Crop Factor and Equivalent Focal Length Calculator

What a crop factor compares

A crop factor is a ratio between two sensor diagonals. The top of the fraction is the diagonal of a full-frame sensor, 36 by 24 mm, which works out to 43.27 mm. The bottom is the diagonal of the sensor in the camera you are holding. Divide one by the other and you have the number printed on every spec sheet: 1.0 for full frame, about 1.5 for most APS-C bodies, 2.0 for Micro Four Thirds, and 5.6 for the tiny sensor in a budget phone.

The name comes from what the number describes. A smaller sensor sits inside the image circle a full-frame lens projects, so it records a smaller rectangle and the picture looks cropped. The factor tells you how much smaller. A 1.6 crop means the diagonal is 1.6 times shorter than full frame, so the frame covers a little less than two thirds of the diagonal.

Two sensors with the same crop factor can still have different shapes. Micro Four Thirds uses a 4:3 rectangle while full frame uses 3:2, so the diagonals match the factor exactly while the corners do not line up. That is why the diagonal is the fair comparison: it is the one measurement that does not depend on aspect ratio.

The formula in one line

Every number on this page comes from two steps. First, crop factor equals the full-frame diagonal divided by the sensor diagonal, and each diagonal is the square root of width squared plus height squared. Second, the equivalent focal length equals the real focal length times that factor.

For a Canon APS-C body the sensor measures 22.3 by 14.9 mm, which Canon lists on the EOS R50 specification page. The diagonal is the square root of 22.3 squared plus 14.9 squared, which is the square root of 497.29 plus 222.01, which is the square root of 719.30, or 26.82 mm. Then 43.27 divided by 26.82 is 1.613, and 50 mm times 1.613 is 80.7 mm.

That is the entire calculation. The equivalent focal length is not a different lens, it is a way of saying "this framing matches what a 81mm lens does on full frame". The glass in your hand has not changed, and neither has the aperture you set.

The Micro Four Thirds standard's own FAQ describes its image circle and 4:3 frame, which is where the 17.3 by 13.0 mm imaging area comes from. That gives a diagonal of 21.64 mm, and 43.27 divided by 21.64 is 2.00, which is why the system is sold as a 2x crop.

Sensor sizes and their factors

The table lists the formats people shop for, with the diagonal and the factor each one produces. Nominal sizes are used, so a specific body can differ by a tenth of a millimeter.

Canon's APS-C is slightly smaller than everyone else's, which is why its factor is 1.61 rather than the 1.53 that Nikon, Fujifilm and Sony use. The difference is small enough to ignore when choosing a lens and large enough to matter when you stack a 1.4x teleconverter on top of an already long lens.

Medium format is the one case below 1.0. A GFX body has a diagonal of 54.8 mm, so 43.27 divided by 54.8 is 0.79, and a 50mm lens on that body frames like a 39mm lens on full frame. The factor works in both directions, which is the part people forget.

Focal length times the factor is the view

Multiply and you have the answer. The table shows the same five focal lengths on four formats, all converted to the full-frame number that produces the same diagonal angle of view.

The practical reading is that a 24mm lens on APS-C is not a wide lens any more. At 39mm equivalent it sits in the normal range, and if you want the 24mm look on that body you need a 15mm lens. The same logic explains why kit lenses for crop bodies start at 18mm: 18 times 1.5 is 27mm, close to the classic 28mm wide angle.

Long lenses gain reach on small sensors. A 200mm lens on a 1-inch body frames like a 545mm lens on full frame, which is how superzoom compacts advertise 600mm equivalent from a lens the size of a coffee cup. Nothing was magnified. The sensor recorded a smaller slice of the image circle.

Angle of view follows the same ratio. A 50mm lens on full frame covers 46.8 degrees diagonally. The same lens on Canon APS-C covers 30.0 degrees, and on Micro Four Thirds 24.4 degrees, which is the identical view a 100mm lens gives on full frame.

Aperture, depth of field and light

This is where the shorthand causes real confusion. The f-number you set does not change when you change bodies. f/1.8 is f/1.8 for exposure on every format, so the shutter speed and ISO you need for a correct exposure stay the same. If the meter says 1/125 at f/1.8, that holds whether the sensor is full frame or Four Thirds.

Depth of field is a different question. A smaller sensor needs a shorter focal length for the same framing, and a shorter focal length at the same f-number gives a deeper depth of field. To compare fairly, multiply the f-number by the crop factor as well. A 50mm f/1.8 on Canon APS-C frames like an 81mm lens on full frame, and it blurs the background like an 81mm lens at f/2.9.

Total light works the same way. At the same f-number and the same scene brightness, light per square millimeter is equal, but the smaller sensor has fewer square millimeters, so it collects less light in total. That is why a 1-inch sensor at f/1.8 looks noisier than a full-frame sensor at f/1.8 when both are printed at the same size, even though the exposure is identical.

None of this makes small sensors worse. It makes them a trade. You get a smaller, lighter kit with more reach per millimeter of glass, and you give up some control over background blur and some low-light headroom.

Two bodies, one lens: worked examples

Take a 50mm f/1.8 and put it on three bodies in turn. On full frame it is a 50mm f/1.8 with a 46.8 degree diagonal view, and at 10 feet it frames a width of 7.2 feet. On Canon APS-C the same lens becomes an 81mm equivalent at f/2.9 for depth of field, the view narrows to 30.0 degrees, and the frame at 10 feet is 4.5 feet wide. On Micro Four Thirds it reaches 100mm equivalent, f/3.6, and 24.4 degrees.

Now swap the glass instead of the body. A 25mm f/1.8 on Micro Four Thirds lands at exactly 50mm equivalent, with a 46.8 degree view and 6.9 feet of width at 10 feet. That is the standard fast prime for the system, and it exists because 25mm is what you need to reproduce the full-frame 50mm look on a 2x sensor.

Telephoto cases show the same arithmetic with bigger numbers. A 200mm lens on a 1-inch sensor is a 545mm equivalent with a 4.5 degree view, which at 10 feet frames 0.7 feet, about the width of a shoebox. A 35mm f/1.8 on Nikon DX is a 53mm f/2.7 equivalent, close enough to a normal lens that most people never think about the factor.

The reverse direction surprises people. A 50mm f/2.8 on a GFX body behaves like a 39mm f/2.2 on full frame, so medium format gets a wider view and shallower depth of field from the same focal length. The factor of 0.79 is doing the work.

Where the shorthand misleads

Marketing copy uses "equivalent" loosely, and three habits are worth knowing. The first is quoting a focal length range in full-frame terms while printing the real focal length on the barrel. A compact sold as a 24 to 720mm lens usually carries something like 4.3 to 129mm of real glass, and the 30x on the box is the ratio between those two real numbers, not the equivalent ones.

The second is treating the crop factor as magnification. It is not. A 300mm lens on a 1.5x body does not resolve more detail than the same lens on full frame. It puts fewer pixels on the subject unless the crop body has a denser sensor, and that pixel density is what decides whether you gain reach. A 24 megapixel APS-C body puts about as many pixels on a distant bird as a 56 megapixel full-frame body would.

The third is comparing depth of field without converting the aperture. Two shots at f/2.8 on different formats do not have the same background blur, and a review that compares them without saying so is comparing two different pictures.

Aspect ratio adds a small wrinkle on top. The factor is built from diagonals, so a 4:3 sensor and a 3:2 sensor with the same diagonal will have different horizontal and vertical coverage. For most framing decisions the difference is under 5 percent, which is smaller than the difference between two zoom settings.

Buying with the factor in mind

Start from the view you want and divide. If you shoot portraits and like the 85mm look on full frame, a 50mm lens on Canon APS-C gets you to 81mm, and a 45mm lens on Micro Four Thirds gets you to 90mm. Working backward from the look is faster than memorizing a table.

For travel, the factor explains why a 12 to 40mm zoom on Micro Four Thirds covers the same range as a 24 to 80mm zoom on full frame while weighing a fraction as much. The glass is smaller because the image circle is smaller, and the factor is the price you pay in background blur and high ISO room.

For wildlife, the factor is a way to get reach from shorter, cheaper glass, with the pixel density caveat above. A 100 to 400mm zoom on a 1.53x body covers the same view as a 153 to 612mm zoom on full frame, and it costs and weighs far less than that lens would.

Two numbers are worth writing on the lens cap: the factor for your body, and the equivalent aperture you get at your favorite f-number. Those two numbers answer most format questions before you open a spec sheet.

Sensor dimensions come from published manufacturer specifications and can differ slightly between models. Treat the figures here as a close guide for planning, not as a measurement of any specific camera.