Rain Garden Size Calculator: equations, variables, units and worked solution

The rain garden size calculator calculates Rain Garden Size — required size from Drainage Area, Runoff Coefficient, Design Rain, Ponding Depth. It does not hide the arithmetic: the result panel shows the governing formula, canonical-unit conversion, numeric substitution, unrounded evaluation and final rounded answer for every output.

Variables and measurement units

For the Rain Garden Size Calculator, Drainage Area, Runoff Coefficient, and Design Rain are normalized to m², ratio, and m before drainageArea*runoffCoefficient*designRain/pondingDepth is evaluated. The unrounded value used for Rain Garden Size — required size is retained internally; formatting is applied only to the result cards.

Formula model

Primary scientific relationship: drainageArea*runoffCoefficient*designRain/pondingDepth.

Formula-based worked derivation

1. Rain Garden Size — required size
   1. Formula: Rain Garden Size — required size = drainageArea × runoffCoefficient × designRain ÷ pondingDepth
   2. Default substitution: Rain Garden Size — required size = (2000) × (0.8) × (1) ÷ (0.5)
   3. Unrounded evaluation: 3200 ft²
   4. Displayed answer: 3200 ft²

In the Rain Garden Size Calculator, changing Drainage Area, Runoff Coefficient, and Design Rain rebuilds the numeric substitution for drainageArea*runoffCoefficient*designRain/pondingDepth. The engine converts selected measurements to m², ratio, and m, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify Rain Garden Size — required size with a numerical residual.

Input and output interpretation

Use measured or documented values for Drainage Area, Runoff Coefficient, Design Rain, Ponding Depth. The calculated outputs are Rain Garden Size — required size. Check each intermediate line before relying on the final value; an implausible intermediate quantity usually identifies a unit, range or assumption error.

Algorithm and verification

The Rain Garden Size Calculator uses its own `rain-garden-size` JavaScript engine to calculate Rain Garden Size — required size from Drainage Area, Runoff Coefficient, and Design Rain with drainageArea*runoffCoefficient*designRain/pondingDepth. Calculator-owned boundary and mode tests check that workflow; an external frozen-reference oracle checks the numeric outputs, and physical source mutation testing confirms that a changed `rain-garden-size` engine is rejected.

Visual interpretation

In the Rain Garden Size Calculator, this guidance applies to Drainage Area, Runoff Coefficient, and Design Rain and the reported Rain Garden Size — required size. The `rain-garden-size` workflow evaluates drainageArea*runoffCoefficient*designRain/pondingDepth in m², ratio, and m; Laboratory, environmental and treatment decisions require validated methods, calibrated instruments and qualified review.. Verification context: dbdd42.

Dimensional formula audit

The rain garden size calculator normalizes drainageArea (Drainage Area, m²), runoffCoefficient (Runoff Coefficient, ratio), designRain (Design Rain, dimensionless), pondingDepth (Ponding Depth, m) before evaluating the equations. Its reported quantities are Rain Garden Size — required size in ft². This separation matters because a numerical value without its measurement dimension can produce a plausible-looking but physically or financially incorrect answer. Conversion factors are applied before substitution, and output conversion occurs only after the canonical result has been calculated at full precision.

• Rain Garden Size — required size = drainageArea × runoffCoefficient × designRain ÷ pondingDepth

Formula sensitivity and boundary verification

To verify the rain garden size calculator, hold all other inputs fixed and change drainageArea within its permitted range. The live substitution line shows exactly where that value enters the equation for Rain Garden Size — required size. Repeat the check with runoffCoefficient. The result must follow the displayed algebra, remain finite, and retain the stated output unit. At minimum and maximum boundaries, the validator rejects undefined domains, impossible denominators and nonphysical values rather than silently returning a number.

Manual reproduction of the result

For an independent hand check, first convert every selected unit to the canonical units shown in the variable table. Next copy the governing equation, replace each symbol with the canonical value shown in the live derivation, and calculate the intermediate expression without early rounding. Finally round only once to the displayed precision and compare both the numerical value and unit with the calculator card. This process makes the rain garden size calculator reproducible instead of relying on an unexplained result.

Limitations

For the Rain Garden Size Calculator, Laboratory, environmental and treatment decisions require validated methods, calibrated instruments and qualified review.. The calculator applies drainageArea*runoffCoefficient*designRain/pondingDepth to Drainage Area, Runoff Coefficient, and Design Rain and reports Rain Garden Size — required size; confirm the real-world data, code, product specification, or professional standard before acting on a consequential result.