Strokes and letters set the scaling limit
When a logo shrinks, the thinnest stroke and the smallest letter hit their limit long before the overall width does. Once a stroke fills in on press or the lettering closes up, there is no room left to go smaller. Enter the original stroke and letter height with the limits you must keep and you get the smallest scale that satisfies both, plus the width at that scale.
How it is calculated
Stroke ratio = the stroke you must keep divided by the original stroke. Letter ratio = the letter height you must keep divided by the original letter height. The larger of the two is the smallest usable scale. It is rounded up for safety and the width follows the same direction. Millimetres and inches convert at 1 in = 25.4 mm, and a DPI value converts the same figures into px.
Limits
The stroke and letter limits you must keep depend on the printing method, the stock and the screen density, and no official standard exists, so this tool asks for them instead of proposing values. Tight wordmark spacing closing up, falling color contrast and antialiasing are not modeled, so proof the result at the scale it reports.
Frequently Asked Questions
There is no single official figure because it depends on the printing method, the stock and ink spread. Use the minimum stroke your printer quotes, or the thickness that lands on 1 px on screen.
No. This tool works backwards to the scaling limit. Listing the sizes to test is the job of the logo scale test size calculator instead.
If either the stroke or the lettering disappears first, the logo stops reading. The larger of the two ratios is the smallest scale that satisfies both conditions at once.