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.
Square: s = sqrt(A) Rectangle: L = A / W (or W = sqrt(A / r), L = W * r) Circle: r = sqrt(A / pi)
- A = area
- s = side length of a square
- L, W = length and width of a rectangle
- r = aspect ratio (length divided by width)
- r (circle) = radius
Area and length units must match before solving. The calculator converts everything to square feet internally, solves, then converts to your chosen output unit. For rectangles, you must supply either a known width or an aspect ratio. There is no unique solution otherwise.
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) = 10 ft, so diameter = 20 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.
