📷 Camera Sensor Crop Factor & Focal Length Equivalent
Calculate 35mm full-frame equivalent focal length (mm), field of view classification, and equivalent depth of field aperture across APS-C and Micro 4/3 sensors.
Short telephoto — the classic portrait range
A 50mm f/1.8 on aps-c (sony, nikon, fuji) frames like a 76mm on full frame and gives the depth of field of f/2.7 — the exposure is still f/1.8, so the shutter speed does not change. Only the depth of field and the total light gathered scale.
Field of view is not proportional to focal length. On this sensor, doubling to 100mm gives 13.5° rather than half of 26.6° — it is an arctangent, so the change is steep at wide angles and shallow at long ones. That is why 16mm and 24mm look worlds apart while 200mm and 210mm look identical.
Crop factors are computed from the sensor diagonals shown, not looked up, so they may differ in the second decimal from a manufacturer’s rounded figure. Sensor sizes vary slightly between bodies of the same nominal format, and “1-inch” and “1/1.7-inch” are legacy vidicon-tube measurements that have nothing to do with any actual dimension of the sensor. Field of view assumes a rectilinear lens and focus at infinity; fisheyes and close focus both change it.
What Camera Sensor Crop Factor & Focal Length Equivalent Does
Crop factor compares a sensor's diagonal to that of 35mm film, which measures 36 by 24mm and so has a 43.27mm diagonal. An APS-C sensor at 23.6 by 15.7mm has a 28.3mm diagonal, giving a factor of 1.53. Multiply a lens's focal length by that and you get the full-frame lens that would frame the same scene.
But crop factor is only a proxy for the thing you want, which is field of view — and the relationship between focal length and angle is an arctangent, not a proportion. On full frame, 24mm covers 73.7° horizontally, 48mm covers 41.1°, and 96mm covers 21.2°. Doubling the focal length does not halve the angle, which is why 16mm and 24mm look like different worlds while 200mm and 210mm look identical.
Equivalence has three parts and most discussions only cover two. Focal length scales by the crop factor for framing. The f-number scales by the same factor for depth of field. And ISO scales by the factor squared for noise, because total light gathered depends on sensor area. Leaving out the third is where most of the arguing online comes from.
One thing that does not scale: exposure. A 50mm f/1.8 on APS-C frames like a 76mm and has the depth of field of f/2.7, but it is still f/1.8 for metering. The shutter speed does not change.
How to Use Camera Sensor Crop Factor & Focal Length Equivalent
- Select your camera sensor format (Full Frame, APS-C Sony/Nikon/Canon, Micro 4/3)
- Enter physical lens focal length in mm and aperture f-stop
- Review 35mm equivalent focal length and depth-of-field aperture
Formula Used by Camera Sensor Crop Factor & Focal Length Equivalent
Crop factor, field of view, and full equivalence
crop = 43.27 ÷ sensor diagonal · FOV = 2·arctan(sensor dimension ÷ (2 × focal length)) · equivalent = (focal × crop, f-number × crop, ISO × crop²)
- 43.27mm
- the diagonal of a 36 × 24mm full-frame sensor
- sensor dimension
- width for horizontal FOV, height for vertical, diagonal for diagonal
- crop²for ISO
- total light scales with area, and area scales with the square of the linear factor
Worked example
A 50mm f/1.8 at ISO 400 on APS-C (23.6 × 15.7mm).
- Crop factor: 43.27 ÷ 28.34 = 1.53
- Equivalent focal length: 50 × 1.53 = 76mm
- Equivalent aperture for depth of field: f/1.8 × 1.53 = f/2.7
- Equivalent ISO for noise: 400 × 1.53² = ISO 932
Result: Horizontal field of view 26.6° — and a 76mm on full frame gives 26.5°, which is the check that the equivalence holds.
Sensor formats and their crop factors
Computed from the diagonals shown, not quoted — manufacturer figures are usually rounded.
| Format | Dimensions | Diagonal | Crop factor |
|---|---|---|---|
| Medium format 44×33 | 43.8 × 32.9mm | 54.8mm | 0.79× |
| Full frame 35mm | 36 × 24mm | 43.3mm | 1.00× |
| APS-C (Sony, Nikon, Fuji) | 23.6 × 15.7mm | 28.3mm | 1.53× |
| APS-C (Canon) | 22.3 × 14.9mm | 26.8mm | 1.61× |
| Micro Four Thirds | 17.3 × 13mm | 21.6mm | 2.00× |
| 1-inch | 13.2 × 8.8mm | 15.9mm | 2.73× |
| Phone 1/1.7-inch | 7.6 × 5.7mm | 9.5mm | 4.55× |
Horizontal field of view on full frame
The relationship is an arctangent — steep at the wide end, almost flat at the long end.
| Focal length | Horizontal FOV |
|---|---|
| 14mm | 104.3° |
| 24mm | 73.7° |
| 35mm | 54.4° |
| 50mm | 39.6° |
| 85mm | 23.9° |
| 200mm | 10.3° |
| 400mm | 5.2° |
How to Read Your Result
A crop sensor does not make a lens longer
The lens projects the same image circle; the smaller sensor records less of it. Nothing about the optics changes — the focal length is a property of the glass and it is the same number on any body. What changes is how much of the projected image you keep.
Exposure does not scale, depth of field does
f/1.8 is f/1.8 everywhere for metering, because the f-number is the ratio of focal length to aperture diameter and describes light per unit area. What scales is the total light collected, which is why the equivalent ISO term exists, and the depth of field, which is why the equivalent aperture does.
Phone sensor names are historical fiction
"1-inch" and "1/1.7-inch" measure nothing on the sensor. They come from the outside diameter of the vidicon tubes these sizes replaced in the 1950s, where the usable image area was roughly two thirds of the tube. A "1-inch" sensor has a 15.9mm diagonal. The dimensions in millimeters are the only figures worth using.
Perspective belongs to distance, not focal length
The flattening people attribute to telephoto lenses comes from standing further away, not from the lens. Shoot the same subject at the same distance with a wide lens and crop to match, and the perspective is identical. Focal length changes framing; where you stand changes perspective.
Limitations & Accuracy Notes
- Sensor dimensions vary slightly between bodies of the same nominal format, so crop factors may differ in the second decimal from a manufacturer's figure.
- Field of view assumes a rectilinear lens focused at infinity. Fisheyes follow a different projection, and close focus narrows the angle.
- Aspect ratios differ between formats, so matching the diagonal does not match the framing exactly.
- Equivalent aperture describes depth of field and total light, not exposure. Metering is unaffected.
- Ignores lens transmission, sensor efficiency and differences in read noise, all of which affect the real-world comparison.
Frequently Asked Questions
What is camera sensor crop factor?
How does crop factor affect lens focal length?
What does crop factor actually change?
Does crop factor change the aperture?
Does it change compression or perspective?
What are the common crop factors?
Does a crop sensor give me extra reach for wildlife?
Is my data stored?
References & Further Reading
- Wikipedia — crop factor — Definitions of crop factor, equivalence and the sensor-size naming conventions