Focal Length Calculator

Focal length is field of view wearing a millimetre costume — the same angle, priced by sensor size. Enter the view you want (or the lens you own), choose your sensor, and this calculator converts between the two in both directions: the focal length that frames your shot, and the field of view your lens actually delivers.

The Tangent at the Heart of Every Lens

The geometry is a single right triangle: from the lens’s rear node, half the sensor’s width spans half the field of view, so f = (d ÷ 2) ÷ tan(FOV ÷ 2) — and reversed, FOV = 2 × atan(d ÷ 2f). Everything the calculator does is that triangle evaluated carefully, which is why the sensor selector matters as much as the millimetres: the same 50 mm lens is a mild telephoto on Micro Four Thirds (its 17.3 mm width halves the angle), a standard on full frame, and would be a wide angle on medium format. Focal length is a property of the lens; field of view is a property of the marriage between lens and sensor, and confusing the two is the entire content of the internet’s “crop factor” wars — settled, as this page settles them, by one tangent and no opinions.

Worked Example: Forty Degrees on Full Frame

The defaults ask the portraitist’s question: what lens gives a 40-degree horizontal view on full frame? f = 18 ÷ tan(20°) = 18 ÷ 0.3640 ≈ 49.5 mm — which is why the 50 mm “nifty fifty” became photography’s standard lens: its field of view approximates the attentive human gaze, wide enough for context, narrow enough for intent. Run the conversion the other way on the crop sensors to feel the factor: the same 40 degrees on APS-C (23.6 mm) needs about 32.4 mm, and on Micro Four Thirds about 23.8 mm — each system’s “normal” lens is a different physical object delivering the same triangle. The calculator’s equivalence line states the outcome in the dialect every photographer already speaks (full-frame-equivalent field), while its note guards the border: equivalence translates framing only, and the photons never signed the treaty.

Why Product Pages Quote the Diagonal (and You Should Quote the Horizontal)

Manufacturers advertise the diagonal field of view because it is the largest number the sensor supports — a 50 mm full-frame lens is a “46.8-degree lens” diagonally, 39.6 horizontally, 27 vertically, and all three are true, which is precisely the marketing opportunity. Working photographers think horizontally (the frame’s long dimension in landscape orientation, and the dimension that video’s 16:9 crop samples), architects and interior shooters think vertically more often than they admit, and nobody outside a spec sheet thinks diagonally at all. The calculator standardises on horizontal and says so, converting your chosen dimension consistently; if your planning lives in another dimension, run the same tangent against that dimension’s sensor measurement — the triangle does not care which side of the rectangle you feed it, as long as lens and sensor meet in the same units.

The Rectilinear Limit and the Fisheye Escape

The tangent formula carries an asymptote the calculator refuses politely at 179 degrees: as the desired field approaches 180, the required focal length approaches zero, because a rectilinear lens must stretch the edges of a hemisphere infinitely — corners racing to infinity is what “rectilinear” costs. Real optics escapes the asymptote by changing the projection: fisheye lenses map angle to radius by other laws (equidistant, equisolid and friends), accepting curved straight lines as the price of a 180-degree embrace. The divide is the deepest in lens design — one family preserves straightness and surrenders the hemisphere; the other takes the hemisphere and bends the world — and every wide lens ever sold is a vote in that election. Your calculator’s refusal line is therefore a small monument: the exact point where one geometry hands photography over to another, marked in a web form.

Anamorphic and the Squeezed Triangle

One beloved format breaks this page’s tidy assumption that a lens has a single focal length: anamorphic lenses squeeze the horizontal field by a factor (1.33×, 1.5×, 2×) while leaving the vertical untouched, so their horizontal and vertical fields correspond to different effective focal lengths — a 50 mm 2× anamorphic frames horizontally like a 25 mm and vertically like a 50. The calculator handles the honest halves separately (run it with the horizontal field for the squeezed behaviour, the vertical for the native) and the desqueezed image’s oval bokeh and horizontal flares are the aesthetic receipts of the double geometry. Cinema’s widescreen romance turns out to be two triangles sharing one lens — and a standing reminder that “focal length” is a sphere of behaviours of which the rectilinear spherical lens, this page’s subject, is merely the best-behaved citizen. Directors choose the squeeze partly for its fields of view and partly for its artefacts; the calculator prices the fields honestly and leaves the artefacts, as it should, to taste.

Related Tools

More from the Other Calculators hub: the Camera Field of View Calculator — the sibling page, run from lens to coverage at distance — and the Depth of Field Calculator for the other half of a lens’s behaviour.

Frequently Asked Questions

What focal length is “normal” for my camera?

The one whose focal length roughly equals your sensor’s diagonal — about 43 mm on full frame (the industry settled on 50 for manufacturing convenience), about 28–30 mm on APS-C, about 21–25 mm on Micro Four Thirds. “Normal” names the field that renders perspective the way unaided attention feels — but note that the calculator’s framing definition is the operational one: dial your desired horizontal field into it and accept whichever millimetres the tangent returns. Normality is a starting point for a kit, not a law for a photograph.

Does a crop-sensor lens change focal length on a smaller sensor?

No — the lens’s focal length is engraved physics and travels with the glass; what changes is how much of its image circle the smaller sensor samples, narrowing the field exactly as the crop factor describes. A 50 mm lens on APS-C remains a 50 mm lens (its depth of field at a given aperture is a 50 mm lens’s) that frames like an 80 mm on full frame. The calculator’s equivalence line is careful to say “frames like,” because the distinction decides real purchases: you cannot buy your way to a full-frame 85 mm f/1.4’s rendering with a crop 56 mm that merely frames like it.

How accurate is the simple tangent formula?

It is the rectilinear ideal — exact for a perfect pinhole and for lenses corrected to project rectilinearly — and real lenses deviate where their designs do: fisheyes abandon rectilinearity deliberately (their fields follow other projections, which is why the calculator refuses them past 179 degrees), and ordinary lenses breathe a percent or two of focal shift with focus distance, at close range especially. For planning framing and comparing formats, the tangent is the profession’s shared fiction and amply precise; for stitching panoramas and photogrammetry, the lens’s calibrated distortion model takes over where this page’s triangle gracefully ends.

What focal length do I need for the moon, a portrait, a room?

Work backwards from the field: a flattering head-and-shoulders portrait wants roughly 15–24 degrees horizontally (about 85–135 mm full-frame equivalent); a room interior wants 60–75 degrees (24–28 mm equivalent, with the rectilinear stretching at the edges duly feared); the moon’s half-degree disc becomes a respectable frame-filler around 2–4 degrees (600 mm and beyond, or a crop sensor’s help). Each of these is the calculator with a different field entered — the craft is choosing the field for the subject, and that choice, unlike the tangent, cannot be automated.

Why do zoom lenses list two focal lengths?

Because the triangle’s f is a variable in a zoom: the listed pair (24–70 mm, say) is the range’s ends, and every field between them is available by turning the ring — run the calculator at both ends to know the fields your zoom actually spans on your sensor (on APS-C, that 24–70 frames like roughly 38–112). The two numbers also smuggle in the aperture story (a constant f/2.8 across the range is the expensive engineering; a variable f/3.5–5.6 is the honest budget), but as framing, the zoom is simply this page’s formula with a dial where the constant used to be.

Does focal length affect perspective?

No — position does; focal length merely crops the perspective your position creates, and the calculator’s silence on the matter is doctrinal. Stand in one spot and a 24 mm and a 200 mm render identical perspective (the telephoto’s frame is a magnified crop of the wide one’s centre); move closer with the wide lens and the perspective changes because you moved. The “telephoto compression” of stacked mountains is the photographer’s distance doing the work, with the long lens framing the result. Knowing this converts the focal-length question back into the two honest ones: where will I stand, and how much of what I see from there do I want in the frame — the second of which this page answers.