# calculation of focal length

Discussion in 'Digital Photography' started by TS, Aug 7, 2004.

1. ### TSGuest

I am trying to calculate the focal length of the lens in my digital camera.

I understand that a smaller number such as 18mm is wide angle and a larger
number such as 200mm is a tele-foto lens.

If I calculate the angle of view of the camera, can I calculate the focal
length?
If so, how - and do I use the horizontal angle or the vertical plane
(assuming the camera is used in landscape).

Is this calculation an absolute or does it differ for 35mm cameras and
digital cameras?

Thanks

TS, Aug 7, 2004

2. ### Matt IonGuest

18mm/200mm IS the focal length.

--
"Few people are capable of expressing with equanimity opinions which differ
from the prejudices of their social environment. Most people are even
incapable of forming such opinions."
-- Albert Einstein

"TS" <> wrote in message
news:cf38p2\$eic\$...
> I am trying to calculate the focal length of the lens in my digital

camera.
>
> I understand that a smaller number such as 18mm is wide angle and a larger
> number such as 200mm is a tele-foto lens.
>
> If I calculate the angle of view of the camera, can I calculate the focal
> length?
> If so, how - and do I use the horizontal angle or the vertical plane
> (assuming the camera is used in landscape).
>
> Is this calculation an absolute or does it differ for 35mm cameras and
> digital cameras?
>
> Thanks
>
>

Matt Ion, Aug 7, 2004

3. ### TSGuest

Also, If i add a 0.5x adaptor, does this half the focal length, or does it
half the area (i.e. the square of the increase in focal length)?

"TS" <> wrote in message
news:cf38p2\$eic\$...
> I am trying to calculate the focal length of the lens in my digital

camera.
>
> I understand that a smaller number such as 18mm is wide angle and a larger
> number such as 200mm is a tele-foto lens.
>
> If I calculate the angle of view of the camera, can I calculate the focal
> length?
> If so, how - and do I use the horizontal angle or the vertical plane
> (assuming the camera is used in landscape).
>
> Is this calculation an absolute or does it differ for 35mm cameras and
> digital cameras?
>
> Thanks
>
>

TS, Aug 7, 2004
4. ### Dankwart KoehlerGuest

Matt: The focal length is not a ratio but a dimension in mm.

tspill:
For conventional cameras:
the distance to your object divided by the width of your object as you see
it is equal to the distance to your film (sensor) inside the camera, which
is the focal length, divided by the width of the film (which equals 36mm in
35mm film)

or
Focal Length = 36mm x (Distance to Object/Width of Object)

This should hold also for digital cameras if you think in terms of your
focal length like that for a 35 mm camera. If you think in temrs of medium
size cameras you use 60 mm instead of 36 mm and think of focal length in
terms of the focal length for a medium size camera.

"Matt Ion" <> wrote in message
news:vJ9Rc.38137\$gE.29243@pd7tw3no...
> 18mm/200mm IS the focal length.
>
> --
> "Few people are capable of expressing with equanimity opinions which

differ
> from the prejudices of their social environment. Most people are even
> incapable of forming such opinions."
> -- Albert Einstein
>
>
> "TS" <> wrote in message
> news:cf38p2\$eic\$...
> > I am trying to calculate the focal length of the lens in my digital

> camera.
> >
> > I understand that a smaller number such as 18mm is wide angle and a

larger
> > number such as 200mm is a tele-foto lens.
> >
> > If I calculate the angle of view of the camera, can I calculate the

focal
> > length?
> > If so, how - and do I use the horizontal angle or the vertical plane
> > (assuming the camera is used in landscape).
> >
> > Is this calculation an absolute or does it differ for 35mm cameras and
> > digital cameras?
> >
> > Thanks
> >
> >

>
>

Dankwart Koehler, Aug 7, 2004
5. ### BillyJoeJimBobGuest

TS wrote:
>
> I am trying to calculate the focal length of the lens in my digital
> camera.
>
> I understand that a smaller number such as 18mm is wide angle and a
> larger number such as 200mm is a tele-foto lens.
>
> If I calculate the angle of view of the camera, can I calculate the
> focal length?
> If so, how - and do I use the horizontal angle or the vertical plane
> (assuming the camera is used in landscape).

I cannot determine from your post exactly what you want to do, but I
am going to assume you want to determine what focal length you are
using (or need to use) in a given situation.

To do this, you will need three measurements, which are as follows:

1. The horizontal (or vertical) size of an object you're going to take
a picture of.
2. The distance from that object to your camera when said object
completely fills the image horizontally (or vertically if you used
vertical in #1 above).
3. The horizontal (or vertical, if you used vertical in #1 above)
size of the sensor in your camera.

Items #1 and #2 must be measured using the same units (i.e. both of
them are measured in feet, or both of them are measured in meters,
or furlongs, or whatever you want, as long as the units are the same).

Item #3 should be measured in millimeters. Most manuals for cameras
list the sensor dimension in the specifications section.

Take the distance from the object to your camera, divide it by the
object's size (#2 / #1). Multiply the result by the size of the
sensor, and you have a pretty good approximation of your current
focal length. For wide angle lenses, the calculation is less
accurate, but it should be good enough for most purposes.

For example, suppose I want to find the focal length that lets me
just fit a one foot ruler in the frame while standing ten feet away.

#1 = 1 foot
#2 = 10 feet

The camera I'm using is a Canon 300D. Its sensor measures about
22.7 millimeters horizontally.

#3 = 22.7

#2 / #1 = 10 feet / 1 foot = 10
That result multiplied by #3 gives us 10 * 22.7 = 227 millimeters.

At ten feet, I would need a 227 millimeter focal length to fill the
frame of my 300D with a ruler measuring one foot across. I would
probably use a 200mm lens.

> Is this calculation an absolute or does it differ for 35mm cameras
> and digital cameras?

As long as you completely fill the frame with the object you've
measured, the calculation above should be independent of the type of
film or size of sensor. Crop factor is irrelevant for the calculation
above.

BJJB

BillyJoeJimBob, Aug 7, 2004
6. ### BillyJoeJimBobGuest

TS wrote:
>
> Also, If i add a 0.5x adaptor, does this half the focal length, or
> does it half the area (i.e. the square of the increase in focal
> length)?

As I understand it, a 0.5x adaptor (which is probably also known as
a focal reducer) will cut your focal length in half, resulting in a
linear field of view that is around twice as wide as before. If your
field of view encompassed a region ten feet across when you are
standing ten feet away, adding the 0.5x adaptor should give you a
field of view measuring about twenty feet across when you are standing
ten feet away.

BJJB

BillyJoeJimBob, Aug 7, 2004
7. ### TSGuest

I was giving these as examples. I need to calculate the focal length of
another digital camera/lens to allow me to enter the lens details into a
stiching/360 panorama application. And I asumed that you cna do this from
the angle of the image from the camera.

"Matt Ion" <> wrote in message
news:vJ9Rc.38137\$gE.29243@pd7tw3no...
> 18mm/200mm IS the focal length.
>
> --
> "Few people are capable of expressing with equanimity opinions which

differ
> from the prejudices of their social environment. Most people are even
> incapable of forming such opinions."
> -- Albert Einstein
>
>
> "TS" <> wrote in message
> news:cf38p2\$eic\$...
> > I am trying to calculate the focal length of the lens in my digital

> camera.
> >
> > I understand that a smaller number such as 18mm is wide angle and a

larger
> > number such as 200mm is a tele-foto lens.
> >
> > If I calculate the angle of view of the camera, can I calculate the

focal
> > length?
> > If so, how - and do I use the horizontal angle or the vertical plane
> > (assuming the camera is used in landscape).
> >
> > Is this calculation an absolute or does it differ for 35mm cameras and
> > digital cameras?
> >
> > Thanks
> >
> >

>
>

TS, Aug 7, 2004
8. ### Paul W. RossGuest

You need to know the diagonal measurement of the sensor. The FL is
then the distance a pinhole would be from this sensor to give the same
ANGULAR view. TYpically, a "normal" lens is one whose FL is the same
as the diagonal. WA is a larger angle, and TF is less. The specs for
the sensor should be in the camera manual. Also, some digital cameras
tell you the relationship between their lenses and a 35mm camera. Try
that..

Paul W. Ross, Aug 7, 2004
9. ### Matt IonGuest

"Dankwart Koehler" <> wrote in message
news:YAaRc.184314\$...
> Matt: The focal length is not a ratio but a dimension in mm.

That's what I said. Okay, I typed it poorly: 18mm and 200mm (as specified
in the original post) are focal lengths. They don't need to be calculated;
they are specified by the lens or camera manufacturer.

Matt Ion, Aug 8, 2004
10. ### Matt IonGuest

You don't calculate the focal length; the camera or lens manufacturer tells
you what the focal length is. 18mm and 200mm, in your example, are focal
lengths. You can use the focal length to calculate the angle of view, not
vice-versa.

--
"Few people are capable of expressing with equanimity opinions which differ
from the prejudices of their social environment. Most people are even
incapable of forming such opinions."
-- Albert Einstein

"TS" <> wrote in message
news:cf3eok\$p2g\$...
> I was giving these as examples. I need to calculate the focal length of
> another digital camera/lens to allow me to enter the lens details into a
> stiching/360 panorama application. And I asumed that you cna do this from
> the angle of the image from the camera.
>
>
>
> "Matt Ion" <> wrote in message
> news:vJ9Rc.38137\$gE.29243@pd7tw3no...
> > 18mm/200mm IS the focal length.
> >
> > --
> > "Few people are capable of expressing with equanimity opinions which

> differ
> > from the prejudices of their social environment. Most people are even
> > incapable of forming such opinions."
> > -- Albert Einstein
> >
> >
> > "TS" <> wrote in message
> > news:cf38p2\$eic\$...
> > > I am trying to calculate the focal length of the lens in my digital

> > camera.
> > >
> > > I understand that a smaller number such as 18mm is wide angle and a

> larger
> > > number such as 200mm is a tele-foto lens.
> > >
> > > If I calculate the angle of view of the camera, can I calculate the

> focal
> > > length?
> > > If so, how - and do I use the horizontal angle or the vertical plane
> > > (assuming the camera is used in landscape).
> > >
> > > Is this calculation an absolute or does it differ for 35mm cameras and
> > > digital cameras?
> > >
> > > Thanks
> > >
> > >

> >
> >

>
>

Matt Ion, Aug 8, 2004
11. ### Matt IonGuest

That would halve the focal length, which would give you a 4X increase in
coverage.

--
"Few people are capable of expressing with equanimity opinions which differ
from the prejudices of their social environment. Most people are even
incapable of forming such opinions."
-- Albert Einstein

"TS" <> wrote in message
news:cf3aoi\$h3s\$...
> Also, If i add a 0.5x adaptor, does this half the focal length, or does

it
> half the area (i.e. the square of the increase in focal length)?
>
>
> "TS" <> wrote in message
> news:cf38p2\$eic\$...
> > I am trying to calculate the focal length of the lens in my digital

> camera.
> >
> > I understand that a smaller number such as 18mm is wide angle and a

larger
> > number such as 200mm is a tele-foto lens.
> >
> > If I calculate the angle of view of the camera, can I calculate the

focal
> > length?
> > If so, how - and do I use the horizontal angle or the vertical plane
> > (assuming the camera is used in landscape).
> >
> > Is this calculation an absolute or does it differ for 35mm cameras and
> > digital cameras?
> >
> > Thanks
> >
> >

>
>

Matt Ion, Aug 8, 2004
12. ### Ken BurnsGuest

The focal length used for a particular shot is recorded in the EXIF data.
Just use any software that can read this data and you will know exactly.

KB

"TS" <> wrote in message
news:cf38p2\$eic\$...
> I am trying to calculate the focal length of the lens in my digital

camera.
>
> I understand that a smaller number such as 18mm is wide angle and a larger
> number such as 200mm is a tele-foto lens.
>
> If I calculate the angle of view of the camera, can I calculate the focal
> length?
> If so, how - and do I use the horizontal angle or the vertical plane
> (assuming the camera is used in landscape).
>
> Is this calculation an absolute or does it differ for 35mm cameras and
> digital cameras?
>
> Thanks
>
>

Ken Burns, Aug 8, 2004
13. ### Marvin MargoshesGuest

"Matt Ion" <> wrote in message
news:GekRc.46314\$M95.12442@pd7tw1no...
> "Dankwart Koehler" <> wrote in message
> news:YAaRc.184314\$...
> > Matt: The focal length is not a ratio but a dimension in mm.

>
> That's what I said. Okay, I typed it poorly: 18mm and 200mm (as

specified
> in the original post) are focal lengths. They don't need to be

calculated;
> they are specified by the lens or camera manufacturer.
>
>
> For digicams, they are usually specified as the equivalent fl for a 35 mm

camera.

The formula for focal length has been discussed frequently on this and other
NGs, it is surely avalable on the Web (sorry, I don't have time to search
for it), and in most physics textbooks.

Marvin Margoshes, Aug 8, 2004