Flag Calculator | USA

How to use this U.S. flag proportion calculator

What this calculator does

This calculator scales the geometry of the current 50-star U.S. flag from any one known linear dimension. It is useful when laying out a sewn flag, painted panel, sign, woodworking template, classroom model, vector drawing, or other proportional construction. The underlying geometry follows the standard proportions associated with Executive Order 10834; the National Archives text of Executive Order 10834 explains that the constituent parts of the flag conform to the proportions in its attachment. This tool scales those proportions only. It does not decide whether a commercially common flag size, a particular material, or a display practice is suitable for your situation.

When to use it

Use it when you know the desired flag height and need the matching fly length; when a project gives you a fixed stripe width and you need the full flag size; when you need the union and star-layout measurements for a fabrication template; or when you have one existing dimension and want to verify that the rest of the design is proportional.

How to calculate

1. The calculator opens with a ready-to-use 3 ft demonstration height, so all results and the Excel workbook are valid immediately.
2. Choose a Measurement unit of feet, inches, centimeters, or meters. Changing the unit converts the current physical flag rather than changing its size.
3. Replace any one measurement – Width (A), Length (B), Stripes width (H), Union width (C), Union length (D), Star gaps – width (E), Star gaps – length (F), or Stars diameter (G). The edited field becomes the scale anchor and all other measurements are recalculated.
4. Optionally enable Show proportion coefficient (x). The revealed Proportion coefficient (x) is the normalized A dimension and can itself be edited as the anchor.
5. Read Overall flag size first, then use the supporting cards and Dimension table for fabrication details. Select Download Excel to export the current validated dimensions. Reset clears the demonstration and all measurements; the export then stays unavailable until you enter a complete valid scale again.

Input guide

Width (A) is the flag's hoist height even though the short UI label says width; enter a required positive decimal such as 3 ft. Length (B) is the fly length; a realistic example is 5.7 ft when A is 3 ft. Stripes width (H) is one of the 13 equal stripe heights; 0.2308 ft is the demonstration value. Union width (C) represents the union's vertical dimension and is 7/13 of A; the sample is 1.6154 ft. Union length (D) is the horizontal union dimension and is 0.76 of A; the sample is 2.28 ft.

Star gaps – width (E) is the vertical star-center interval used by this proportion system; the sample is 0.1615 ft. Star gaps – length (F) is the horizontal star-center interval; the sample is 0.19 ft. Stars diameter (G) is the diameter of each circumscribed star; the sample is 0.1846 ft. All measurement fields accept ordinary base-10 decimal notation with a period as the decimal separator, must be greater than zero, and must not contain unit text, commas, scientific notation, or unsupported symbols. A common mistake is entering several dimensions as if they were independent requirements: because the flag is a fixed-ratio design, the most recently edited valid dimension becomes the controlling scale.

Measurement unit is required and affects every displayed and exported measurement. Show proportion coefficient (x) is optional and only reveals another scale input; it does not change the formula. Proportion coefficient (x), when shown, must be a positive decimal in the selected unit and has the same geometric meaning as A in the normalized equations.

Output guide

Height and Length in the summary pills repeat A and B in the active unit. Union reports C × D. Overall flag size presents A × B and is the quickest cutting or canvas-size reference. Aspect ratio is the exact identity 10:19 for the standard geometry. Stripe width, Star diameter, Vertical star gap, and Horizontal star gap are direct scaled dimensions; larger anchor values increase all of them proportionally, while no valid positive anchor can produce a negative result. Scale coefficient (x) appears only when requested and equals A. The Dimension table lists code, dimension name, exact or conventional ratio to A, and scaled value. These are proportional calculations, not recommendations about material tolerances.

Worked example

With the startup value A = 3 ft, the main ratio gives B = 1.9 × 3 = 5.7 ft. Each stripe is H = 3/13 = 0.230769... ft, displayed as 0.2308 ft. The union height is C = 7/13 × 3 = 1.615384... ft, and the union length is D = 0.76 × 3 = 2.28 ft. The vertical star-center interval is E = C/10 = 0.161538... ft; the horizontal interval is F = D/12 = 0.19 ft; and the star diameter is G = 4/5 × H = 0.184615... ft. Those values are the same startup values shown in the results, detail table, and downloadable workbook.