How Datum calculates

Tire geometry

Everything is computed in millimetres and converted for display.

sidewall          = width × aspect ratio ÷ 100          (metric sizes)
sidewall          = (diameter − wheel diameter) ÷ 2         (inch sizes)
overall diameter  = wheel diameter × 25.4 + 2 × sidewall
circumference     = π × overall diameter
revolutions/mile  = 1,609,344 mm ÷ circumference

These are nominal dimensions taken from the size markings. A real tire’s diameter depends on the model, the tread depth, wear and inflation, so it can differ by a few tenths of an inch. If you have the maker’s figure, enter it under “Exact figures from the tire maker” and it replaces the calculated value.

Revolutions per mile are nominal too: they come from the calculated circumference. Makers publish a figure measured on a loaded, rolling tire, which is usually a few percent higher because the loaded tire rolls on a slightly smaller radius. Use the maker’s figure if you need it for gearing work. Both setups in a comparison use the same basis, so the percentage difference between them is unaffected.

Speedometer and gearing

ratio              = new diameter ÷ old diameter
true speed         = indicated speed × ratio
error (%)          = (ratio − 1) × 100
engine rpm change  = (1 ÷ ratio − 1) × 100     (same road speed, same gear)

This assumes the speedometer was accurate on the original tires, and that it takes its signal from the wheels, as it does on almost every modern vehicle.

The summary’s wording follows common rules of thumb: up to 1.5% is a close match, up to 3% is the guideline many tire shops use, up to 5% is noticeable, and beyond 5% is a large change. These are conventions, not standards, and your vehicle may tolerate more or less.

Wheel position

Positions are measured from the hub mounting face, which is where the wheel bolts on. The stamped wheel width is measured between the flanges, so the overall width is approximated as the stamped width plus one inch.

overall width       = wheel width + 1 in
backspacing         = overall width ÷ 2 + offset
inner lip distance  = backspacing                      (toward the vehicle)
outer lip distance  = overall width − backspacing        (toward the fender)
wheel centerline    = −offset from the hub face       (outward is positive)
track width change  = 2 × (offset A − offset B)

The one-inch allowance is the convention wheel makers’ calculators use. Wheel designs differ a little, so measure the wheel if the last few millimetres matter.

Tire width on the wheel

A tire’s published section width is measured on a specific measuring rim. On a wider wheel the tire spreads, and on a narrower wheel it pinches, by roughly 0.2 in (5 mm) for every half inch of wheel width.

width on wheel = section width + 0.4 × (wheel width − measuring rim width)

Tire makers publish a measuring rim for each size but not as a formula. Datum estimates it as 76% of the section width for metric sizes and 80% for inch sizes, rounded to the nearest half inch. It is an approximation and can be off by half an inch or more for some sizes. Each half inch of error moves the width estimate by about 5 mm, so treat the result as roughly ±5 mm or more for unusual sizes, which is why it is labelled an estimate. Enter a measured width to replace it.

The tool also warns when a wheel is more than 1.5 in wider or narrower than the estimated measuring rim, because tire makers usually approve a limited range of wheel widths. The approved range for your exact tire is in the maker’s data and takes priority.

Clearance

Datum never reports clearance from the size alone. If you enter your own measurements, it compares each tire’s widest point with them:

• Outboard room: the measured distance from the hub face to the fender edge, minus the tire’s outer extent.
• Inboard room: the measured distance from the hub face to the nearest inboard part, minus the tire’s inner extent.
• Gap above the tire: the measured gap, minus the increase in tire radius.

These checks use the tire’s widest point at axle height. They do not include steering lock, suspension travel, camber, body roll, the shape of the fender or the inside of the wheel, and they are only as good as the measurement.

What the drawings show

Widths, diameters, wheel width, offset and the positions of the lips and tire edges are drawn exactly from the numbers entered, at one shared scale. The curve of the tire’s sidewall and the wheel’s inner profile are simplified because they depend on the specific product, so do not read detail off them.

Checking the maths

The calculations are covered by automated tests, written with worked examples calculated by hand rather than by the code under test. For example, a 265/70R17 is 802.8 mm tall, a 285/70R17 is 830.8 mm tall (so an indicated 60 mph is 62.09 mph), and an 8.5 in wheel at offset +35 has 6.13 in of backspacing. The code is plain TypeScript with no external services, so the results are the same every time.

What this tool will not tell you

It will not say a tire or wheel fits a vehicle, that a combination is safe, or that a tire is approved for a wheel. Those depend on the specific vehicle and products. Use the results to ask better questions and to decide what to measure, then confirm with the tire and wheel makers or a good shop.