Angle of view and equivalent focal length
Change focal length and the first thing that changes is the angle of view, how much fits in the frame. What usually makes the picture look different, though, is where you had to stand to use the lens. Once that clicks, you stop memorising numbers.
1. How focal length sets the angle of view
Angle of view = 2 × arctan( d ÷ (2f) ), where f is focal length
and d is the sensor dimension you are measuring along. Full frame is 36×24mm:
diagonal d = √(36² + 24²) = 43.27mm, horizontal d = 36mm, vertical d = 24mm. The diagonal angle
is always the wider one, so say which you mean when you quote degrees.
For 50mm: diagonally 2 × arctan(43.27 ÷ 100) = 2 × 23.40° = 46.8°; horizontally 2 × arctan(36 ÷ 100) = 2 × 19.80° = 39.6°. There is no shooting distance in the formula. Angle of view depends on lens and sensor alone.
2. Angle of view by focal length
All figures come from that formula on full frame (43.27mm diagonal, 36mm horizontal), to one decimal place.
| Focal length (full-frame equivalent) | Diagonal | Horizontal | Typical use |
|---|---|---|---|
| 14mm | 114.2° | 104.3° | Architecture, very tight interiors, astro |
| 16mm | 107.0° | 96.7° | Big landscapes, small rooms |
| 24mm | 84.1° | 73.7° | Landscape, environmental portraits, street |
| 35mm | 63.4° | 54.4° | Documentary, everyday, portraits with context |
| 50mm | 46.8° | 39.6° | General purpose, half-length portraits |
| 85mm | 28.6° | 23.9° | Portrait close-ups |
| 135mm | 18.2° | 15.2° | Stage, portraits from a distance |
| 200mm | 12.3° | 10.3° | Sport, wildlife, compressed distant scenes |
The angle does not shrink evenly. 14mm to 35mm loses 50° of horizontal coverage; 135mm to 200mm loses 5°. 16mm and 20mm differ by 12.7°, which you see at once; 135mm and 150mm differ by 1.5°, which you won't. Choose wide lenses to the millimetre and long ones by range.
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Open Mark — try one for free3. Equivalent focal length and crop factor
The same 50mm frames differently on different bodies because d has changed.
Full frame is the usual reference, and equivalent focal length converts
everything to it.
Equivalent focal length = marked focal length × crop factor, where crop factor = 43.27mm ÷ that format's diagonal:
| Format | Size and diagonal | Crop factor | A 50mm behaves like |
|---|---|---|---|
| Full frame | 36×24mm, diagonal 43.3mm | 1.0× | 50mm |
| APS-C (Sony / Nikon / Fujifilm) | 23.5×15.6mm, diagonal 28.2mm | 43.3 ÷ 28.2 = 1.53 ≈ 1.5× | 75mm |
| APS-C (Canon) | 22.3×14.9mm, diagonal 26.8mm | 43.3 ÷ 26.8 = 1.61 ≈ 1.6× | 80mm |
| Micro Four Thirds | 17.3×13.0mm, diagonal 21.6mm | 43.3 ÷ 21.6 = 2.0× | 100mm |
| 1 inch | 13.2×8.8mm, diagonal 15.9mm | 43.3 ÷ 15.9 = 2.73 ≈ 2.7× | 135mm |
It works backwards too. For the 50mm "standard" view you need 33mm on APS-C (1.5×), 25mm on Micro Four Thirds and 18.5mm on 1-inch. Same equivalent focal length, same angle of view, so read any result off the table above.
Only the angle converts, not the exposure. f/1.8 is f/1.8 on any format and meter readings carry over; depth of field at the same framing is what changes. Equivalent focal length also sets your safe shutter speed.
4. Where "compression" and "distortion" come from
Telephoto compresses, wide angle stretches faces, or so the saying goes. Strictly, perspective depends only on camera-to-subject distance, not focal length.
Test it: from one spot, shoot at 24mm and 85mm, then crop the 24mm frame to match. The perspective is identical.
The idea sticks because focal length and distance change together. A wide portrait forces you close, and closeness enlarges the nose. At 200mm you stand tens of metres back, near and far objects end up closer in size, and that reads as compression.
You can put numbers on it. At the same head-and-shoulders framing, subject distance
scales with focal length: 2.00m at 85mm means 2.00 × 50 ÷ 85 = 1.18m at 50mm. Treat
the nose tip as a point 10cm in front of the cheeks; its relative enlargement is
d ÷ (d − 0.1):
| Focal length (full frame) | Distance for the same head-and-shoulders frame | Nose enlarged relative to cheeks |
|---|---|---|
| 24mm | 0.56m | +22% |
| 35mm | 0.82m | +14% |
| 50mm | 1.18m | +9% |
| 85mm | 2.00m | +5% |
| 135mm | 3.18m | +3% |
| 200mm | 4.71m | +2% |
That column is the "wide lenses make faces fat" effect. The gap between +22% and +5% comes from standing at 0.56m instead of 2.00m. Shoot 24mm from 2.00m, crop to head and shoulders, and you are back at +5%.
5. Choosing by subject
- For a first prime, pick 35mm or 50mm equivalent. A 35 takes in more of the surroundings for everyday shooting; a 50 is closer to what the eye focuses on and makes clean backgrounds easier.
- For one lens all day, a 24–70mm equivalent zoom covers most things but is a stop or two slower than primes at the same price.
- For portraits, start at 85mm equivalent. The distance keeps faces in proportion and cleans up the background.
- For landscapes, 16–35mm equivalent does most of the work, but pack something long. A 200mm slice of a distant ridge often beats another wide vista.
Focal length is stored in EXIF, so it can go straight into an EXIF watermark. For how it works with aperture on depth of field, see aperture and depth of field; for prime versus zoom, see prime or zoom.
6. FAQ
What is the angle of view of a 50mm lens?
On full frame: 46.8° diagonal, 39.6° horizontal, 27.0° vertical, from 2 × arctan(d ÷ 2f) with d = 43.27, 36 and 24mm. On APS-C (1.5×) the same lens is 75mm equivalent, about 32° diagonal; on Micro Four Thirds (2.0×) it is 100mm equivalent, about 24°.
How do I calculate equivalent focal length?
Multiply the marked focal length by the crop factor, which is 43.27mm divided by your format's diagonal: 1.5× for most APS-C, 1.6× for Canon APS-C, 2.0× for Micro Four Thirds, 2.7× for 1-inch. A 35mm on APS-C is 52.5mm equivalent; a 25mm on Micro Four Thirds is 50mm equivalent. Only the angle converts, not the aperture.
Does crop factor change the aperture?
Not for exposure. f/2.8 gives the same illumination on any format, so meter settings carry straight over. At matched framing a smaller format gives more depth of field, which is why people quote an "equivalent aperture" for blur. Keep that separate from exposure.
Are zooms worse than primes?
Not necessarily. Good modern zooms come close to primes optically. The real differences are maximum aperture, usually a stop or two slower, plus size, weight and price.
Why is 50mm called a "standard" lens?
Its diagonal angle of view is close to what one eye comfortably takes in, so spatial relationships look much as they do in life. It is a historical convention, not a law of physics.