Projector Throw Distance Calculator
An Epson Home Cinema 2350 ($1,000) with a 1.32-2.15 throw ratio produces a 100 to 163-inch image from 12 feet away. Miss the throw ratio lookup and you either overshoot your screen or leave a gap around the edges.
This calculator divides throw distance by throw ratio to get image width, then converts to diagonal for 16:9 screens. It also checks whether your projector's lumens are sufficient for the resulting screen size and ambient light level.
Run this before you mount a projector or order a screen to make sure the geometry works.
How Projector Throw Distance Is Calculated
The Formula
The core math is simple: image_width = throw_distance / throw_ratio. A zoom lens has a range of throw ratios, giving you a range of screen sizes at any distance. The diagonal is: diagonal = width / cos(atan(9/16)), which is width / 0.8716 for a 16:9 aspect ratio.
Worked Example
Projector at 15 feet (180 inches) from the screen. Throw ratio: 1.3 to 2.1. At the wide end (1.3): 180 / 1.3 = 138.5" wide = 159" diagonal. At the telephoto end (2.1): 180 / 2.1 = 85.7" wide = 98" diagonal. So at 15 feet you can fill any screen from 98 to 159 inches. A standard 120-inch screen sits comfortably in that range, and the ambient light check estimates you need about 1,500 lumens in a dark room for 15 foot-lamberts on a 1.0-gain screen.
Standards
Throw ratio is defined by ANSI/INFOCOMM as the ratio of throw distance to image width. The ambient light gating uses foot-lambert targets from the ISF (Imaging Science Foundation): 15 fL for dark rooms (SDR), 25 fL for dim rooms, 40 fL for moderate ambient light, and 50+ fL for bright rooms. HDR content targets are higher: 25 fL minimum in the dark.
Limitations
This calculator assumes a flat screen perpendicular to the projector's lens axis. Ceiling mounts with steep angles introduce keystone distortion that effectively shrinks the usable image. The lumens check uses the projector's rated output, but real-world brightness in a calibrated color mode (like Cinema or Reference) is typically 50 to 70% of the rated figure.