A crop factor calculator translates a lens from one sensor format into the language of another. Because 35mm film dominated photography for most of a century, almost every intuition photographers carry about focal length — that 50mm looks normal, that 24mm is wide, that 200mm is long — is calibrated to a 36 by 24 millimetre frame. Put the same lens in front of a smaller sensor and the picture changes, not because the lens changed but because a smaller rectangle is being cut out of the same projected image circle.
Arb Digital publishes this in its free tools library beside the camera field of view calculator, which gives the actual angle and ground coverage rather than an equivalence, and the depth of field calculator, which computes the sharp zone directly for whatever format you are on. This page converts between formats; those pages answer the underlying optical questions in absolute terms.
What This Crop Factor Calculator Does
It computes four things. First, the crop factor itself: the ratio of the full frame diagonal to your sensor's diagonal. Second, the equivalent focal length — the full frame lens that would produce the same angle of view. Third, the equivalent aperture, which is the f-number a full frame lens would need to match both the depth of field and the total quantity of light collected. Fourth, the equivalent ISO, which is where the noise comparison lives.
The comparison format is selectable rather than fixed, because full frame is not always the reference anyone cares about. A cinematographer moving between Super 35 and a full frame body, or a photographer comparing Micro Four Thirds against APS-C rather than against 35mm, needs the ratio between those two formats and not both of their ratios against a third.
The bar display shows sensor area alongside diagonal, because area is the quantity that governs light collection and it falls off with the square of the crop factor. A format with a crop factor of 2.0 does not have half the sensor area of full frame — it has one quarter of it, and that squared relationship is the reason equivalent apertures and equivalent ISOs move so much further than equivalent focal lengths do.
How to Use It
- Choose the format you are actually shooting. If a camera crops the sensor in a particular video mode or with a lens designed for a smaller image circle, use the active area for that mode rather than the sensor's full dimensions.
- Enter the focal length exactly as marked on the lens. Never enter an equivalent figure here. The calculator applies the crop factor itself, and supplying a pre-converted number applies it twice.
- Enter the aperture you would actually set. The equivalent aperture is an output, never an input, and it is a statement about the resulting image rather than about metering.
- Pick the comparison format that matches the conversation you are having. Most published lens reviews and rules of thumb are stated in full frame terms, which is why that is the default.
- Read the equivalent focal length for framing and the equivalent aperture for look. Those two figures together describe what the resulting photograph would resemble on the comparison format.
The Formula / How It's Calculated
The crop factor is a diagonal ratio:
crop factor = 43.267 ÷ sensor diagonal, where the sensor diagonal is √(width² + height²) in millimetres and 43.267 is the diagonal of a full 36 by 24 millimetre frame.
From that single number everything else follows. Equivalent focal length = f × crop factor. Equivalent aperture = N × crop factor. Equivalent ISO = ISO × crop factor². When comparing two non-full-frame formats directly, the ratio to use is diagonal of comparison format ÷ diagonal of your format.
Worked example, matching the values the page loads with. A Micro Four Thirds sensor measures 17.3 by 13 millimetres, so its diagonal is √(299.29 + 169) = √468.29 = 21.640mm and its crop factor is 43.267 ÷ 21.640 = 2.00×. A 25mm f/1.8 lens on that body therefore frames like a 50mm lens on full frame. Its equivalent aperture is 1.8 × 2.00 = f/3.6, meaning a full frame camera at 50mm f/3.6 would render approximately the same depth of field and collect the same total light. ISO 400 on the smaller sensor corresponds to 400 × 2.00² = ISO 1600 on full frame in noise terms. Stanford's CS178 notes on the operation of a thin lens set out the imaging geometry that makes the diagonal ratio the correct scaling term.
Equivalent Aperture Is About Depth of Field, Not Exposure
This is the most misunderstood output on the page, and it causes genuine arguments online, so it is worth being precise.
An f-number is a ratio: focal length divided by the diameter of the entrance pupil. It describes illuminance at the image plane — how much light falls on each square millimetre of sensor. That figure has nothing to do with sensor size. A lens set to f/1.8 delivers the same illuminance whether it is projecting onto a phone sensor or a large format sheet, which is why a handheld light meter can give a single reading that works on any camera. If someone tells you that f/1.8 on Micro Four Thirds "is really f/3.6" for exposure purposes, they are wrong, and setting your camera accordingly would underexpose by two stops.
What the equivalent aperture does describe is the image. Depth of field depends on the physical diameter of the aperture, not the ratio: a 25mm lens at f/1.8 has an entrance pupil of about 13.9mm, while a 50mm lens at f/1.8 has one of about 27.8mm. The larger physical opening produces the shallower depth. To match the smaller format's depth of field you must stop the larger format's longer lens down to f/3.6, at which point its pupil is also about 13.9mm.
The same physical pupil also governs total light. Illuminance per square millimetre is identical at f/1.8 on both formats, but the smaller sensor has one quarter of the area, so it collects one quarter of the photons over the same exposure time. Fewer photons means a worse signal-to-noise ratio, which is precisely what the equivalent ISO output is expressing. Both formats will produce a correctly exposed image at the same settings; the larger one will produce a cleaner file.
Both statements are true simultaneously, and they are not in conflict. Exposure is per unit area. Noise and depth of field follow the physical aperture and the sensor area. A page that reports only one of the two is telling half the story.
What Crop Factor Does Not Change
Several properties survive the format change untouched, and mistaking any of them for something crop factor affects is a common source of confusion.
Perspective is the big one. Compression and stretching are functions of camera-to-subject distance alone. A 50mm lens on APS-C does not have "the perspective of a 75mm lens" — it has the perspective of wherever you are standing, and the only reason a crop body seems to change perspective is that the tighter framing usually makes you step backwards. Stand in the same place, shoot both, crop the full frame image to match, and the two are indistinguishable in perspective terms.
The minimum focus distance and maximum magnification of the lens itself do not change either, although the magnification relative to the frame does. A macro lens achieving 1:1 on full frame still achieves 1:1 on a crop body, but that life-size subject now fills a smaller frame, so the subject appears larger in the final image. That is a framing effect and not an increase in the lens's optical magnification. Stanford's CS178 treatment of the Gaussian lens formula works through how lateral magnification relates to object and image distances, which is the relationship being described.
Diffraction behaves in a way that trips people up in both directions. The physical size of the Airy disc at a given f-number is identical on every format, because it depends only on the f-number and the wavelength of light. What changes is how large that disc is relative to the frame: on a smaller sensor the same disc occupies a larger share of the picture, so the format becomes diffraction-limited at a wider aperture. In practice a Micro Four Thirds camera softens noticeably by f/11 while a full frame body has room to f/16.
Shutter speed guidance for handholding does shift, because it was always a rule about angular blur relative to the frame. The old advice to use a shutter speed of one over the focal length was written for 35mm, so on a crop body it should be one over the equivalent focal length. That is the one place where the equivalent focal length figure feeds directly into a camera setting rather than into a comparison.
Where the Simple Diagonal Ratio Falls Down
Crop factor as a single number assumes both formats share an aspect ratio. Full frame and APS-C are both close to 3:2, so the approximation is excellent. Micro Four Thirds is 4:3, and a 4:3 sensor with the same diagonal as a 3:2 sensor is taller and narrower. Convert a Micro Four Thirds lens by the diagonal ratio and the vertical framing will match the prediction well while the horizontal framing comes out slightly tighter than the equivalent number implies.
This is why the horizontal and vertical angles from the camera field of view calculator are worth checking whenever aspect ratios differ. The diagonal ratio is the industry convention and it is the right default, but it is a compromise that spreads the mismatch across both axes rather than eliminating it.
Anamorphic cinematography breaks the model entirely. A 2× anamorphic lens squeezes a wide field horizontally onto a standard gate, so its horizontal angle of view corresponds to a focal length half of what is engraved on the barrel while its vertical angle corresponds to the engraved figure. No single crop factor describes that, and anamorphic shooters work from published tables for their specific lens and gate combination instead.
Finally, equivalence says nothing about lens quality. Two lenses that are equivalent on paper can differ enormously in sharpness across the frame, flare resistance, distortion, colour rendering, focus breathing and the character of out-of-focus areas. Equivalence is a framing and light-collection calculation. It is not a verdict on which lens takes better photographs, and it never was.
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See Web Design Services Talk to Arb DigitalCommon Mistakes to Avoid
- Entering an already-converted focal length — type the number engraved on the lens, because the calculator applies the crop factor for you.
- Setting the camera to the equivalent aperture — that would underexpose. Equivalent aperture describes the resulting depth of field and light collected, not the meter reading.
- Believing a crop body gives extra reach for free — it crops the same projected image, so it delivers a tighter frame at a lower pixel count than cropping a larger sensor to the same angle would.
- Comparing a 4:3 format to a 3:2 format on diagonal alone — the diagonal ratio matches neither axis exactly, so check horizontal and vertical angles separately when framing matters.
- Treating equivalence as a quality ranking — it is a geometry and light-collection calculation and says nothing about sharpness, distortion, flare or rendering.
Related Free Tools From Arb Digital
Get absolute angles and ground coverage from the camera field of view calculator, find the sharp zone with the depth of field calculator, and set the everything-sharp focus point with the hyperfocal distance calculator. Balance shutter, aperture and ISO with the exposure value calculator, work through lens geometry with the thin lens equation calculator, plan framing with the aspect ratio calculator, and size storage with the image file size calculator. Everything else is in the free online tools hub.
Frequently Asked Questions
It is the ratio of the full frame diagonal, 43.27 millimetres, to your sensor's diagonal. Multiplying a focal length by that ratio gives the full frame focal length that would produce the same angle of view, which is why it is sometimes called the focal length multiplier.
For depth of field and total light collected, yes. For exposure, no. An f-number describes light per unit area at the image plane and is independent of sensor size, so an f/1.8 lens meters as f/1.8 on every camera. Setting the camera to the equivalent figure would underexpose by two stops.
Because sensor area scales with the square of the diagonal. A format with a crop factor of two has one quarter of the full frame area, so at the same settings it collects one quarter of the light and shows the noise you would expect from four times the ISO on the larger sensor.
They give tighter framing from the same lens and distance, which is genuinely useful. They do not add optical magnification. The image is the same projection with a smaller rectangle taken from it, so the result is comparable to cropping a larger sensor to the same angle, at whatever pixel count each body provides.
No. Perspective is set entirely by the distance between camera and subject. A crop body appears to compress because the tighter framing usually makes you step back, and stepping back is what changes the perspective.
It is a compromise. Two sensors with the same diagonal but different aspect ratios do not match on either axis, so the diagonal ratio spreads the difference across both. When exact framing matters, compare the horizontal and vertical angles of view directly rather than relying on a single equivalence number.
Not the physics. The Airy disc is the same physical size at a given f-number on any format. Because it occupies a larger share of a smaller frame, small formats reach their diffraction limit at wider apertures, typically around f/8 to f/11 rather than f/16.
Yes. The old guidance of one over the focal length was written for 35mm, so use one over the equivalent focal length instead. That is the one case where the equivalent figure feeds into an actual camera setting rather than a comparison.
