Bits, bytes, and the square
An image file has one honest size before compression, and it comes from four numbers: page width, page height, resolution and bit depth. Multiply the inches by the dpi to get pixels on each side, multiply those together for the pixel count, multiply by bits per pixel, divide by eight for bytes. That is the whole derivation, and the division by eight is where half the confusion in this subject lives, because bit depth is quoted in bits and storage is sold in bytes.
The consequence people underestimate is the square. Resolution appears twice, once on each side of the page, so bytes go with the square of dpi. Going from 300 to 600 does not double the file, it quadruples it. An 8.5 by 11 page in 24 bit colour is 8.4 megapixels at 300 dpi and 33.7 megapixels at 600, which before compression is about 25.2 MB against about 101 MB.
| Resolution | Megapixels, 8.5 x 11 in | MB before compression, 24 bit | Times the 300 dpi figure |
|---|---|---|---|
| 200 dpi | 3.74 | 11.22 | 0.44 |
| 300 dpi | 8.42 | 25.25 | 1.00 |
| 400 dpi | 14.96 | 44.88 | 1.78 |
| 600 dpi | 33.66 | 100.98 | 4.00 |
Bit depth is the other multiplier and it is linear rather than squared. The same page bitonal at one bit per pixel is a twenty-fourth of the colour figure before compression. That is a large lever, and it is also the one where the decision has nothing to do with storage, which is the next section.
The settings are not a storage decision
This calculator will happily tell you that bitonal at 200 dpi is cheap, and that is not an argument for scanning anything that way. What resolution, what bit depth and what file format a particular collection should be captured at is a preservation judgement about the specific material — its condition, what is on it, what it will be used for, and whether anybody will ever be able to go back to the original. It belongs to a conservator or an archivist and there is published professional guidance on it. There is none here, deliberately.
What the arithmetic is good for is the reverse question. Once somebody has told you what the capture should be, this tells you what it costs in hours, in bytes and in the copies you have to keep, and it lets you see which of your assumptions the total is most sensitive to. Usually it is the compression ratio and not the resolution.
Compression is the widest unknown, so measure it
The uncompressed size is arithmetic and it is exact. What the file actually lands at is a property of the image, and for scanned paper it varies far more than people expect. A clean laser-printed page of text compresses enormously. A foxed, stained letter with pencil annotations and a photograph tipped in compresses hardly at all, because most of what is in it is noise, and noise is what compression cannot remove. Between those two the ratio can differ by five to one on the same settings.
The measurement is easy and there is no substitute for it. Scan twenty pages that look like the rest of the collection, at the settings you intend to use, and add up what they came to. Divide the uncompressed figure this page gives you by the average you got, and enter that. A number from your own material beats any default, and it is the input the total is most sensitive to.
The hours, and the part that is not scanning
Sheet-fed throughput sounds like the number that matters and it is usually the smaller half. Preparation is removing staples and paper clips, unfolding, flattening things that have been folded for forty years, separating carbon sets, and sorting what has to be scanned flat because it will not go through a feeder. On old files that can take longer than the scanning, and it does not speed up with a better scanner.
Rescans are the third component and they behave differently from the other two: they cost time and they cost no storage, because the bad image is replaced rather than kept. The calculator handles them that way, which is why the page count through the scanner is higher than the page count in the output.
The number worth carrying away is minutes per page all in. It is the figure that makes a quote comparable, it is the figure that tells you whether a project is a fortnight or a year, and it is almost always two or three times what the scanner throughput alone suggests.
Storage conventions, and where the copies go
Drives are sold in decimal units and reported in binary ones. A gigabyte as a manufacturer means it is 1,000,000,000 bytes; a gibibyte, which is what most operating systems show while labelling it GB, is 1,073,741,824. The gap is about seven percent at that scale and grows to about nine percent at terabyte scale. Both are shown in the output so a plan made against one does not get checked against the other. The data size converter handles the units on their own.
Copies multiply everything, which is the last place a plan goes wrong. Deciding on three copies is not a storage decision made once; it is a multiplier applied to every future growth in the collection, and it lands on the backup window and the retention policy too. The backup retention calculator shows what keeping old restore points costs on top, and the RAID capacity calculator shows how much of a set of drives is actually usable. For the paper side of the same project, the records carton take-off counts what the originals occupy once they go back in boxes.
Questions people ask
How big is a scanned page?
Before compression it is exact arithmetic: page area in square inches, times dpi squared, times bits per pixel, divided by eight. An 8.5 by 11 page at 300 dpi in 24 bit colour is 8.42 megapixels and 25.25 MB. After compression it depends entirely on what is on the page, which is why the compression ratio is a field you measure rather than a constant. Clean text compresses far harder than a stained, annotated original.
Why does doubling the dpi quadruple the file?
Because resolution applies to both dimensions. Doubling from 300 to 600 doubles the pixels across the page and doubles them down the page, and two times two is four. It is the same reason a photograph twice as wide and twice as tall has four times the area. This is the single most useful thing to know about scanning storage, because it means the difference between 300 and 600 dpi is not a detail — it is a factor of four on every copy and every backup for the life of the files.
What resolution should I scan at?
That is not a question this page will answer, and you should be suspicious of any calculator that does. Capture settings are a preservation decision about the specific material: what it is, what condition it is in, what is on it, what it will be used for and whether the original will survive to be scanned again. Conservators and archivists have professional guidance on it. Get the setting from somebody qualified to give it, then come back here to find out what it costs.
Why are the pages through the scanner more than the pages I keep?
Rescans. A page that comes out skewed, double-fed or cropped wrong has to go through again, and the second image replaces the first rather than joining it. So the rescan percentage adds to the time and adds nothing to the storage. Four percent is a plausible starting figure for reasonable material in good condition; fragile, folded or mixed-format originals run much higher, and that is worth measuring on a real batch before committing to a schedule.
Is a gigabyte 1,000 or 1,024 megabytes?
Both are in use and that is the problem. Storage manufacturers use decimal: 1 GB is 1,000,000,000 bytes. Most operating systems display binary quantities, where 1 GiB is 1,073,741,824 bytes, and many of them label it GB anyway. That is why a 1 TB drive shows as about 931. The calculator gives both figures for every total so that a plan made in one convention does not get checked in the other, which is a mismatch of about seven percent at gigabyte scale and about ten at terabyte scale.