Line Ratio Game

About Line Ratio

Line Ratio gives you two straight lines and one question: how long is the shorter one compared with the longer one, in percent? If the short line is half as long, the answer is 50. If it is nearly as long, it is somewhere around 90. You answer with a slider, and the true value appears as a marker after you lock in.

On the first levels both lines are horizontal and stacked, which is the easiest case for the eye. On the later levels they stand side by side at different tilts, which forces you to compare lengths without a common baseline. At the top levels the shorter line often carries arrow-shaped fins at its ends, a trick from a famous optical illusion that makes lines look longer than they are.

How to play

1. Look at both lines and decide which one is shorter. Do not worry about the tilt.
2. Imagine laying the short line on top of the long one. How many copies of the short line would fit, or what fraction of the long line would it cover?
3. Drag the slider to the percentage. The slider runs from 5 to 100 percent.
4. Lock in. The correct ratio is shown on the slider track, and a score appears right away.

Two lines are shown. Drag the slider to the length of the shorter line as a percentage of the longer one.

How scoring works

The score is based on the absolute error in percentage points. You get 100 for a perfect answer and 0 when you are 26 points off on level 1 or 12 points off on level 10. At the top level, being 6 points away from the true ratio still gives you 50 points.

The timer starts at 13 seconds and drops to 10 seconds. If it runs out, your current slider value counts at half. The true ratio is always a whole number, which is why the plus and minus buttons are useful for the last bit of precision.

What it trains

This game trains length comparison and proportional reasoning. Judging a length relative to another length is a basic ingredient of drawing, carpentry, map reading and page layout, and it underlies estimates like 'this board is about two thirds of that one'.

Because the lines are tilted, the game also exercises your ability to compare things that do not line up. That skill is much harder than it feels, and it is good to know exactly how well, or how badly, you do it.

Tips for a higher score

• Use simple fractions as anchors: 50 percent is one half, 67 is two thirds, 75 is three quarters, 33 is one third. Decide which of them is closest, then adjust.
• Mentally rotate one of the lines so both have the same direction. Your eye is far better at comparing parallel lines than lines at different angles.
• For lines with fins, ignore the fins completely. They are decoration that tries to fool you, and the length of the shaft is all that counts.
• Count units. Imagine the short line as a ruler and see how many times it fits in the long line; two and a half copies means 40 percent.
• Keep your eyes moving between the two ends of each line. Staring at one end makes you overestimate that line.

The idea behind it

The arrow illusion used in the later rounds is the Müller-Lyer illusion, published by Franz Carl Müller-Lyer in 1889. A line with outward-pointing fins looks longer than an identical line with inward-pointing ones. The effect persists even after you know about it, which is what makes it so instructive.

People are good at judging length differences when lines are close together and parallel, but make larger errors when the lines are separated and tilted. Weber's law also applies: the smallest noticeable difference grows in proportion to the length. The game's tolerance in percentage points accounts for that to some extent.

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Free, no account. Your best scores are saved on your device.