Vanishing Point Distance Calculator
Rotation and lens in, vanishing points and measuring points out, in picture widths and pixels.
Where the points go
In two-point perspective the two vanishing points are not free choices; they are fixed by two things: the angle the object is turned relative to the picture plane, and the lens (the distance from the eye to the picture). For an object turned by θ, seen through a lens with focal length f (in picture units), the points sit at f · tan(θ) on one side of the centre and f ⁄ tan(θ) on the other. At 45° they are symmetric, each one focal length from the centre; at smaller angles one point comes in close and the other races away.
This calculator gives those positions in pixels and in picture widths for any rotation and lens. It also reports the distance between the two points, which is the quickest check of whether a drawing will look natural: under about one and a half picture widths and the corners start to splay.
Measuring points
To mark off true distances along a receding edge (fence posts every 2 m, windows every 3 m) you need the measuring point for that direction. It lies on the horizon at the same distance from the vanishing point as the station point (the eye) is from it. Draw the real distances along a horizontal line at the base of the near edge, connect each mark to the measuring point, and where those lines cross the receding edge are the correctly foreshortened positions. The calculator gives both measuring points for the rotation and lens you set.
From numbers to a drawing
The 2-point grid draws exactly this geometry; the button above opens it with the same rotation and lens, so you can check the numbers visually and export the grid. For a quick feel for how the points move, drag that grid sideways and watch the two points trade places.
Questions
How far apart should the vanishing points be in 2-point perspective?
Far enough that the drawing does not look distorted: as a rule of thumb, at least one and a half picture widths apart, often two or three. Their exact positions follow from the object's rotation and the lens: VP1 = f · tan(θ) and VP2 = −f ⁄ tan(θ) from the centre, where f is the focal length in picture units and θ the rotation.
Why does my 2-point drawing look distorted?
The vanishing points are too close together, which is the same as drawing with a very wide lens. Move them apart (use a longer lens) or reduce how much of the scene sits near the edges.
What are measuring points?
Points on the horizon used to transfer true lengths along a receding edge. Each vanishing point has one, found by swinging the distance from the vanishing point to the station point (the eye) up onto the horizon. This calculator gives their positions.