# US Flag Proportions Calculator

URL: https://speedycalculator.com/calculators/other/flag/
Last updated: 2026-10-30

> The flag calculator works out every official dimension of the United States flag – hoist, fly, union, stripes, star spacing and star diameter – from any single measurement, using the proportions of Executive Order 10834, and draws the flag to scale.

## Inputs

- Proportions
- The dimension I know
- Its size (ft, in, m, cm, mm, yd)
- Hoist (height) (ft, in, m, cm, mm, yd)
- Fly (length) (ft, in, m, cm, mm, yd)

## Results

- Drawing to scale
- Hoist A (height)
- Fly B (length)
- Union height C (7 stripes)
- Union length D
- E – union top edge to first star row
- F – spacing between star rows
- G – union side edge to first star column
- H – spacing between star columns
- K – star diameter
- L – stripe width
- Length-to-height ratio
- Flag area
- Union (canton) area

## Formula

```
Hoist A = 1.0 · Fly B = 1.9 · Union C = 0.5385 (7/13) by D = 0.76 · E = F = 0.054 · G = H = 0.063 · Star diameter K = 0.0616 · Stripe L = 0.0769 (1/13) — all × the hoist
```

## Explanation

The design of the Stars and Stripes is fixed by law: 4 U.S. Code § 1 sets thirteen alternating red and white stripes and one star per state, and Executive Order 10834 (1959) gives the exact proportions for the 50-star flag. Every dimension is a multiple of the hoist (the flag's height): the fly is 1.9 times the hoist, each stripe is 1/13 of it, and the blue union covers the top seven stripes and 0.76 of the hoist in length.

The 50 stars sit in nine rows that alternate between six and five stars. Rows are 0.054 hoist apart and columns 0.063 hoist apart, measured between star centres, and each star has a diameter of 0.0616 hoist. Because everything scales together, you only need one measurement – the height, the length, the stripe width or even the star size – to find all the others.

Many flags sold in shops are 3 × 5 ft or 4 × 6 ft, which is shorter than the official 1.9 ratio. The second mode keeps the vertical proportions tied to the hoist and the horizontal ones tied to the fly, which is how such retail flags are usually laid out.

### How to use the US Flag Proportions Calculator

- **Proportions**
- **The dimension I know**
- **Its size**
- **Hoist (height)**
- **Fly (length)**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose official proportions and enter one known dimension, or choose a retail size and enter both height and length. The calculator scales the Executive Order 10834 ratios (A to L) and draws the result.

### Worked example

An official flag with a 3 ft hoist: fly = 3 × 1.9 = 5.7 ft; union = 3 × 7/13 = 1.615 ft high and 3 × 0.76 = 2.28 ft long; stripes 3/13 = 0.231 ft (2.77 in); star rows 0.162 ft (1.94 in) apart, columns 0.189 ft (2.27 in) apart; stars 0.185 ft (2.22 in) across. In retail mode a 3 × 5 ft flag gets a 2 ft long union (0.4 × fly) and columns 2/12 = 0.167 ft apart.

### Official proportions (Executive Order 10834)

LetterDimensionRatio to hoistAHoist (height)1.0BFly (length)1.9CUnion hoist0.5385DUnion fly0.76E, FStar row offsets0.054G, HStar column offsets0.063KStar diameter0.0616LStripe width0.0769

## Worked example

Inputs — Proportions: Official (Executive Order 10834, fly = 1.9 × hoist); The dimension I know: Hoist A – flag height; Its size: 3 ft.

Results — Hoist A (height) = 0.9144; **Fly B (length) = 1.7374**; Union height C (7 stripes) = 0.4924; Union length D = 0.6949; E – union top edge to first star row = 0.0494; F – spacing between star rows = 0.0494.

## Key terms

- **Hoist**: The height of the flag, along the pole – dimension A.
- **Fly**: The length of the flag, from the pole to the free end – dimension B.
- **Union (canton)**: The blue field with the stars in the upper corner next to the pole.
- **Executive Order 10834**: The 1959 order that fixed the proportions of the 50-star flag.

## FAQ

**What are the official proportions of the US flag?**
Height 1.0 to length 1.9 under Executive Order 10834. A 3 ft high official flag is 5.7 ft long.

**Why is my 3 × 5 ft flag not 1.9 to 1?**
Retail flags use convenient sizes (3 × 5, 4 × 6, 5 × 8 ft). Executive Order 10834 binds federal agencies; private flag makers are free to use other ratios.

**How wide is each stripe?**
One thirteenth of the hoist: 2.77 in on a 3 ft flag, 7.38 in on an 8 ft flag.

**How big are the stars?**
The star diameter is 0.0616 of the hoist – about 2.2 in on a 3 ft flag and 4.4 in on a 6 ft flag.

**How are the 50 stars arranged?**
In nine rows alternating six and five stars (6-5-6-5-6-5-6-5-6), which places them on a grid of 11 columns.

**What are the official colors?**
Old Glory Red and Old Glory Blue. Common screen equivalents are #B22234 and #3C3B6E; the government specifies them as cloth color standards.

**What size flag fits a 5 × 9.5 ft burial flag?**
That is the official 1.9 ratio with a 5 ft hoist; enter 5 ft as the hoist to get the union (2.69 × 3.8 ft) and a stripe width of 4.6 in.


## Sources

- [Executive Order 10834 – The Flag of the United States (National Archives)](https://www.archives.gov/federal-register/codification/executive-order/10834.html)
- [4 U.S. Code § 1 – Flag; stripes and stars on (Cornell LII)](https://www.law.cornell.edu/uscode/text/4/1)
- [Wikipedia – Flag of the United States](https://en.wikipedia.org/wiki/Flag_of_the_United_States)