behind the subject than the camera is in front approaches the lens’s maximum blur; and a phone’s pupil of about 4 mm can hardly blur anything optically, which is why portrait mode is computational. The model is a thin lens with a round aperture focused exactly on the subject; real lenses with focus breathing, internal focusing or non-circular apertures differ somewhat.
Worked example
An 85 mm f/1.8 on full frame (24 MP) focused on a subject 2.5 m away, with the background 8 m from the camera. Magnification = 85 ÷ (2,500 − 85) = 0.03520 and the pupil = 85 ÷ 1.8 = 47.22 mm. The blur disc = 47.22 × 0.03520 × 5,500 ÷ 8,000 = 1.143 mm, which is 3.17% of the 36 mm frame width, about 190 px of the 6,000 px across: a strong, creamy blur, 69% of the 4.62% you would get with the background at infinity. The frame covers 102 cm of scene (half body) and depth of field runs from 2.46 m to 2.55 m. With the same framing a 50 mm f/1.4 (camera at 1.47 m) gives 2.76% and a phone about 0.33%.
Sources: Bob Atkins: bokeh and background blur · Lewis Collard: background blur vs focal length and aperture · How Much Blur: lens background blur comparison · Wikipedia: depth of field (blur disc and hyperfocal distance)
Frequently asked questions
Is more blur always better bokeh?
No. Blur size and bokeh quality are different things: this calculator measures size. Quality (smooth or busy discs, cat’s-eye shapes near the corners, onion rings from aspherical elements) depends on the lens design and the shape of the aperture blades.
Does a longer lens really blur more at the same f-number?
Yes, if you keep the same framing. You step back to frame the subject the same way, the magnification stays the same, and the longer lens has a bigger entrance pupil (85 ÷ 1.8 = 47 mm against 50 ÷ 1.8 = 28 mm), so the background discs are bigger. Long lenses also show a narrower slice of background, which makes it look even smoother.
Why does the crop factor apply to the aperture too?
Because f/2 on a small sensor is a physically smaller opening, and the blur disc is measured against a smaller frame. To match the look, scale both the focal length and the f-number: a Micro Four Thirds 42.5 mm f/1.2 matches a full-frame 85 mm f/2.4 in framing, blur and depth of field.
How do I get more background blur?
In order of usual effect: move the subject farther from the background, open the aperture, get closer (or frame tighter), and use a longer lens while stepping back. The table of blur by background distance shows how much each extra metre behind the subject is worth.
How much blur do I need for a portrait?
As a rough guide, under 0.5% of the frame width the background is still recognisable, 1.5–3% gives clear subject separation and over 3% looks creamy. A blur disc tens of times larger than the circle of confusion is clearly out of focus.
Why do phones use portrait mode?
A phone main camera has a focal length of about 7 mm, so even at f/1.8 its pupil is under 4 mm and the optical blur is a small fraction of what an 85 mm lens gives. Portrait mode builds a depth map and adds blur in software.
Related calculators
Standard optics arithmetic with idealised assumptions (thin lens, circular aperture, focus exactly on the subject). Real lenses, focus breathing and aperture shapes differ; use it for planning and comparison.