[Brightcolours]

Lets take a 135mm f2.8 lens on full frame as starting point.



Focal length: 135mm

f-value: f2.8

Aperture: 135 / 2.8 = 48mm



Now lets figure out an equivalent lens on APS-C (using 1.5x crop factor in this calculation example).

To get the same field of view:

135 / 1.5 = 90mm



To get an equivalent DOF, the hole (aperture) has to be the same size.

So....

Focal length: 90mm

Aperture: 48mm

f-value: 90 / 48 = f1.86666667 (used the not rounded of aperture size in the actual calculation).



That is the "official" way to calculate it.



Now the fast way (and happens to give exactly the same results):

Just use the crop factor for both the f-value and the focal length to get the equivalents.

135 / 1.5 = 90mm

2.8 / 1.5 = 1.86666667



Simple, isn't it?



Also works the other way around:

APS-C 1.5x crop 85mm f1.8 lens

85mm x 1.5 = 127.5mm

f1.8 x 1.5 = f2.7

Equivalent on FF: 128mm f2.7 lens



APS-C 1.6x crop 85mm f1.8 lens

85mm x 1.6 = 136mm

f1.8 x 1.6 = f2.88

Equivalent on FF: ~135mm f2.8



The difference between APS-C and FF is about 1 1/3rd stop.

The difference between 4/3rds and FF is about 2 stops.

The difference between 4/3rds and APS-C is about 2/3rds of a stop.