Projector Calculator

This calculator relies on established optical geometry and industry standards from organizations like THX and SMPTE. First, screen width is determined using the Pythagorean theorem and the chosen aspect ratio: width = (aspect_ratio × diagonal) / √(aspect_ratio² + 1). Once the width and height are established, the throw distance is found by multiplying the screen width by the projector's throw ratio range (min_throw_distance = width × min_throw_ratio). Image luminance (brightness) is evaluated using screen gain, projector lumen output, and the physical surface area in square feet, while viewing distance thresholds use trigonometric tangent functions to ensure comfortable human field-of-view angles.

Imagine you are setting up a home theater with a 16:9 widescreen projector. You want a screen with a diagonal size of 120 inches. First, we calculate the screen width using the aspect ratio formula, which yields approximately 104.6 inches (or 8.7 feet) wide and 58.8 inches (4.9 feet) high. Next, if your chosen projector has a throw ratio ranging from 1.35:1 to 1.5:1, we multiply the width by these ratios: the minimum throw distance is 104.6 × 1.35 = 141.2 inches (about 11.8 feet), and the maximum throw distance is 104.6 × 1.5 = 156.9 inches (about 13.1 feet). This tells you precisely where to mount your projector relative to the screen.

Always measure your throw lens-to-screen distance rather than from the back chassis of the projector to avoid mounting errors. Account for ambient room light when evaluating projector brightness; rooms with high natural light require higher lumen output or specialized high-gain screens. Finally, adhere to THX viewing angle recommendations to ensure viewers in the front row do not experience eye fatigue while maintaining an immersive experience.