Quick answer
A US flag with hoist (height) H has a fly (length) of 1.9 × H, stripes of H ÷ 13, a union 7/13 of the hoist tall and 0.76 × H long, and stars of diameter 0.0616 × H. For a 10-foot hoist the fly is 19 ft.
Enter the hoist of the flag. The calculator returns the fly, union dimensions, stripe width and star diameter. It gives the proportions of the US flag for any hoist size.
Related tools: Height Comparison Calculator: Difference and ratio between two heights. Sleep Calculator: Wake-up times that line up with 90-minute sleep cycles. Birthday Calculator: Next birthday, days until it, and your current age.
How to use the US Flag Proportions Calculator
- Enter hoist (height) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Hoist (height) | A number | > 0 |
Formula and method
Formula
fly = 1.9 × hoist; union: 7/13 hoist × 0.76 hoist; stripe = hoist ÷ 13; star = 0.0616 × hoist
IEEE-754 double precision; shown to the decimals indicated.
Proportions from Executive Order 10834 (1959).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Hoist (height) = 10.
| Result | Value |
|---|---|
| Fly (length) | 19 |
| Union hoist | 5.3846 |
| Union fly | 7.6 |
| Stripe width | 0.7692 |
| Star diameter | 0.616 |
Example 2
Inputs: Hoist (height) = 3.
| Result | Value |
|---|---|
| Fly (length) | 5.7 |
| Union hoist | 1.6154 |
| Union fly | 2.28 |
| Stripe width | 0.2308 |
| Star diameter | 0.1848 |
Example 3
Inputs: Hoist (height) = 5.2.
| Result | Value |
|---|---|
| Fly (length) | 9.88 |
| Union hoist | 2.8 |
| Union fly | 3.952 |
| Stripe width | 0.4 |
| Star diameter | 0.3203 |
The first line is the headline result (fly (length)). Below it the uS Flag Proportions Calculator lists union hoist, union fly, stripe width and star diameter, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
From the official proportions
The proportions follow the executive order that fixed the flag's design: the hoist is 1.0, the fly 1.9, the union height 0.5385 (7/13) and its width 0.76, each stripe 0.0769 (1/13) and each star 0.0616 across. For a 10 ft hoist, stripes are 0.769 ft wide.
Standard sizes
Common sizes such as 3×5 ft do not follow the 1.9 ratio exactly (3×5 is 1.67); they are cut for convenience. The table shows what a true-proportion flag would measure.
How the result changes with hoist
Holding every other input at the first worked example, this table changes only hoist. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Hoist | Fly (length) | Union hoist | Union fly |
|---|---|---|---|
| 5 | 9.5 | 2.6923 | 3.8 |
| 10 | 19 | 5.3846 | 7.6 |
| 20 | 38 | 10.7692 | 15.2 |
| 40 | 76 | 21.5385 | 30.4 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Hoist (height): entering "0" shows "Hoist (height) must be greater than 0." beside that field and no result.
Choosing between the US Flag Proportions Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Height Comparison Calculator](/lifestyle/height-comparison-chart/) | person A and person B | Height difference |
| [Sleep Calculator](/lifestyle/sleep-calculator/) | bedtime | 4 cycles (6 h) |
| [Birthday Calculator](/lifestyle/birthday/) | date of birth and reference date | Next birthday |
| [Baby Age Calculator](/lifestyle/baby-age/) | date of birth and reference date | Age |
| [Age Difference Calculator](/lifestyle/age-difference-calculator/) | first birth date and second birth date | Age difference |
Assumptions and limitations
- Use one length unit
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for hoist (height) to confirm this.
Frequently asked questions
What is the proper US flag ratio?
The official ratio is 1 : 1.9 for hoist to fly, with a union 7/13 of the hoist tall.
How many stripes?
Thirteen, seven red and six white.
Is a 3×5 flag correct?
It is a common size, not the exact ratio.
What does the US Flag Proportions Calculator calculate?
Dimensions of a US flag from its hoist. It returns Fly (length), Union hoist, Union fly, Stripe width and Star diameter.
What formula does the US Flag Proportions Calculator use?
fly = 1.9 × hoist; union: 7/13 hoist × 0.76 hoist; stripe = hoist ÷ 13; star = 0.0616 × hoist. Proportions from Executive Order 10834 (1959).
What do I need to enter in the uS Flag Proportions Calculator?
You enter Hoist (height).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Use one length unit.
What is an example of a uS Flag Proportions result?
With hoist (height) 10, the fly (length) is 19.
Where does the method come from?
The method follows: Executive Order 10834 (US flag proportions).
Related calculators
- Height Comparison Calculator — Difference and ratio between two heights.
- Sleep Calculator — Wake-up times that line up with 90-minute sleep cycles.
- Birthday Calculator — Next birthday, days until it, and your current age.
- Baby Age Calculator — A baby's age in weeks, months and days.
- Age Difference Calculator — Time between two birth dates.
Sources
- Executive Order 10834 (US flag proportions)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.