What the length-to-width ratio is
The length-to-width ratio describes the outline of a fancy-shaped diamond seen face up: how much longer it is than it is wide. GIA’s oval buying guide gives the definition plainly: the ratio is calculated by dividing the diamond’s length by its width. It is written as a figure followed by ":1", so an oval of 8.10 × 5.60 mm has a ratio of 8.10 ÷ 5.60 = 1.45:1.
A ratio of 1.00:1 means the stone is as wide as it is long. Round brilliants, and squares such as most princess and Asscher cuts, sit at or very close to it. The further the ratio rises above 1, the longer and narrower the outline.
Where the measurements come from
A grading report lists a fancy shape’s measurements as length × width × depth, in millimetres. The ratio uses the first two. The depth plays no part in it, which is the first thing to understand about what the ratio can and cannot tell you: two ovals with the same ratio can have very different depths, and so very different weights and face-up sizes for their carat weight.
If you are measuring a loose stone yourself with a caliper, length is the longest dimension of the outline and width the greatest dimension at right angles to it. The calculator takes the longer of the two figures as the length, so the order you enter them in does not change the result.
A worked example
An oval measuring 7.70 × 5.50 mm has a ratio of 7.70 ÷ 5.50 = 1.40:1, and is 40% longer than it is wide. A pear of 9.00 × 6.00 mm is 1.50:1. An emerald cut of 7.20 × 5.10 mm is 1.41:1. A cushion of 6.10 × 5.80 mm is 1.05:1, which is close to square.
Ratios are usually quoted to two decimal places. At that precision a difference of 0.05 mm in either dimension can move the second decimal, so a ratio worked out from rounded figures may differ slightly from one printed by a seller.
Why this tool names no "ideal" ratio
Lists of the "ideal" ratio for each shape are everywhere, and they are not a standard. They are seller conventions, and they disagree. Whether a longer or a rounder outline looks better is a matter of taste, and GIA’s own oval guide frames the choice that way: it describes how ovals in different ratio bands tend to look, from shorter and rounder below about 1.30:1 to long and narrow above 1.50:1, and notes that very long ovals are rarely seen because they are impractical to cut from diamond crystals. That is a description of appearance and availability, not a quality scale.
GIA does not grade a fancy shape’s cut from its ratio. A ratio says nothing about how the stone was cut, how bright it is, or whether it shows a dark "bow-tie" across its centre, which GIA’s guide notes can vary even between ovals in the same ratio range. Those are things to see in the stone or in a video of it, not to infer from a number.
Ratio and face-up size
Carat weight, outline and depth are linked, and a ratio alone does not tell you how large a stone will look. The diamond size calculator on this site works out face-up area from millimetre measurements, and the diamond shapes gallery draws each outline to scale at the same carat weight, so the effect of shape on face-up size can be seen rather than assumed. Neither, like this page, puts a price on a stone.