Scale in artefact photography

Since the 1950s, archaeological handbooks have asked for a scale in every photograph, and a ruler or a scale bar laid beside the object has become the usual way to show size; before that, plates mostly stated the reduction, such as 1:4. It shows the size of the ruler. Whether it also shows the size of the object depends on things the picture does not say — and once the file has been resized for a web page or a report, even the ruler no longer tells the truth about pixels.

What a ruler beside the object tells you

A camera sees a nearer thing larger. How many millimetres one pixel covers depends on how far that part of the scene is from the lens, so a ruler gives the scale for its own plane: its upper surface, at its distance from the camera. Anything higher or lower than that surface is measured with a scale that is not its own.

A flat sherd lies almost in the ruler's plane, and the error is small. A brooch, a bead, a spindle whorl or a fragment of pottery standing on its edge does not.

1. CAMERA — d above the surface
2. THE TOP OF THE VENUS — h above; too large by h ÷ (d − h)
3. RULER — its scale holds for its own plane

How much it matters

The error is the ratio of the two distances. Measured with the scale of the surface the object lies on, a part of the object that is higher up comes out too large by:

What is measured	Above the surface	Lens at 500 mm	Lens at 1000 mm
Outline of a flat sherd	2 mm	+0.4 %	+0.2 %
Upper face of a brooch	10 mm	+2.0 %	+1.0 %
Top of a large bead	25 mm	+5.3 %	+2.6 %

Two things follow. Height matters more than people expect: five per cent is two millimetres on a forty-millimetre bead. And distance helps: photographing from twice as far, with a longer lens, roughly halves the error. Lenses built to remove it altogether — telecentric lenses — are used in industrial measurement and are rarely seen in museum photography.

The same holds the other way round. A ruler a few millimetres thick lies nearer the camera than the outline of a flat object, and makes the object measure slightly too small — about one per cent in a typical set-up.

Where to take the scale from

A measurement taken off a ruler is a measurement of the ruler. It tells you how long the ruler is, in the ruler's plane, at the ruler's distance from the lens. The measurement taken with a digital caliper is the one that holds for the object: across its longest side, read to a hundredth of a millimetre and entered with the picture.

PHOTARCH takes the scale in this order of preference:

Whichever it is, the file should say which. A scale with its method and its uncertainty can be judged; a bare number cannot.

Objects with height: what one photograph can measure

A plumb photograph measures an object's outline — its length and width as seen from above — and it measures it exactly in one plane only. It never shows thickness. That is not the weakness of one method: every field that measures from a single picture works to the same rule and states it. Forensic photography puts its scale — usually the L-shaped ABFO No. 2, whose three circles show whether the camera is square to it — in the plane of the evidence; the FADGI guidelines put their targets at the height of the page being imaged; the Portable Antiquities Scheme, which records archaeological finds, asks that scales "lie at the same level as the object's centre"; medical imaging records in the file how a calibration was made, and its standard says it holds only near the central ray, at the depth where it was made. Radiography has also measured what ignoring it costs: in planning hip surgery, a calibration marker at the wrong depth gave errors of 6.8 % on average and up to 26 %. For archaeological objects it has barely been measured: two small studies, neither peer-reviewed (Gantt 2002; Göldner 2022).

Where the outline lies

How the object rests decides how high its outline is above the surface:

1. LYING FLAT · AT THE SURFACE — coin Ø 20 × 2 mm: its top, 2 mm up
2. ROUNDED · HALF THE HEIGHT — ball Ø 25 mm: its middle, 12.5 mm up
3. STEEP-SIDED · AT THE TOP — cylinder Ø 40 × 25 mm: its top, 25 mm up
4. THE BOARD'S SCALE — holds here, at 0 mm

Off-centre, the error grows

Away from the middle of the frame a raised edge is also pushed outward — what aerial photography calls relief displacement. A steep-sided object 25 mm high, 100 mm from the middle, photographed from 500 mm, measures about 16 % too wide along the line to the middle, against 5.3 % in the middle. A 25 mm bead in the same place measures 4.7 % large, against 2.6 %. Lay the object in the middle of the frame.

1. CAMERA · 500 MM ABOVE — drawn to scale with the board and objects
2. OPTICAL AXIS — straight down through the middle of the frame
3. IN THE MIDDLE — 42.1 mm, 5.3 % too wide, along the line and across
4. 100 MM FROM THE MIDDLE — along the line: 46.3 mm, 15.8 %; across it: 42.1 mm, 5.3 %
5. PUSHED OUTWARD — the far top edge lands beyond the base

The caliper and the board measure different planes

The board gives the scale at its own surface, so a raised outline measures large, always in the same direction. The caliper, read across the longest side and matched to the same line in the picture, gives the scale in the plane of that outline: the plane that is compared. That is why the caliper comes first. With both, they check each other — the difference between the two scales gives the height of the outline, and a result outside the object's own height means it is tilted or the wrong line was measured.

1. THE CALIPER'S SCALE — the plane of her outline: 100.00 mm
2. THE BOARD'S SCALE — its surface: from 500 mm she measures 104.6 mm
3. THE DIFFERENCE — 500 × (1 − 100.00 ÷ 104.6) ≈ 22 mm, her outline's height

An error margin that can be stated

The international guide to measurement uncertainty, the GUM, says to correct a known error rather than widen the margin, and when the correction rests on something known only within a range, to correct to the middle of that range and add its spread. For an outline somewhere between the surface and the object's height H, photographed from D: correct to half the height, and add an uncertainty of H ÷ (√12 × D). Measured with the board's scale, a 25 mm bead at 500 mm comes out 2.6 % large; corrected, it carries a standard uncertainty of about 1.4 %, or 0.7 % once it is known to be round. Stated as a margin that holds about 95 times in 100 — two standard uncertainties, as the GUM recommends and as PHOTARCH shows it — that is ± 2.9 %.

Measure the object's depth — how high it stands as it lies — with the caliper, and record it. Without it no error margin can be given: the error grows with it, and a plumb photograph does not show it. The other figure is the distance, which can be rough — a distance a tenth wrong moves a 2.6 % correction by a quarter of a point. A lens's EXIF data is good enough for that, but not for the scale itself: no study has shown the focus distance it records to be accurate enough to set millimetres.

1. THE DEPTH · CALIPER — how high she stands as she lies: 47.67 mm
2. THE DISTANCE — board to lens: rough is enough

How far to stand back

To stay within 1 %	Camera at least	10 mm high	25 mm high
Scale at the surface, outline anywhere in the height	101 × the height	1.0 m	2.5 m
Corrected to half the height, or the caliper at mid-height	51 × the height	0.51 m	1.28 m

An object lying flat needs only 101 times its own thickness: 0.2 m for a 2 mm coin. A longer lens lets the camera stand further back for the same picture, which reduces the error but never removes it. A telecentric lens removes it, but one that covers a field of 31 × 21 cm is a metre long and weighs about 39 kg; none is known in use for museum objects.

What this means for comparison

Two objects photographed this way can be compared at true size when the difference between them is larger than both their margins together. An 8 mm bead beside a 70 mm figure: always. Two brooches a few per cent apart: only with the caliper on each, the thickness recorded and the margin stated.

What PHOTARCH records, and what is still calculated

Every exported picture says which plane its scale holds for — the board's surface, the outline as seen from above, or the ruler's plane — and how certain the scale is. Where the scale holds at the surface and the object's thickness and the camera's distance are given, the PHOTARCH app corrects the size to half the depth, as above, and the figure covers the height as well as the markers' fit or the caliper's reading; the file then names the object's middle height as its plane. Beside every size and measurement it shows the margin at about 95 %, and asks for the thickness or the distance when one is missing. These figures are calculated from the model on this page. PHOTARCH is testing the error on its own set-up with objects of known size — steel spheres, a stepped block, straight-sided cylinders — at different heights, distances and places in the frame. The results will replace the calculated figures on this page with measured ones.

1. STEEL SPHERES — Ø 10, 20, 25.4, 40 and 50 mm
2. A STEPPED BLOCK — targets at 0, 5, 10, 25 and 50 mm up
3. STRAIGHT-SIDED CYLINDERS — Ø 40 × 10 and Ø 40 × 25 mm
4. PLACES IN THE FRAME — 0, 50, 100 and 150 mm from the middle

Why the scale belongs in the file

A scale bar burnt into the picture cannot be re-used or checked. Resizing the file — as every web gallery, report template and messaging app does — silently changes how many millimetres a pixel covers. And the resolution fields that TIFF and EXIF already have are read by software as print settings, not as a measurement of the object.

Medicine met the same problem with X-rays and solved it decades ago: the file says how large a pixel is, on which pixel grid, and how that was found, so that every viewer can show true size. Image Scale Metadata (ISM) asks the same three things of a photograph, in a handful of XMP fields: millimetres per pixel, the grid it applies to, how it was measured — and how certain it is. A reader can then draw a correct scale bar after the file has been resized or turned; a copy cropped to another shape is recognised, and its scale is not used.

ISM is an open format, independent of PHOTARCH: the specification is published under CC BY 4.0 and its reference libraries under MIT, so that any program can read and write it. PHOTARCH writes it into every exported picture of a measured object. More in the manual.

Old photographs with a ruler in them

A collection's older pictures need not be thrown away. The ISM viewer opens a picture in the browser, without sending it anywhere, and can write a scale into one that has a ruler in it: measure the ruler once, and the file carries its scale from then on. The viewer records how the scale was obtained, so a scale taken from a ruler says so, and nobody takes it for more than it is.

References · measuring objects with height

• standardANSI/ASB (2021). Best Practice Recommendation 050: Photographic documentation of footwear and tire impression evidence, 1st ed. AAFS Standards Board. A revision of SWGTREAD's guide of 2006.An L-shaped scale on the same plane as the bottom of the impression, the camera's focal plane parallel to it.
• standardHyzer, W. G. & Krauss, T. C. (1988). The bite mark standard reference scale — ABFO No. 2. J Forensic Sci 33(2), 498–506. Specification as quoted by Ferrucci et al.An L-shaped scale; three circles 80 mm apart show whether the camera is square to it. It defines a plane and says nothing of height.
• guidanceSWGDE (2019). General photography guidelines for the documentation of evidence items in the laboratory, 18-P-001.The scale in the same plane as the item.
• practicePortable Antiquities Scheme. How to take a photograph. British Museum (accessed 4 October 2026)."Ensure that scales are straight and lie at the same level as the object's centre."
• standardFADGI (2023). Technical Guidelines for Digitizing Cultural Heritage Materials, 3rd ed.Targets at the height of the imaged plane; reproduction-scale tolerances of about ±1–3 %.
• standardNEMA. DICOM PS3.3 §10.7, Basic Pixel Spacing Calibration.A calibrated spacing holds near the central ray, at the depth of the calibration.
• empiricalClunie, D. A. (2007). On the matter of size and distance measurements in digital mammography. IHE white paper.The same depth error in radiography, worked through.
• empiricalSinclair, V. F. et al. (2014). Assessment of accuracy of marker ball placement in pre-operative templating for total hip arthroplasty. J Arthroplasty 29(8), 1658–1660.Mean 6.8 %, up to 26 %, over 112 radiographs.
• empiricalBoese, C. K. et al. (2015). Calibration markers for digital templating in total hip arthroplasty. PLOS ONE 10(7).Moving a marker 100–175 mm sideways adds 1–2 %.
• empiricalCardini, A. (2014). Missing the third dimension in geometric morphometrics. Hystrix 25(2), 73–81.Size from lateral photographs about 1.7 % too large, the scale lying behind the measured plane.
• empiricalRayeed, S. M. et al. (2026). A continental-scale dataset of ground beetles with validated morphological trait measurements. arXiv:2601.10687.Scale bars at the specimens' height; image and caliper agree to about 0.15 mm.
• empiricalFerrucci, M. et al. (2013). Dimensional review of scales for forensic photography. NIST / NIJ.ABFO No. 2 scales from four makers: every length scale met the ±1 % specification, but the circles were often off size and more than half the rulers were not square within two minutes of arc.
• empiricalGantt, E. M. (2002). The Claude C. and A. Lynn Coffin Lindenmeier Collection. MA thesis, Colorado State University, pp. 77–79.Caliper, photograph and scan means for Folsom stone tools differ by up to 7.9 %.
• empiricalGöldner, D. (2022). ArchaeoScale protocol: inserting digital scale bars into scientific images. Zenodo.A scale bar 10 cm off the plane: −24 % and +19 %.
• standardJCGM 100:2008. Guide to the expression of uncertainty in measurement (GUM), §3.2.4, §4.3.7, §F.2.4.5.Correct a known error; a correction known only within a range is made to its middle, with its spread as uncertainty.
• methodUS Army Corps of Engineers (1993). EM 1110-1-1000, Photogrammetric Mapping, ch. 10.Relief displacement: a raised point off-centre is pushed outward.
• standardCIPA DC-008-2026. Exif 3.1, English translation, January 2026.The subject distance is defined only as the distance to the subject, in metres (§4.6.6.7.18): no reference point, no accuracy.