What will my pinhole camera see?

January 28, 2008

OK, last post I ran through (or rode roughshod) what it takes to figure exposures for a pinhole converted camera.  But what about the angle of view?  What will be in the picture?

Without going into a lot of derivations on the physics of light and how it bends and how the pinhole’s diffraction effect is doing all our heavy lifting, the equation is:

angle = 2 * arctan(d / 2f)

Here the value “d” refers to the distance across the film.  This can be the horizontal or vertical measurement of the film or more typically the measure of the diagonal.  And f is the focal length of the camera.

Great, now how do I get the diagonal of the film?  Well, you could measure it directly or tap into the spirit of a dead Greek, Pythagoras.  I’ll do that one for you.

So, example time:

Lets say I have an APS-C sized sensor dSLR.  Google tells me the sensor measures 23.7mm x 15.7mm.  This varies slightly from camera maker to camera maker but it may be listed in your manual.  Pythagoras tells me that the diagonal measurement will be the square root of the sum of the squares of height and width.  Huh you say?

d = sqrt(h^2 + w^2) = sqrt(23.7^2 + 15.7^2) = 28.4mm

In the other post I suggested we might have a focal length of 45mm with a body cap on the dSLR.  So f=45mm in this example too.

Quick word of warning about cheap calculators, and Excel spreadsheets.  Often times they like to use radians as the unit of measure for angles, not degrees.  What is a radian you ask?  Well there are “pi” radians in a circle.  There, did that help?  No?  OK, just make sure you have your calculator in DEGREES mode or read carefully in the Excel help files how to convert from radians to degrees.  We want the answer in degrees because the little protractor we used in 7th grade is marked in degrees, not radians. 🙂

Also, “arctan” may be given as “tan-1” or similar text on the calculator buttons  YMMV!

2*arctan(28.4 / 2*45)  =  35 degrees (dropping the fraction).  What does this mean to you and me?  Well, depending on who you ask and how you measure things, we have a field of view about 55 degrees wide.  So 35 degrees is narrower.  So the camera is seeing a bit less than you.  It will be a mildly telephoto depiction of the scene.  By the way, the pinhole angle of view (and a lens for that matter) is really a cone, not square or rectangular like your film or sensor.

So now that I know the angle, I still want to know how to estimate the view for my picture before I take it!.  OK, get out the little plastic protractor you had in Jr. High.  Or go buy one at the dollar store.  On some cardboard, we are going to trace out the angle above.  Do this by making three marks.  One is the center point of the straight edge of the protractor, remember which point this is (the apex), it will be important later.  The other two will be at 1/2 the desired angle, left and right from the center point of the curved part of the protractor.  We said 35 degrees, so that would be 17 1/2 degrees each side.  Don’t fret the accuracy.  Now connect the dots, all three ways and you have a triangle.  Cut it out.

Hold the triangle such that the important apex point is over the pinhole of your camera (or close to it) and the flat side (base) faces you.  Sight along the sides of the triangle and you have the field of view left to right.  Move the triangle to the side of the camera and you can sight the view up and down.

If you are using a dSLR, you can check your work immediately.  Don’t be surprised if things aren’t EXACTLY the field of view.  But with your little triangle you can “frame loose” and crop a little later if needed.



  1. Yikes!! I’m confused. No suprise I’m sure. :c) I am however looking forward to pinhole workshops this year.

  2. Yeah, well it sounds a LOT harder than it really is… Trust me.

    The light coming into the camera (pinhole or lens) forms a cone, with the tip of the cone at the pinhole or iris. The base of the cone is on the film. The cross-section of a cone is a triangle. That pretty much covers the mechanics of the geometry. And the angle at the tip of the cone inside the camera will be the same as the angle of the lightrays outside the camera. Everything within that angle (cone) looking out from the pinhole (iris) will be in view of the film.

    Insert visual aid here… 🙂

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