Calculate a flag width-to-height ratio, scale common proportions, compare the nearest standard, and add edge allowances for a fabric cut plan.
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Flag Ratio Formula
The calculator measures a hoist-to-fly proportion from finished dimensions, or solves finished width or height from a selected proportion. Optional per-edge allowances produce a simple rectangular cut plan.
Ratio mode finds the height-to-width ratio from two measurements:
If a ratio is selected and only one dimension is given, the missing side is solved as:
Illustrative pole-sizing arithmetic below is separate from this calculator; it does not rate structural or wind-load suitability:
U.S. design reference uses the 10:19 proportion; a matching outline alone does not establish compliance with the complete design:
- Height (hoist): the vertical edge of the flag, measured along the pole.
- Width (fly): the horizontal edge of the flag, measured away from the pole.
- h : w: the parts of the chosen ratio, such as 2 and 3 in a 2:3 flag.
- PoleHeight: the exposed height of the flagpole above ground or mount.
- D: the divisor for display setting (3, 4, or 5).
The ratio mode reports 1 : (width ÷ height), compares the selected reference and finds the closest absolute fly/hoist ratio among 1:1, 2:3, 3:5, 10:19 and 1:2. Midpoint ties show both. Width and height modes scale the selected reference. All modes report finished area, perimeter and cut dimensions with twice the entered allowance added to each dimension. At the explicit U.S. design preset or a measured 10:19 match within numerical rounding, stripe height H/13 and union hoist 7H/13 by fly 0.76H are shown. Star spacing and pole loading are not calculated.
Common Flag Ratios and Pole Sizing
Most national flags fall into a small set of ratios. Use the table below to identify or pick one.
| Ratio (H:W) | Width ÷ Height | Examples |
|---|---|---|
| 1:1 | 1.000 | Switzerland, Vatican City |
| 2:3 | 1.500 | France, India |
| 3:5 | 1.667 | Germany |
| 10:19 | 1.900 | United States |
| 1:2 | 2.000 | United Kingdom, Australia, Canada |
The following table illustrates a fly near one quarter of the listed pole height. It is a geometric display example, not an engineering rule; use the pole manufacturer’s permitted flag area and site wind-load requirements. Sizes are rounded and do not all exactly equal a 10:19 outline.
| Pole Height | Standard Flag (2:3) | U.S. Flag (10:19) |
|---|---|---|
| 15 ft | 2.5 × 3.75 ft | 2 × 3.8 ft |
| 20 ft | 3.33 × 5 ft | 2.6 × 5 ft |
| 25 ft | 4.17 × 6.25 ft | 3.3 × 6.25 ft |
| 30 ft | 5 × 7.5 ft | 4 × 7.5 ft |
| 40 ft | 6.67 × 10 ft | 5.3 × 10 ft |
| 50 ft | 8.33 × 12.5 ft | 6.6 × 12.5 ft |
Examples and FAQ
Example 1. You have a flag measured at 3 ft hoist by 5 ft fly. Width ÷ height = 1.667, which matches 3:5.
Example 2. You bought a 25 ft pole and want a U.S. flag. Use width = 25 ÷ 4 = 6.25 ft. Height = 6.25 × (10/19) ≈ 3.29 ft. Stock sizes may have a different outline ratio; select a size permitted by the pole manufacturer rather than inferring a wind-load rating from this arithmetic.
Why does the U.S. flag use 10:19? Executive Order 10834 set the standard design proportions in 1959. Its official proportion table gives union, stripe and star geometry. This calculator returns only stripe height and union dimensions for the modeled design. The order also lists authorized agency sizes and permits specified adjustments; this tool is not a legal compliance check.
What if my flag does not match a standard ratio? Enter both dimensions in Ratio mode. The calculator normalizes to 1 : (fly ÷ hoist), then compares five listed proportions using absolute ratio distance. It does not search denominators or infer a flag’s nationality. Reference deviation is the absolute ratio difference divided by the selected reference ratio, expressed as a percentage.
Should the flag width be exactly one quarter of the pole? No. The example uses one quarter only for illustration. Pole, mount and foundation capacity, wind conditions and the manufacturer’s permitted flag area govern a suitable size; this calculator does not determine those.
Does hoist mean height or width? Hoist is the vertical edge next to the pole. Fly is the horizontal edge that flaps in the wind. Flag sizes are usually quoted as hoist × fly.
