Your required throw distance will be displayed here.
Understanding Projector Throw Distance
The 'throw distance' of a projector is the distance between the projector lens and the screen surface. This distance, along with the projector's capabilities and the desired screen size, determines the size of the projected image. Understanding this is crucial for proper home theater setup, business presentations, and any application where screen placement is critical.
The calculation relies on the screen's dimensions and the projector's 'throw ratio'. The throw ratio is a specification provided by the projector manufacturer. It's typically expressed as a range (e.g., 1.18-1.52:1) or a single number (e.g., 1.5:1) for standard lens projectors. The ratio indicates how many feet (or meters) wide the projected image will be for every foot (or meter) of distance between the projector and the screen. A lower throw ratio generally means a 'short-throw' projector (can create a large image from a short distance), while a higher ratio indicates a 'long-throw' projector.
How the Calculation Works:
The core of the calculation involves determining the width of the screen based on its diagonal size and aspect ratio, and then using the throw ratio to find the required distance.
Calculate Screen Width:
The relationship between screen diagonal (d), width (w), and height (h) depends on the aspect ratio (ar). For a ratio of x:y, the aspect ratio value is typically ar = x/y.
We know that d² = w² + h².
Also, h = w / ar.
Substituting 'h' into the Pythagorean theorem:
d² = w² + (w / ar)²d² = w² (1 + 1/ar²)w² = d² / (1 + 1/ar²)w = d / sqrt(1 + 1/ar²)
Alternatively, using the aspect ratio directly as a multiplier (e.g. 16/9 = 1.777…):
If aspect ratio is a:b, then ar = a/b.
w = d / sqrt(1 + (b/a)²)
Let's use the common approach where `aspectRatio` is given as "16:9". We parse this to get `a=16` and `b=9`.
Then `ar_decimal = a / b`.
Width `w = d / sqrt(1 + (b/a)^2)`
Or, a simpler derivation:
Let aspect ratio be `R` (e.g., 16/9). Width `W`, Height `H`, Diagonal `D`.
D^2 = W^2 + H^2H = W/RD^2 = W^2 + (W/R)^2 = W^2 * (1 + 1/R^2)W = D / sqrt(1 + 1/R^2)
To avoid issues with float precision and direct calculation, we can use:
For 16:9: `width = diagonal * (16 / sqrt(16^2 + 9^2)) = diagonal * (16 / sqrt(256 + 81)) = diagonal * (16 / sqrt(337)) = diagonal * 0.865`
For 4:3: `width = diagonal * (4 / sqrt(4^2 + 3^2)) = diagonal * (4 / sqrt(16 + 9)) = diagonal * (4 / sqrt(25)) = diagonal * (4 / 5) = diagonal * 0.8`
The general formula derived from `w = d / sqrt(1 + 1/ar²) ` is:
Let aspect ratio be `X:Y`. Decimal aspect ratio `R = X/Y`.
Screen width `W = D / sqrt(1 + (Y/X)^2)`
W = D / sqrt(1 + (1/R)^2)
Calculate Throw Distance:
The throw ratio is defined as Throw Ratio = Distance / Image Width.
Therefore, Distance = Throw Ratio * Image Width.
If the throw ratio is given as a range (e.g., 1.18-1.52), the minimum distance is calculated using the minimum throw ratio, and the maximum distance is calculated using the maximum throw ratio.
Example Calculation:
Let's say you have a screen with:
Screen Diagonal: 120 inches
Aspect Ratio: 16:9
Projector Throw Ratio: 1.5 (meaning 1.5:1)
First, calculate the screen width:
For 16:9, the aspect ratio factor is approximately 0.865 (derived from 16 / sqrt(16^2 + 9^2)).
Screen Width = 120 inches * 0.865 = 103.8 inches.
Now, calculate the throw distance:
Throw Distance = Throw Ratio * Screen Width
Throw Distance = 1.5 * 103.8 inches = 155.7 inches.
This distance is often more useful in feet:
Throw Distance (feet) = 155.7 inches / 12 inches/foot = 12.98 feet.
Note: This calculator assumes the throw ratio is provided as a single number representing the width for 1 unit of distance (e.g., 1.5 means 1.5 units wide per 1 unit distance). If your projector has a range (e.g., 1.18-1.52), this calculator will provide a single value based on the input. For ranges, you'd typically calculate the minimum and maximum throw distances separately.
function calculateThrowDistance() {
var screenDiagonal = parseFloat(document.getElementById("screenDiagonal").value);
var aspectRatioInput = document.getElementById("aspectRatio").value;
var throwRatioInput = document.getElementById("throwRatio").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = 'Your required throw distance will be displayed here.'; // Reset
// Validate inputs
if (isNaN(screenDiagonal) || screenDiagonal 0) {
// Calculate width using Pythagorean theorem approach
// w = d / sqrt(1 + (y/x)^2)
var aspectRatioFactor = Math.sqrt(1 + Math.pow(arY / arX, 2));
screenWidth = screenDiagonal / aspectRatioFactor;
} else {
resultDiv.innerHTML = "Please enter a valid aspect ratio (e.g., 16:9).";
return;
}
} else {
resultDiv.innerHTML = "Please enter aspect ratio in the format X:Y (e.g., 16:9).";
return;
}
var throwRatio = parseFloat(throwRatioInput);
if (isNaN(throwRatio) || throwRatio <= 0) {
resultDiv.innerHTML = "Please enter a valid projector throw ratio (e.g., 1.5).";
return;
}
// Calculate throw distance in the same units as screen diagonal
var throwDistance = throwRatio * screenWidth;
// Convert to feet for a more common measurement if needed
var throwDistanceInInches = throwDistance;
var throwDistanceInFeet = throwDistance / 12;
resultDiv.innerHTML = 'Required Throw Distance: ' +
throwDistanceInInches.toFixed(2) + ' inches (approximately ' +
throwDistanceInFeet.toFixed(2) + ' feet)';
}