Calculators

Perspective calculators, by the numbers.

Small calculators for the questions that come up at the drawing desk: what lens is this, how big should that person be, where does the horizon go, how far apart are the points. Each one opens the matching grid with the answer loaded.

Camera & lens
Lens to Field of ViewFocal length in, angle of view out, or the other way round. Any sensor. Then open a grid at exactly that lens.
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Figure Height at DistanceHow tall does a 1.8 m person look at 12 metres through a 35 mm lens? Exactly this tall, and their feet go exactly here.
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Horizon & Eye LevelTilt the camera and the horizon moves. Put the horizon where you want it and read off the tilt. Then find where the ground at ten metres lands.
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Vanishing Point DistanceRotation and lens in, vanishing points and measuring points out, in picture widths and pixels.
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Which perspective calculator do I need?

You know the lens, you want the grid. The focal length to field of view calculator turns 24 mm, 35 mm or 85 mm on any sensor into the horizontal angle the grid tools use, and back again. It is also the one to use when a client sends a photo and asks for a drawing that matches it.

You are putting people in the picture. The figure height calculator gives the apparent height of a 1.75 m person (or a car, or a door) at any distance, as a fraction of the frame and in pixels, and tells you where their feet land relative to the horizon. It is the fastest cure for crowds where everyone is a different size.

The horizon looks wrong. The horizon line calculator shows where the eye level falls for a given camera tilt and lens, or works backwards from where you have drawn the horizon to the tilt that implies. Looking up puts the horizon low in the frame; looking down puts it high; most beginners draw it in the middle regardless.

Two-point drawings look stretched. The vanishing point distance calculator tells you how far apart the two points should be for the rotation and lens you have chosen. Points that are too close together are the single most common perspective error; the measuring points it gives you fix depth as well.

How to use the results

Each answer comes with an “open this grid” button that loads the matching interactive grid with the lens, tilt or rotation already set, so the drawing you export agrees with the numbers. All four calculators use the same pinhole camera model as the grids and the printable templates, and every formula is written out on its page.

Questions

Which perspective calculator do I need?

If you know the lens and want the grid: Lens to Field of View. If you are placing people or cars in a drawing: Figure Height at a Distance. If your horizon looks wrong for the tilt: Horizon and Eye Level. If your two-point drawing looks distorted: Vanishing Point Distance.

Do these calculators work for photography as well as drawing?

Yes. They use the same pinhole camera model as the grids, so a 24 mm full-frame lens gives the same field of view, horizon and figure sizes as the photograph would. Sensor sizes for APS-C, Micro Four Thirds, 1-inch and phones are built in.

Where do the formulas come from?

Standard projective geometry: field of view from focal length and sensor width, apparent height from distance and focal length, horizon position from tilt, and vanishing point spacing from the object rotation and lens. Each calculator page shows the formula it uses.

Can I use the result directly in a grid?

Every calculator has an 'open this grid' button that loads the matching interactive grid with the lens, tilt or rotation already set, so the numbers and the drawing agree.