American Flag Size & Proportions Calculator - Inch Calculator - Free Printable

The image you've provided is a diagram of the U.S. flag with labeled dimensions, based on official specifications. This diagram illustrates the geometric proportions and layout of the American flag, as defined by the U.S. government's official guidelines (specifically, the U.S. Flag Code and standard flag-making specifications).

Let’s break down what this diagram shows and explain the meaning of each labeled part.

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🔹 Overview of the U.S. Flag Design

The U.S. flag consists of:
- 13 horizontal stripes (7 red and 6 white), representing the original 13 colonies.
- A blue rectangle (union) in the upper left corner containing 50 white stars, representing the 50 states.

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🔸 Key Labels Explained

#### A – Total Height of the Flag
This is the total vertical dimension of the flag.

> *Note:* The flag is typically designed with a specific ratio of width to height.

#### B – Total Width of the Flag
This is the full horizontal length of the flag.

> Standard proportion: B = 1.9 × A
> That is, the flag is 1.9 times wider than it is tall.

#### C – Height of the Union (Blue Field)
The blue field (where the stars are located) has a height that is 7/13 of the total flag height (A), because there are 13 stripes, and the union covers 7 of them vertically.

> So:
> $ C = \frac{7}{13} \times A $

#### D – Width of the Union
The width of the blue field is 10/13 of the total flag width (B), since it spans 10 stripes horizontally.

> So:
> $ D = \frac{10}{13} \times B $

> But since $ B = 1.9A $, we can also write:
> $ D = \frac{10}{13} \times 1.9A \approx 1.4615A $

#### E – Height of the Top Stripe
Each stripe is equal in height. Since there are 13 stripes, each stripe is:

> $ E = \frac{A}{13} $

#### F – Height of the Red Stripes
All red and white stripes are the same height. So:

> $ F = \frac{A}{13} $

> There are 7 red stripes and 6 white ones.

#### G – Width of the Outer White Stripes
The outer edges of the union have two narrow white margins (G) on the top and bottom. These are not part of the stripes themselves but frame the union.

> G = 1/12 of the width of the union (D), or more precisely:
> $ G = \frac{1}{12} \times D $

#### H – Width of the Inner White Stripes
The inner white stripes (between the red ones) are narrower than the red ones, but actually, all stripes are the same width. However, in this diagram, H represents the width of the individual segments into which the union is divided.

Wait — let's clarify:

Actually, H appears to represent the horizontal spacing between the stars or the segmented width of the union. The union is divided into 11 equal parts (as shown by 11 H's between two G's), so:

> $ D = 2G + 11H $

But from standard specs:
- The width of the union (D) is divided into 11 equal parts, each called "H", and the two ends (G) are slightly smaller.

However, officially, the stars are arranged in rows, and their spacing is governed by specific rules.

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🔸 Star Arrangement

There are 50 stars arranged in 9 rows:
- 6 rows with 6 stars
- 5 rows with 5 stars

They are arranged in a staggered pattern.

#### K – Diameter of a Star
The diameter of a star is labeled as K. According to U.S. flag standards:
- Each star is incribed in a circle of diameter K.
- The diameter K is equal to 1/10 of the height of the union (C).

So:
> $ K = \frac{1}{10} \times C = \frac{1}{10} \times \frac{7}{13}A = \frac{7}{130}A $

Also, the center-to-center distance between stars is usually equal to the diameter of the star, ensuring even spacing.

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🔸 L – Height of Each Stripe

As mentioned earlier:
> $ L = \frac{A}{13} $

And this matches E, F, and L — all refer to the height of one stripe.

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🔸 "A" Divided Into 13 Equal Parts Equals "L"

This note on the right confirms:
> $ L = \frac{A}{13} $

So every stripe is exactly $ \frac{1}{13} $ of the total flag height.

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🔸 Summary of Key Proportions

| Label | Meaning | Formula |
|------|--------|--------|
| A | Total height | Base unit |
| B | Total width | $ B = 1.9A $ |
| C | Union height | $ C = \frac{7}{13}A $ |
| D | Union width | $ D = \frac{10}{13}B $ |
| E, F, L | Stripe height | $ \frac{A}{13} $ |
| G | Edge margin of union | $ G = \frac{1}{12}D $ |
| H | Segment width (union division) | Part of $ D = 2G + 11H $ |
| K | Star diameter | $ K = \frac{1}{10}C = \frac{7}{130}A $ |

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✔ Example Calculation (for a 3x5 ft flag)

Let’s say the flag is 3 feet high (A = 3'), then:
- B = 1.9 × 3 = 5.7 feet
- C = 7/13 × 3 ≈ 1.615 ft
- D = 10/13 × 5.7 ≈ 4.385 ft
- L = 3 / 13 ≈ 0.231 ft (about 2.77 inches per stripe)
- K = 1/10 × 1.615 ≈ 0.1615 ft (about 1.94 inches)

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🎯 Conclusion

This diagram is a technical blueprint for constructing a U.S. flag according to official standards. It ensures consistency in proportions, stripe widths, and star placement.

If your task was to solve a problem related to this diagram (e.g., find a missing dimension, verify proportions, or calculate star size), please specify the exact question. But based on the image alone, this is a comprehensive explanation of the U.S. flag's geometry.

Let me know if you'd like to:
- Calculate dimensions for a specific flag size
- Draw a scaled version
- Understand star positioning mathematically

I'm happy to help!