How tall does it look from here?
How tall something looks depends on its height and its distance: once it stands several times farther away than it is tall, twice as far away looks about half as tall. The calculator below turns a height and a distance into the angle it fills, the length it covers on a ruler held out at arm’s length, and the distance from which a 5 ft 9 in person would look just as tall.
How tall it looks from where you stand
Example: the Burj Khalifa from 6 miles away. Type your own over it.
- From 6 mi away, something 2,717 ft tall fills 4.9° of your view, about 10 times the width of the full Moon.
- On a ruler held upright at arm’s length, 25 in from your eye, it covers 2.1 in.
- A 5 ft 9 in person looks as tall from 67 ft away.
- From this far, the Earth’s curve hides about 6 ft of its base from someone standing on level ground; the numbers above count the whole height.
A simple model: how tall something looks is its height divided by its distance. It leaves out haze and the height of your eyes; the last line counts the Earth’s curve.
Why far things look small
What reaches your eye is an angle, not a size. A tower twice as far away fills about half the angle, so it looks about half as tall. That holds once the distance is several times the height; up close it does not: a 1 m (39.4 in) stick 1 m away fills 53°, and 2 m away still 28°, not half of 53°. The calculator works out the exact angle at any distance.
Yet two of the same thing at 5 and 10 meters usually look the same size, though the farther one fills about half the angle: the brain allows for the distance it can see, which is called size constancy. Where nothing shows the distance, as with the Moon or a tower across open water, the angle is all the eye has to go on.
Check it with a ruler
Hold a ruler upright with your arm straight, close one eye, and line up its end with the base of what you are looking at. Where its top meets the ruler is how tall it looks. Ask someone to measure from your eye to the ruler: that is the arm’s length the calculator asks for.
It works the other way too. If you know how tall something is, its distance is your arm’s length times its height, divided by the length it covers on the ruler: a 2,717 ft tower that covers 2.1 in of a ruler 25 in from your eye is about 6 miles away.
The Moon at the horizon
The full Moon looks bigger as it rises than when it is high in the sky, but the angle it fills stays about half a degree, and is even slightly smaller at the horizon, which is about 1.5% farther away. A pebble a third of an inch (8.4 mm) wide, held at arm’s length, covers it in both places: the difference is in how we see it, not in the sky.
What the calculator leaves out
Beyond about 2.9 miles (4.7 km), the horizon for someone standing on level ground, the Earth’s curve starts to hide the base of what you look at; the calculator says how much, without the slight bending of light near the ground. Haze can hide far things altogether. And the eye can make out about 1 arcminute, a sixtieth of a degree: about 1 ft (0.3 m) at 1 km.
The next useful step
- How tall a mirror do you need to see your whole body?
- Couple height difference: what a 10, 15 or 20 cm gap looks like
How the charts work explains the shared scale, source precision and custom inputs.