Calculate square side, rectangle length, or circle radius from area in square feet, meters, yards, or acres with perimeter and diameter results.
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Reverse Area Formula
The calculator inverts the standard area equation for the shape you select.
- A = area
- s = side length of a square
- L, W = length and width of a rectangle
- q = aspect ratio (length divided by width)
- r (circle) = radius
The calculator converts area to square meters and known dimensions to meters, solves, then converts to your result unit. A rectangle needs a known side or a length-to-width ratio. Triangle height is perpendicular to its base; ellipse inputs and main outputs are full axes, not semi-axes. Units use the international foot: one acre is 43,560 ft², or 4,046.8564224 m²; one hectare is 10,000 m².
Reference Tables
Use these to sanity-check your result against common real-world sizes.
| Area | Square side | Circle radius |
|---|---|---|
| 100 sq ft | 10 ft | 5.64 ft |
| 500 sq ft | 22.4 ft | 12.6 ft |
| 1,000 sq ft | 31.6 ft | 17.8 ft |
| 2,500 sq ft | 50 ft | 28.2 ft |
| 10,000 sq ft | 100 ft | 56.4 ft |
| 43,560 sq ft (1 acre) | 208.7 ft | 117.8 ft |
| Aspect ratio (L : W) | Width factor | Length factor |
|---|---|---|
| 1 : 1 | 1.000 × sqrt(A) | 1.000 × sqrt(A) |
| 3 : 2 | 0.816 × sqrt(A) | 1.225 × sqrt(A) |
| Golden (1.618 : 1) | 0.786 × sqrt(A) | 1.272 × sqrt(A) |
| 2 : 1 | 0.707 × sqrt(A) | 1.414 × sqrt(A) |
| 16 : 9 | 0.750 × sqrt(A) | 1.333 × sqrt(A) |
Worked Examples
Square room from area. You have 225 sq ft and want a square layout. s = sqrt(225) = 15 ft per side.
Rectangle with known width. A 1,500 sq ft space against a 25 ft wall. L = 1,500 / 25 = 60 ft.
Rectangle by ratio. 1,200 sq ft at a 3:2 ratio. W = sqrt(1,200 / 1.5) = 28.28 ft. L = 28.28 × 1.5 = 42.43 ft.
Circle from area. A 314 sq ft circular patio. r = sqrt(314 / pi) ≈9.9975 ft, so diameter ≈19.9949 ft.
Why two answers for a rectangle? Area alone does not fix the shape. A 1,000 sq ft rectangle can be 10 × 100 or 25 × 40. You need a width or a ratio to pin it down.
