Sometimes, they ask me what distance will be to the subject, if you photograph on a particular lens. In this article, I derived a simple calculation formula.
Viewing angle, focal length and focusing distance
For calculations, I used a full-format camera with a physical sensor size of 36 X 24 mm.
I recommend reading the text under the images.
Here is the information about the viewing angle of the Nikon AF-S 50mm 1: 1.8G Nikkor lens on the Nikon official website. Please note that the viewing angle is indicated along the diagonal of the frame.
The viewing angle can be found in brochures, instructions or on the official websites of the lens manufacturer. But there is one small nuance, which for some reason few people take into account - the angle of view of the lens is indicated for the diagonal of the frame.
I work as a photographer and do not shoot “diagonal shots” at all (to take a shot with a diagonal fill of the frame), and therefore this data gives me only an approximate idea of the angle of view when shooting in normal portrait (vertical camera orientation) or landscape (horizontal camera orientation) mode ...
Model for calculations. The base of the pyramid is the matrix of the camera.
Output: the physical size of the matrix w * h and the focal length of the lens f.
Search for: formula for calculating the viewing angle diagonally, vertically, horizontally. Check the found Beta angle for f = 50mm.
Data
Solving and checking the diagonal viewing angle for f = 50mm (focal length of the lens), w = 36mm (sensor width), h = 24mm (sensor height)
Thus, the data taken from the official website (47 °) and verification (46,79 °) are the same.
Now let's find the angle of view horizontally (Xi) and vertically (Tau):
Calculation of the viewing angle for horizontal and vertical
Formulas for calculating the viewing angle diagonally, horizontally, vertically. Counting example. w = 36mm (sensor width), h = 24mm (sensor height), f = 50mm (lens focal length)
It turns out that if we shoot a portrait at a 50 mm focal length (vertical position of the camera), then the viewing angle at which we will need to enter the model will be only 40 degrees.
Now find formula for calculating the distance L, with which we will need to shoot so that an object with the given dimensions fits in the frame H.
Distance calculation. H is the length of the object being filmed, L is the distance to the object, we can find out the lambda angle from the previous formulas.
The formula for the distance to the object turned out to be quite simple. L is the distance to the subject, f is the focal length of the lens, H is the size of the object (width or height), w is the physical width of the camera sensor, h is the physical height of the camera sensor.
Thus, if we shoot a model with a height of 180 cm on a full-frame camera with a lens that has a 50 mm focal length, then in order for the heels and the crown of the head to get into the frame with the vertical orientation of the camera, we will need to move back 2.5 meters, horizontally, to fit the entire model into the frame, you will need to step back 3.75 meters.
Two main types of camera orientation. Please note that for different camera orientations, in order to place the same subject in the frame, you need to observe different focusing distances, and the size of the object itself in the frame will be different. The gray rectangles in this illustration are completely identical in their linear dimensions.
To be more precise, 5 cm of the focal length (or any other number of the focal length) from the focus plane to the plane of the matrix should be added to these numbers, because the distance is calculated from the object to the focal plane. And you also need to take into account the effect of changing the viewing angle of the lens at different focusing distances, because the same fifty dollars has the declared 47 ° only when focusing on infinity, more about this here.
If we shoot the same model for the same fifty dollars with the horizontal orientation of the camera, but already on the Nikon DX camera (Kf = 1.5), then we will need to move 5,6 meters. And if you take into account that in addition to the model itself, you still need to capture a bit of space from below and from above, then by fifty dollars it will be necessary to retreat by 7 meters.
To use the count for cropped cameras, use the formulas to specify the width w and height h for your camera. For Nikon DX cameras: w = 23.5 mm, h = 15.6 mm. The focal length f should be taken as indicated on the lens without any conversion. Basic formulas are highlighted. If you cannot find the value of w and h in the instruction, then usually w = 36 / Kf, h = 24 / Kf, where Kf is the value crop factor cameras.
It is very simple to find out the focusing distance to the subject from the already taken photo. To do this, just check EXIF photo using http://regex.info/exif.cgi (The site supports any photo format)
An example of how regex works. The value 'At 60cm' indicates that the picture was taken from a distance of 60 cm.
Thank you for attention. Arkady Shapoval.
You need to rest Arkady)
I prepared the article long before NG, and I wanted to start 2014 with something useful :)
Purely mechanically I went to the site, not expecting to see anything here on January 1st, but surprise! Yes, what!
I already had time to forget what the arc tangent of a corner is, by God she hadn’t heard this word for 20 years, but thanks to Arkady, I made him get it from the depths of my memory!
Happy New Year, peace to your home!
Yeah, for sure) New Year, well)
Very interesting, thanks)
brain explosion)
Class, gorgeous article turned out !!! What else remains to be done on the morning of January 1, how to contemplate the three-story formulas and calculations.
Happy new year dear friends!!! And this kind of article, Yevtifeyev will really check it out))) LOOOOOYS
Arkasha, you are a monster!
The article is super, only there are SO many formulas that they merge on the first of January
Happy New Year to you !!!!!!!!!
Thanks! Lots of fun! I just looked in, but ... super! For photography, this is hardly necessary, but for techies - an orgasm! Thanks! By the way, why did you prefer algebraic analysis? In my opinion the geometric (homothetic way) is easier. But this is for a moment.
In general, this is an easy way to check how many punched fans of the photo and this site are in general and how many of them are techies, and how many non-techies.
RESPECT !!!
I am often asked from what distance it will be necessary to shoot a particular object. Who cares, it will not be difficult for him to multiply two numbers and divide by the third. Yes, it was possible to calculate the distance with the help of such triangles 2 times faster, but the angles would still have to be calculated through trigonometry, but if I started by searching for angles, I also calculated the distance through the angles.
I consider it very important that you drew attention to the fact that the angle is taken diagonal !!! it actually looks like a mockery. Well, at least somewhere it would have been written. And this site has - one more plus (huge) in its favor. I think it is not necessary to calculate the distance to the object for shooting, but then it is interesting to analyze (landscape: knowing the approximate distance to the mountain, for example, you can calculate its approximate height, or vice versa. Portrait: you can find out the approximate height of a person ... etc.) Great !!!
You, dear Arkady confidently bring this site to a leading position.
The article is extremely interesting.
Nonsense. "I think it is not necessary to calculate the distance to the object" - write you. How do you then determine the height of your mountain by the formula))? And why do you need “the approximate height of a person”)))?
It seems that you, dear, 0 not only in photography))) Well, nothing, brace yourself ... just not to constipation. And playing with distance is for fun, just for fun, like all photography is for me. And so the distance to the object is not considered necessary to calculate, as you are (read your post). It's just that this elegant formula can be used in many ways, which I wrote about. But you can read to understand, or you can read to criticize.
The first of January is categorically not perceived! But for trying to plant a reasonable thank you.
Wow! Super! Dap here numbers and squiggles)
But at least kill, I can’t imagine how to put it into practice. That is, if I need to take someone’s portrait, I first sit down for the formulas, consider it as a column, corner and diagonal, then measure the distance to the subject with a tape measure, put a cross there, get up on this cross and take a frame. So chtoli? Or is it for photographers who have a camera without a viewfinder?
Sorry for this post, just FIRST today! Happy New Year! Peace and goodness!
tight with you with the understanding why these formulas are, tight however.
Those. if you need to know the distance to the model with a bosom portrait, I have to measure the model with a tape measure from the top of the navel to substitute this value in the formula? In my opinion, there is an obvious bust. For example, it will not be easier for me if I know this distance. I’ll leave me or myself until what is needed fits into the frame. Besides, you won’t have to carry a tape measure and calculator with you.)))) The mood is great, but Arkady raised it even more!)))) Happy New Year!
I am very often asked from what distance it will be necessary to shoot a person in full growth with this or that lens. To anyone interested, it will not be difficult for him to multiply two numbers and divide by a third to find out approximately. So the same model (height 180 cm) on an 85 and a cropped mirror will have to be shot in full growth from 7 meters with a vertical orientation of the camera. For those who will ask such questions, this note was created. Also, in few places I have come across information that the viewing angle is taken from the lens parameters to the maximum - for the diagonal, but it is of no use for real work :)
By the way, having the vertical and horizontal viewing angles of the lens, we can multiply these values by 17 and get the viewing angles in “thousandths” (1 degree = 17 thousandths). For example, for fifty dollars on FF horizontally 39.59 degreesX17 = 673 thousandths, vertical 26.99X17 = 459 thousandths. Thus, we can determine the width of the field of view horizontally (673m / 1000m, 67.3m / 100m, 6.73m / 10m, 3.36m / 5m, 1.7m / 2.5m, 0.85m / 1.25m 0.67m / 1m, etc.). ) and vertically (459m / 100m, 45.9m / 100m, 4.59m / 10m, 2.3m / 5m, 1.15m / 2.5m, 0.58m / 1.25m 0.46m / 1m, etc.)
You shouldn't look so sarcastically. For example, BEFORE buying a camera, I was wondering what focal length I could take in a confined space, for example, in an apartment. Also, BEFORE buying a telephoto lens, it is interesting to calculate from what distance I can take pictures of sports events when there is no way to come closer or move further away. For example sailing - photographing a yacht with a 12-meter mast from the shore. It will be sad to buy a lens and understand that the FR is not enough or, on the contrary, is too large. And there is no rental in my city.
Again, nowhere besides this article did I come across the mention that the viewing angle from the lens parameters is taken as maximum - for the diagonal
Arkady, thanks for the necessary information and for your attitude to the matter.
Arkady, do not pay attention to indignation. Anyone who needs this information will draw what is needed from it. HAPPY NEW YEAR! Let the plan come true. Forces you to such a difficult job
Interesting article!
Gives answers to the question why cameras with a large matrix are preferable:
Shorter distances are needed for shooting (focus is better, studio is smaller, in nature there is less distortion from air masses at large distances).
...
thank you
Happy New Year, Arkady!
The previous author wrote my thoughts. You are a good photographer. But a person who wants to step on this path, after reading your article, will not step on it - he will be frightened (90% of people, especially the current ones, do not understand mathematics at all (I am a school teacher), and you give them formulas. way, the photo will not come
Why should the country fearful uneducated photographers :)
jva of tea for this photographer!
:)) And I like the calculations. In general, the idea of the geometric world became much more interesting after acquaintance with the concepts of “fractal geometry of nature”. The technical and geometric component of photography must be present and must work. Many people conduct commercial photography (wedding for example) in general in green modes and in Jpeg, not even knowing exactly where the camera focuses.
The previous one meant this:
Lex
01.01.2014/08/55 at XNUMX:XNUMX Reply
You need to rest Arkady)
damn what people are trying Arkady simplified everything, nowhere is easier !!!
Thank you so much for your interesting, useful, work !!!
The legacy of the statute and the next one was eaten and a lot of things, Axel Adams bced him to the grave!
Mr. Shapoval the statistics are not very bad, "the work might be ok, but the reporting is too late!"
Couple with joy Your stats, Chestita Nova Godina!
Milen Ivanov
PPC. buying a camera, I will also buy a calculator with trigonometric functions ...> _
i used google calculator :)
I hope that Nikon's marketers won't read this post :) otherwise a camera with a built-in f-lom will come out. It is necessary to “lure” something other than cheating MP XD (The post is humorous)
Arkady :) Great article and the site as a whole :) it's time to give a prize for the site;)
I am entirely in solidarity, having found the site once (about a year and a half ago) - it settled forever in the list of pinned tabs :)
Thank you, Arkady for your efforts! For an accessible, understandable, easy manner of presentation - which gives you not only a professional of photography, but as a cultured, educated person!
Thanks to your publications, I’m learning to photograph, and not pursuing the technical scrupulousness of photographs.
Merry Christmas and Happy New Year, Health to you and your loved ones :)
All the above calculations will be correct if the aspect ratio of the matrix and the resulting frame are the same. Those. having a 36x24 or 24x16 matrix for the crop and shooting 2: 3 - all calculations are correct. If at the output we have a 3: 4 or 1: 1 frame, then in fact we reduce the size of the matrix participating in the formation of the frame. And those who like to count need to make an amendment. Or vice versa - whoever shoots in 4/3 format - there is an 18x13.5 matrix (aspect ratio 4: 3). If you want a 3: 2 frame, then you need to read 18mm and 12mm. Arkady, correct me, please, if I calculated incorrectly.
Those who wish to count under their sensor can easily do this, because it will be enough to take others w, h. In the formulas, there is virtually no reference to the aspect ratio or crop factor, but only to the linear dimensions of the sensor.
As for the practical application - before reporting, for example, a wedding in a church, when you come to the place, you can estimate the physical dimensions of the room and, depending on the required creative tasks, select the appropriate optics. Of course, many will say that weddings are filmed by quite experienced photographers, who practically know what to shoot. But as they say, practice without theory is blind, and theory without practice is stupid. All creative successes. Respect Arkady for work and fresh thoughts))
When attending a wedding in a church, no one in their right mind would calculate the physical dimensions of the room. Simply take out the EXISTING suitable lens from your backpack and start shooting. Because if a photographer suddenly calculates that he should have a 20mm lens, but there are 24 in his backpack, he will still take out 24 and no amount of calculations will change this.
Arkady, thanks for the work done. I am sure your work will be in demand by many (not all, but by many, for very many did not learn mathematics at XD). A separate praise was awarded to the ease of perception of the material. And you can also take your work as a basis, for example, to write a calculator for a mobile platform (IF anyone needs it). Thank you again for your work!
Arkady, a really gorgeous site. Thank you for your work .. And the article is straight to the point. Recently presented Jupiter 37A .. I thought how to calculate the distance for the portrait .. At least for orientation on the ground ..
Thank you and good luck and creative inspiration.
Arkady, hello!
A little confused in the formulas, explain why the vertical angle is greater than the horizontal? At what position of the camera are these calculations? Or I just misunderstood something.
Look at an example of a photo with a robot.
Good afternoon everyone! I somehow calculated the relationship between the DF and the distance to the object (L) and the width of the resulting panorama (S) for popular DFs. It turned out for 35mm S approx. = 0,7L, for 50mm - 0,5L, 105mm - 0,3L, 200mm - 0,13L. For the crop. You can figure out what will fit into the frame with this fix (FR), although the distance, of course, must be able to evaluate by eye.