Equivalent Square Output
The result appears above the form, as requested.
Corrected equivalent square field size using adjusted dimensions and the chosen correction factor.
| Metric | Value |
|---|---|
| Input Length | 20.000 cm |
| Input Width | 10.000 cm |
| X Margin | 0.000 cm |
| Y Margin | 0.000 cm |
| Adjusted Length | 20.000 cm |
| Adjusted Width | 10.000 cm |
| Area | 200.000 cm² |
| Perimeter | 60.000 cm |
| Equivalent Square | 13.333 cm |
| Corrected Equivalent Square | 13.333 cm |
| Geometric Mean | 14.142 cm |
| Diagonal | 22.361 cm |
| Aspect Ratio | 2.000 : 1 |
Plotly Graph
This graph shows how equivalent square size changes as adjusted width varies while adjusted length remains fixed.
Calculator Inputs
Example Data Table
These sample cases show how the formula behaves across different rectangular fields.
| Length (cm) | Width (cm) | X Margin (cm) | Y Margin (cm) | Adjusted Length (cm) | Adjusted Width (cm) | Equivalent Square (cm) |
|---|---|---|---|---|---|---|
| 6.000 | 6.000 | 0.000 | 0.000 | 6.000 | 6.000 | 6.000 |
| 8.000 | 12.000 | 0.000 | 0.000 | 8.000 | 12.000 | 9.600 |
| 10.000 | 20.000 | 0.500 | 0.500 | 11.000 | 21.000 | 14.438 |
| 15.000 | 25.000 | 1.000 | 0.500 | 17.000 | 26.000 | 20.558 |
| 18.000 | 30.000 | 1.000 | 1.000 | 20.000 | 32.000 | 24.615 |
Formula Used
1. Adjust dimensions for margins
L′ = L + 2Mx and W′ = W + 2My
2. Calculate adjusted area and perimeter
A = L′ × W′ and P = 2(L′ + W′)
3. Sterling equivalent square relation
Equivalent Square = 4A / P = 2L′W′ / (L′ + W′)
4. Optional corrected result
Corrected Equivalent Square = Equivalent Square × Correction Factor
The main relation converts a rectangular field into a square field with similar scatter behavior. It is widely used for quick planning comparisons. The correction factor is optional. Leave it at 1.0 when no local adjustment is needed.
How to Use This Calculator
- Enter the rectangular field length and width.
- Select the working unit for your numbers.
- Add X and Y margins if each side expands.
- Keep the correction factor at 1.0 unless needed.
- Choose the number of decimal places.
- Press the calculate button.
- Review the result summary and Plotly graph.
- Export the result or example table as CSV or PDF.
Frequently Asked Questions
1. What is an equivalent square field size?
It is the side length of a square field that behaves similarly to a rectangular field under the selected approximation. It helps compare field geometry using one simpler number.
2. Which formula does this calculator use?
This page uses the Sterling relation. It computes equivalent square as 4A divided by P, or 2LW divided by L plus W, after any margins are applied.
3. Why are margins included?
Margins let you model expanded field dimensions before calculating the equivalent square. This is useful when practical planning dimensions differ from the original opening.
4. What does the correction factor do?
The correction factor scales the equivalent square result. Keep it at 1.0 for the base formula. Change it only when your workflow requires an extra local adjustment.
5. Which units can I use?
You can use centimeters, millimeters, or inches. The calculator converts values internally, then returns the result in the selected output unit.
6. Why is the graph useful?
The graph shows how equivalent square changes as adjusted width changes. It helps you see sensitivity, compare shapes, and spot trends beyond one single calculation.
7. Is this result the same as the geometric mean?
No. The geometric mean is the square root of area. Equivalent square comes from area and perimeter together, so both measures can differ for the same rectangle.
8. Can I export the outputs?
Yes. You can export the result summary and the example data table as CSV or PDF files directly from the buttons on this page.