# Macro Calculators

by Johan J Ingles-Le Nobel
Last updated September 09, 2017

Tools and calculators for macro photography at extreme-macro.co.uk. This page is a listing of all the tools as and when I add new ones to the website. Please check back periodically, thank you.

I get more questions about these calculators than the rest of the site put together, so here are a few points to consider! Please read before mailing, thank you.

• All these calculators can only ever be approximations, for reasons explained better below. For magnification, ultimately the best way to work out your magnification is just to photograph a ruler: divide sensor size, in mm, by how many mm actually show in your picture and that'll be your actual magnification.
• If regular magnification is known, there is no formula to work out magnification of that lens when that lens is reversed
• Magnification is not related to sensor size (APS/FF/etc). Magnification is ratio between real object size and image size at the sensor plane. The sensor size just determines how much of the image you capture, not the size of it. Magnification is independent of field of view - it only expresses the relationship of the object and the image, and has nothing to do with how much of the object is captured by a particular medium. The same image, captured on 8 x 10 film would also have the same magnification. The film will include more of the scene, but its magnification would remain the same. Where sensor type is a factor I have included them as an option.
• Do not use APSC equivalent lens mm sizes in the equations. They're a complete nonsense; a marketing thing of the devil to be avoided at all costs.
• The magnification formula: 1/S1 + 1/S2 = 1/F. This is a formula for a thin lens, but still works, although for complex zoom and/or inner focus lenses it is less precise. A thin lens has its optical centre at a point; this is behind the difficulty with using it as an exact tool for all lenses as an optical centre is not always known, obvious or even calculable. If extension = focal length (S2= 2*F) S1 will also be 2*F, and magnification will be 1:1. With a 55mm lens this requires 55mm extension, and the lens will sit in the middle between object and sensor, with a total of 220mm from object to sensor (S1+S2, S1=S2=110mm). So 220mm is the shortest possible distance, going beyond 1:1 will increase the object to sensor distance again, and then it will be a good idea to turn the lens around, as it works best with the shortest distance on the bayonet side. Ie reverse a >50mm lens for magnifications larger than 1:1. It just works better.
• If you want the very best possible results, measure, don't use theoretical formulas that only apply to certain specific lens types.

... whilst it is possible to obtain very close to accurate numbers, online tools and calculators for macro photography have to be somewhat approximations because the characteristics of lenses differ during use, and the data that is required is not made available by lens makers. On top of that, focal lengths do not always stay constant, focal lengths differ slightly from what the manufacturers tell us and lenses do not always follow 'thin lens' formulas.

Some of the tools are perfectly accurate and straightforward such as the stacked lens magnification calculator, however others such as an extension tube magnification calculator rely upon knowledge of the lens macro ratio and its optical centre. Since these vary for different lenses - ie they vary as you zoom - it means that the data based just on its focal length must be slightly inaccurate. However calculators do get you in the right area, enough to start using your own observations and measurements from that point on.

## Focus Stack Step Size Macro Calculator

The focus step calculator calculates "safe" step sizes based on 2cn(m+1)/(m*m), where c is the "circle of confusion", n is the nominal f-number, and m is the magnification. CoC values are .019(APS), .023(APSC), .029(FF) .015(4/3), but the calculator also adds a 25% safety margin to ensure some degree of overlap. Note, since the Circle of Confusion is a measure of acceptably sharp, the CoC should also factor in a person's eyesight as well, and therefore a fixed CoC value in a calculator must always be slightly arbitrary - but nevertheless it is the best measure we have. I added effective aperture output to remind ourselves of the danger of using too small an f/stop - ideally adjust your f/stop to stay below (ie wider than) f/22 or thereabouts, otherwise you'll be in diffraction softening territory. This calculates step size - the total depth of focus, not a single-sided sided depth of focus/maximum deviation from perfect focus.

## Na To F/Stop Macro Calculator

The NA calculator calculates the equivalent f/stop for an objective, adjusted for the magnification at which it is being used. Uses working f/stop = Magnification / (2*NA)) where NA is numerical aperture of the objective.

## Infinite Objective Focal Length Macro Calculator

The objective calculator calculates the focal length of an infinite objective. Uses Focal length = Tube length / magnification.

## Extension Tube Magnification Increase And Working Distance Macro Calculator

The extension tube calculator calculates new magnification, new closest focusing distance and effective f/stop when using tubes. Uses thin lens formula: 1/f = 1/d + 1/s where f is the focal length of the lens, d is the object distance between object and lens, and s is the image distance between lens and sensor, and approximates f/stop change based on a simpler equation that does not use an exit pupil calculation. Closest focusing distance is distance from sensor to subject. Things that work against us with a calculator of this type is that our lenses are rarely single element, and its focal length may differ depending where it is focused, so the figures are best treated as ballpark.

## Bellows Magnification Increase And Working Distance Macro Calculator

The bellows calculator calculates new magnification, new closest focusing distance and effective f/stop when using bellows. Uses thin lens formula: 1/f = 1/d + 1/s where f is the focal length of the lens, d is the object distance between object and lens, and s is the image distance between lens and sensor, and approximates f/stop change based on a simpler equation that does not use an exit pupil calculation. Closest focusing distance is distance from sensor to subject. Things that work against us with a calculator of this type is that our lenses are rarely single element, and its focal length may differ depending where it is focused, so the figures are best treated as ballpark.

## Reverse Lens Macro Calculator

The reverse lens calculator calculates new magnification, new closest focusing distance and effective f/stop with reverse lens setup on extension. Uses thin lens formula: 1/f = 1/d + 1/s where f is the focal length of the lens, d is the object distance between object and lens, and s is the image distance between lens and sensor, and approximates f/stop change based on a simpler equation that does not use an exit pupil calculation. Closest focusing distance is distance from sensor to subject. Things that work against us with a calculator of this type is that our lenses are rarely single element, and its focal length may differ depending where it is focused, so the figures are best treated as ballpark.

The Raynox calculator Calculates the macro magnification and working distance with various Raynox adapters, including a stacked 150/250 combo. Uses 1/newfl [new focal length of the combined two] = 1/fm + 1/fc, where fm and fc are respectively the main lens' and closeup filter's focal lengths. Focal length = 1000/diopters. by "depending on where you focus" I am referring to whether the lens is focused at its minimum focus point or whether it is at infinity.

## Closeup Lens Macro Calculator

The closeup lens calculator Calculates the new macro magnification, new focal length when adding a closeup length, and its and its focal length as tube lens. Uses 1/newfl [new focal length of the combined two] = 1/fm + 1/fc, where f1 and f2 are respectively the main lens' and closeup filter's focal lengths. Focal length = 1000/diopters.

## Stacked Lens Magnification Macro Calculator

The stacked lens calculator Calculates magnification of two lenses stacked for macro. Uses standard primary/secondary equation.

Article: Macro Calculators
Article Rating:     5/5 (8)
Don Burton says...
Dear Johan
Thank you so very much for taking the time and sharing your knowledge!

This document is melting my brain, but I have the time and desire to master micro photography!

Be well
Don
4th September 2018 4:22am
David says...
Johan, I utilize your step calculator all the time - it's a really wonderful tool you offer! I recently purchased a fuji GFX, and was wondering how I can calculate step distances with the larger sensor. I assume that the circle of confusion differs and, as such, so will the step distances. Do you have any recommendations?
10th February 2018 4:04pm
Bill P says...
Greetings, Johan and fellow visitors. Regarding the top bulleted point; "...ultimately the best way to work out your magnification is just to photograph a ruler: divide sensor size, in mm, by how many mm actually show in your picture and that'll be your actual magnification." How MANY mm?! That is funny. Using a Shinwa machinist steel rule with 0.5mm graduations, it would appear the width of an individual etch is roughly 1/16th the space between said marks, so 0.03125mm? This mark fills the entire FoV with room to spare! Using the "guessimator" calculators, it seems I'm in the 50-85:1 range. (1200mm + 100m tube + 14mm reversed) I've ordered a 0.01mm increment microscope stage micrometer slide online for \$10usd. That's incredible, that reverse lens macro can go that extreme, but it does pose the question: Is there any sub-millimeter household item standardized enough to act as a measurement scale?
16th July 2017 2:27pm
Daan says...
This remark made my day: "APSC equivalent lens sizes are a complete nonsense; a marketing thing of the devil to be avoided at all costs". Thanks for all the good work!
27th March 2017 9:32pm
Marisano James says...
Very useful information to bring together. Thanks. PS. I think that you must have confused the circle of confusion (CoC) for "APSC" with that of "APS" (Canon-only). Since the sensor size of APS is smaller than that of APSC, the CoC of a full frame camera is largest of all, and that of 4/3 is smallest of all, it then follows that the CoC of APS should be smaller than that of APS-C. Therefore, I think that the values of the two as currently written above should be interchanged. (That is, the value for the APS CoC should read 0.019, and that of APS-C should read 0.023.)
4th June 2016 7:10pm
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