How this instrument works
The United States flag's proportions aren't a design tradition passed down informally — they're set out in precise numeric ratios by federal executive order, all keyed to one reference measurement: the hoist, meaning the flag's vertical edge, the side nearest the pole. Every other dimension — the fly (horizontal length), the width of each of the 13 stripes, the size of the blue union in the corner, and the diameter of each star — is defined as a fixed fraction of that single hoist measurement, which is why a flag can be scaled to any size and still be officially correct as long as every part scales together.
The specific ratios were fixed in 1959, ahead of Hawaii's admission as the 50th state, to standardize a 50-star arrangement: fly length is 1.9 times the hoist, each stripe is 1/13th of the hoist wide (there are 13 stripes for the 13 original colonies), the union's height is 7/13ths of the hoist, its width is 0.76 times the fly length, and each star's diameter is 0.0616 times the hoist. None of these numbers are arbitrary — they were set once, officially, and haven't changed since.
Because every dimension derives from the same hoist figure, this works equally well scaled up or down — enter a 3-foot hoist for a standard house flag, or a 15-inch hoist for a desk flag, and every other measurement scales proportionally to match, exactly as a manufacturer sewing an officially-proportioned flag would calculate it.
- Enter the flag's hoist — its vertical edge, the side that runs along the pole — in whatever unit you're working in (feet, inches, meters all work the same way).
- Read the fly length — the flag's horizontal, outward-facing edge.
- Read the stripe width, the union's height and width, and the star diameter, all scaled to your entered hoist.
Worked example — a standard 3-foot-hoist US flag
A common house flag has a 3-foot hoist. Fly length is 3 × 1.9 = 5.7 feet, giving the familiar '3-foot by 5-foot' flag its actual 5.7-foot length. Stripe width comes out to 3 ÷ 13 = 0.2308 feet (about 2.77 inches) for each of the 13 stripes.
The union — the blue field of stars — measures 3 × 7/13 = 1.6154 feet tall and 5.7 × 0.76 = 4.332 feet wide, and each individual star has a diameter of 3 × 0.0616 = 0.1848 feet (about 2.22 inches).
Questions
Where do these exact ratios come from?
They're set by Executive Order 10834, signed in 1959 ahead of Hawaii's statehood, which standardized the flag's proportions for the new 50-star arrangement effective July 4, 1960. The order specifies each ratio as a precise decimal or fraction of the hoist — 1.9 for fly length, 1/13 for stripe width, 7/13 for union height, 0.76 for union width, and 0.0616 for star diameter — making the design fully reproducible at any scale.
Why are there 13 stripes but 50 stars?
The 13 stripes represent the original 13 colonies and have stayed fixed at that number since the Second Flag Act of 1794 permanently set it — only the star count has changed over time, rising with each new state admitted to the Union, most recently to 50 with Hawaii's statehood in 1959, which is also what prompted the 1959 proportion standardization this calculator uses.
Does the hoist measurement need to be in feet?
No — every output scales proportionally to whatever unit you enter for the hoist, whether that's feet for a house flag, inches for a small desk flag, or meters for a large ceremonial one. The ratios themselves are unitless fractions of the hoist, so the output units always match whatever you entered.
Is a common '3x5 foot' flag exactly 3 feet by 5 feet?
Not quite — '3x5' is retail shorthand, but the officially proportioned fly length for a 3-foot hoist is 3 × 1.9 = 5.7 feet, not an even 5. Many mass-market flags round this off for simpler manufacturing, so a flag advertised as 3x5 may be slightly off from the exact federal ratio, while flags built to spec for government or ceremonial use hold to the precise 1.9 fly-to-hoist ratio.
Do these proportions apply to state flags or other national flags too?
No — these specific ratios (1.9 fly-to-hoist, 1/13 stripe width, and so on) are unique to the US national flag as set by Executive Order 10834. Other countries and US states set their own flag proportions independently, often with completely different ratios, so this calculator's numbers only apply to the Stars and Stripes.