How pool volume is calculated

Standard Geometry Models

For pools with regular geometric shapes, we apply exact analytical formulas: Rectangular: V = L × W × D_avg Circular: V = π × r² × D_avg Oval: V = π × (L/2) × (W/2) × D_avg Kidney/Figure-8: Composite ellipse model with empirical shape factors The average depth (D_avg) accounts for the floor profile - flat, constant slope, hopper bottom, or spoon-shaped - each requiring different averaging methods.

Depth Profile Integration

Most pools have non-uniform depth profiles. Simply averaging the shallow and deep end depths introduces significant error for pools with hopper bottoms or multi-slope floors. Our model divides the pool into longitudinal sections and applies the trapezoidal rule (numerical integration) to compute the true volume under the depth profile curve. For common profiles: • Constant slope: Exact prismoidal formula (no approximation needed) • Hopper bottom: Piecewise linear integration over 3 zones (shallow flat, transition slope, deep flat) • Spoon shape: Cubic spline interpolation between measured depth points • Multi-depth: Composite integration for pools with benches, steps, or ledges

• Prismoidal formula for linearly-varying cross-sections
• Trapezoidal numerical integration for arbitrary depth profiles
• Step/bench volume subtraction for pools with built-in seating
• Spa spillover volume addition for pool/spa combinations

Freeform Pool Estimation

Freeform pools with curved, irregular boundaries cannot be computed with simple formulas. For these shapes, we offer two approaches: 1. Grid method: The pool surface is overlaid with a fine grid, and the area is estimated by counting grid squares that fall within the boundary (Monte Carlo integration principle). 2. Polygon approximation: The user traces the pool outline as a polygon, and the Shoelace formula computes exact area. Combined with depth information, this can give a useful estimate for many freeform pools.

Unit Conversions & Practical Outputs

Volume results are provided in multiple units simultaneously: • Litres (primary unit for Australian chemical dosing) • Cubic metres (for water billing calculations) • Gallons, US and Imperial (for equipment rated in gallons) Additionally, the calculator provides derived values useful for other tools: surface area (for evaporation and cover sizing), water mass (for heating calculations), and recommended turnover flow rate.