Lens Magnification Calculator

Background.

Magnification is the number that actually matters in close-up photography. Not the focal length, not the minimum focus distance printed on the barrel — the ratio between how big something is in life and how big its image is on the sensor. This calculator gives you that ratio three ways, and then tells you the things that follow from it: how far you have to be, how much of the subject fills the frame, what the aperture really behaves like, and how much light you have quietly lost.

Pick your route in. If you know how close you can physically get — a shy insect, a display case, a lens hood that keeps casting a shadow — start from the working distance. If you know how big the subject is and it has to fill the frame, start from the subject width. If you already own a set of extension tubes and want to know what they buy you, start there. All three routes converge on the same geometry.

Two of the outputs are the ones people come here for. The first is the reproduction ratio in the notation lenses are sold in: 1:1 for life size, 1:2 for half, 2:1 for twice. The second is the effective f-number, and it is the one that catches people out. As a lens focuses closer it has to move further from the sensor, which spreads the same cone of light over a longer throw, so the aperture stops behaving like the number engraved on the ring. At 1:1 it behaves like two stops smaller: your f/8 is really f/16. Through-the-lens metering absorbs this silently, which is why so many photographers never notice — until they use manual flash, a studio strobe or a handheld meter, and everything comes out two stops dark.

That same effective aperture is also why macro images soften sooner than expected. Diffraction depends on the effective f-number, not the marked one, so an f/11 setting at 1:1 is diffracting like f/22 and the whole frame goes soft while the depth of field you were chasing barely improves. Combined with the fact that depth of field at high magnification is measured in millimetres, this is the reason focus stacking became standard practice rather than an exotic technique.

The working distance output tends to be the surprise. It is u = f(1 + m)/m, which collapses fast: a 100 mm lens at 1:1 works at 200 mm from the front principal plane, and a 50 mm lens at 1:1 works at 100 mm — close enough that the lens itself shades the subject. That is the whole reason 90 mm, 100 mm and 105 mm macro lenses dominate the category and why 180 mm and 200 mm macros exist for insects.

One honest limit. Everything here is a thin-lens model with a symmetric pupil, and real macro lenses are neither. Fujifilm's XF80mm Macro reaches 1:1 at a published 25 cm minimum focus distance while this model predicts 32 cm from sensor to subject, because internally-focusing lenses shorten their focal length as they focus closer. Treat the geometry as a planning figure accurate to a few centimetres, and the ratios and light losses as reliable.

Below the widget you will find the derivation, three worked examples computed by hand, how the extension-tube figure compares with Canon's own published ranges, and why magnification is a lens property while subject coverage is a sensor one.

What is lens magnification calculator?

Lens magnification, also called the reproduction ratio or the imaging scale, is the transverse magnification m = v/u: the size of a subject's image on the sensor divided by its real size. A ratio of 1:1 means a 36 mm-wide object exactly spans a 36 mm-wide full-frame sensor. From the thin-lens equation 1/f = 1/u + 1/v, three equivalent expressions follow: m = f/(u − f) from a working distance, m = sensor width ÷ subject width from framing, and m = e/f for an extension tube of length e added to a lens focused at infinity. The same equation gives the geometry back: u = f(1 + m)/m and v = f(1 + m). Two photometric consequences follow. First, the effective f-number is N(1 + m/p), where p is the pupil magnification; taking p = 1 for a symmetric lens, N_eff = N(1 + m), so light loss is 2·log₂(1 + m) stops — exactly two stops at 1:1. Second, because diffraction scales with the effective f-number, close-up images diffract at a smaller aperture than the marked one. Note carefully what magnification does and does not depend on. It is a property of the lens and the distance, not of the sensor: a 100 mm lens at 500 mm gives m = 0.25 on every camera ever made. What the sensor changes is how much subject that magnification puts across the frame, which is why a Micro Four Thirds camera at 1:1 fills its frame with a 17.3 mm object while full frame needs a 36 mm one — and why "equivalent magnification" figures quoted by small-format manufacturers are framing claims, not optical ones.

How to use this calculator.

1. 01Choose your starting point. Working distance is the field constraint, subject width is the framing constraint, and extension tube is the gear constraint. They all lead to the same geometry.
2. 02Enter the focal length engraved on the lens. It is used in every mode — directly for extension tubes, and to convert magnification into working distance in the other two.
3. 03Enter the f-number you intend to shoot at. Close up this is not the aperture the light behaves like, and the effective f-number output exists precisely to tell you the difference.
4. 04In working-distance mode, enter the lens-to-subject distance in millimetres. Measure from the front of the lens if you must, but remember the model measures from the front principal plane inside it, so the real clearance in front of the glass is always less than the figure you enter.
5. 05In subject-size mode, enter the real width of the thing that has to fill the frame. A honeybee is about 12 mm, a postage stamp about 22 mm, a credit card 86 mm.
6. 06In extension-tube mode, enter the tube length. The result is the magnification with the lens focused at infinity — racking the lens to its own minimum focus adds more on top, which is why manufacturers publish a range.
7. 07Check the effective f-number before you set a flash or a handheld meter. Through-the-lens metering already compensates; anything metered outside the lens does not, and the stops-lost figure is what you add.
8. 08Use the effective f-number to decide when to stop stopping down. Once it passes about f/16 on full frame the whole frame is diffraction-limited, and further stopping down costs more sharpness than the extra depth of field returns. That is the point at which focus stacking wins.

The formula.

Everything starts from the thin lens, 1/f = 1/u + 1/v, with the transverse magnification m = v/u.

Solving the pair for u and v in terms of m gives the two geometry outputs:

u = f (1 + m) / m v = f (1 + m)

and rearranging the first gives the working-distance route into magnification:

m = f / (u − f)

The framing route is definitional: if a subject of width S spans a sensor of width w, then m = w/S. The extension-tube route follows from v = f + e when a lens focused at infinity is pushed e millimetres further out, so m = v/u = e/f.

The two subject-coverage results are then trivial: S = w/m, and the reproduction ratio is just m written as 1:(1/m) or m:1.

The photometric part is where the useful surprise lives. The f-number is defined at infinity focus as focal length ÷ entrance pupil diameter. When the lens is extended to v = f(1 + m), the same cone of light is thrown over a longer distance, and the illuminance at the sensor falls by (1 + m)². The aperture therefore behaves as though it were

N_eff = N (1 + m)

and the light lost is 2·log₂(1 + m) stops. At m = 0.25 that is 0.64 stops. At m = 0.5 it is 1.17 stops. At m = 1 it is exactly 2 stops. At m = 5, the magnification of a Canon MP-E-class lens at full extension, it is 5.17 stops — the reason such lenses are essentially flash-only tools.

The general form is N_eff = N(1 + m/p), where p is the pupil magnification, the ratio of exit to entrance pupil diameter. This page uses p = 1, and says so, because p is not published for any consumer lens. For a true symmetric macro lens p ≈ 1 and the approximation is excellent. For a strongly retrofocus design p > 1 and the real loss is a little smaller than shown; for a telephoto design p < 1 and it is a little larger.

Two consequences worth carrying away. First, diffraction follows the effective f-number, so an f/11 setting at 1:1 diffracts like f/22 — the whole frame softens while the depth of field you were buying barely moves. Second, depth of field at a fixed magnification is very nearly independent of focal length: Zeiss put it as "The depth of field (almost) does not depend on the focal length at all but rather on the imaging scale." A 50 mm and a 100 mm macro at the same reproduction ratio and the same f-number give you the same depth. What differs is the working distance, the perspective, and how blurred the distant background becomes.

Finally, the model's boundary. Real macro lenses are not thin lenses and most of them focus internally, which shortens their focal length as they focus closer. Fujifilm's XF80mm Macro is published as reaching 1x with a minimum focus distance of 25 cm; this model at m = 1 with f = 80 mm gives u = v = 160 mm, so 320 mm from subject to sensor. The 7 cm discrepancy is the model telling you honestly where it stops. The magnification, the coverage and the light loss remain right; the distances are planning figures.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Nasse, H. H. (2010). 'Depth of Field and Bokeh.' Carl Zeiss Camera Lens Division. Source for the central close-up result quoted on this page: 'The depth of field (almost) does not depend on the focal length at all but rather on the imaging scale', with the entrance-pupil reasoning behind it — 'A focal length that is twice as long creates an image of the same size from an approximately doubled distance, and with the same f-number its entrance pupil diameter is twice as large.'
2. [2]FUJIFILM Corporation. FUJINON XF80mmF2.8 R LM OIS WR Macro Specifications. Lists 'Focal length f=80mm (122mm in 35mm format equivalent)', 'Maximum Magnification 1x' and 'Minimum Focus Distance 25cm – ∞' — the real-lens figures against which this page states the thin-lens model's 32 cm prediction and explains the difference.
3. [3]Canon Inc. EOS R6 Product Manual, Specifications — Image Sensor. Gives the full-frame sensor size as 'Approx. 35.9×23.9 mm', the measured dimension behind the nominal 36 × 24 mm frame used for the subject-coverage output.
4. [4]Nikon Corporation. D7500 Online Manual, Technical Notes — Specifications. Gives the Nikon DX imaging area as '23.5 × 15.7 mm CMOS sensor', the width behind the 94 mm subject-coverage figure quoted in the crop-sensor FAQ.
5. [5]Canon Inc. EOS R7 Product Manual, Specifications. Gives the Canon APS-C sensor as 'Approx. 22.3 × 14.8 mm'.
6. [6]OM Digital Solutions. OM SYSTEM OM-1 Mark II Specifications. Lists the imaging area as 'Aspect ratio & area 4:3 / 17.3 x 13.0 mm', the width behind the 69 mm subject-coverage figure quoted for Micro Four Thirds.
7. [7]FUJIFILM Corporation. GFX100 II Specifications. Lists the image sensor as '43.8mm×32.9mm', the dimensions used for the medium-format preset.
8. [8]Ray, S. F. (2002). Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging, 3rd ed. Focal Press. Standard reference for the effective-aperture relation N_eff = N(1 + m/p), for pupil magnification p and its effect on retrofocus and telephoto designs, and for the exposure-increase factor (1 + m)² at close focus.