Calculate the official dimensions of the U.S. flag based on the hoist (height) or fly (width).
Hoist (Height)
Fly (Width)
Calculated Flag Dimensions:
Understanding Official U.S. Flag Proportions
The design and proportions of the American flag are governed by specific regulations to ensure uniformity and historical accuracy. These standards are primarily defined by Title 4 of the United States Code and executive orders, with further specifications provided by the U.S. Army Institute of Heraldry. The two key dimensions are the 'hoist' (the vertical dimension, or height) and the 'fly' (the horizontal dimension, or width).
The Standard Proportions
The official ratio between the fly (width) and the hoist (height) is 1.9, meaning the fly dimension should be 1.9 times the hoist dimension. This ratio is fundamental to all official U.S. flags, regardless of their size.
Hoist (Height): The dimension parallel to the flagpole.
Fly (Width): The dimension perpendicular to the flagpole.
Additional Proportional Elements
Beyond the overall height and width, other elements of the flag also have standardized proportions relative to the hoist:
Canton (Union) Hoist: The height of the blue field containing the stars. This is 7/10ths of the flag's hoist. (0.7 x Hoist)
Canton (Union) Fly: The width of the blue field. This is 0.4 times the flag's fly. (0.4 x Fly)
Star Hoist: The vertical diameter of the inscribed circle of each star. This is 0.0616 times the flag's hoist. (0.0616 x Hoist)
Star Fly: The horizontal diameter of the inscribed circle of each star. This is 0.076 times the flag's hoist. (0.076 x Hoist)
Stripe Hoist: The height of each stripe. This is 1/10th of the flag's hoist. (0.1 x Hoist)
Union (Staff) Sleave: The length of the sleeve for the flagpole attachment. This is 0.75 times the flag's hoist. (0.75 x Hoist)
How the Calculator Works
This calculator uses the primary ratio to determine the other main dimension when one is provided. The core calculation is based on the fly-to-hoist ratio of 1.9:
If you input the Hoist (Height), the Fly (Width) is calculated as: Fly = Hoist × 1.9
If you input the Fly (Width), the Hoist (Height) is calculated as: Hoist = Fly / 1.9
The calculator then uses these primary dimensions to derive the proportions for the canton (union) and stripes, providing a comprehensive set of official measurements.
Use Cases
This calculator is useful for:
Flag manufacturers ensuring compliance with official standards.
Organizations and government bodies ordering or displaying U.S. flags.
Educators and students learning about U.S. flag specifications.
Enthusiasts interested in the precise details of national symbols.
function toggleInputVisibility() {
var dimensionType = document.getElementById('dimensionType').value;
var heightInputGroup = document.getElementById('heightInputGroup');
var widthInputGroup = document.getElementById('widthInputGroup');
if (dimensionType === 'height') {
heightInputGroup.style.display = 'flex';
widthInputGroup.style.display = 'none';
document.getElementById('flagHeight').value = ";
document.getElementById('flagWidth').value = ";
} else {
heightInputGroup.style.display = 'none';
widthInputGroup.style.display = 'flex';
document.getElementById('flagWidth').value = ";
document.getElementById('flagHeight').value = ";
}
document.getElementById('result').style.display = 'none';
}
function calculateFlagDimensions() {
var dimensionType = document.getElementById('dimensionType').value;
var flagHeightInput = document.getElementById('flagHeight');
var flagWidthInput = document.getElementById('flagWidth');
var resultDiv = document.getElementById('result');
var calculatedHeightDisplay = document.getElementById('calculatedHeight');
var calculatedWidthDisplay = document.getElementById('calculatedWidth');
var hoist = 0;
var fly = 0;
var calculatedHeight = 0;
var calculatedWidth = 0;
if (dimensionType === 'height') {
var inputHeight = parseFloat(flagHeightInput.value);
if (isNaN(inputHeight) || inputHeight <= 0) {
alert("Please enter a valid positive number for the flag's height (hoist).");
return;
}
hoist = inputHeight;
fly = hoist * 1.9;
calculatedHeight = hoist;
calculatedWidth = fly;
calculatedHeightDisplay.textContent = "Hoist (Height): " + calculatedHeight.toFixed(2) + " inches";
calculatedWidthDisplay.textContent = "Fly (Width): " + calculatedWidth.toFixed(2) + " inches";
} else { // dimensionType === 'width'
var inputWidth = parseFloat(flagWidthInput.value);
if (isNaN(inputWidth) || inputWidth <= 0) {
alert("Please enter a valid positive number for the flag's width (fly).");
return;
}
fly = inputWidth;
hoist = fly / 1.9;
calculatedHeight = hoist;
calculatedWidth = fly;
calculatedHeightDisplay.textContent = "Hoist (Height): " + calculatedHeight.toFixed(2) + " inches";
calculatedWidthDisplay.textContent = "Fly (Width): " + calculatedWidth.toFixed(2) + " inches";
}
resultDiv.style.display = 'block';
}
// Initialize visibility on page load
document.addEventListener('DOMContentLoaded', toggleInputVisibility);