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Volume of a Roman pool

Calculate the volume of a Roman pool (rectangle with curved semicircular ends) in gallons or litres. Free.

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The formula

(Length × Width + π × (Width ÷ 2)²) × Average Depth × 7.48 = US gallons

Worked example

A Roman pool has a rectangular middle with two rounded (semicircular) ends. With a 30 ft straight run and 15 ft width, the area is 30 × 15 plus a full circle of the two ends (π × 7.5² ≈ 177), so about 627 sq ft. At 5 ft average depth that's ≈ 23,450 gallons. We model the curved ends exactly rather than using a rough multiplier.

This calculator uses the precise cubic-foot-to-gallon value (about 7.48 US gallons per cubic foot) for your Roman pool and lets you switch between US gallons, imperial gallons, litres, and cubic metres.

How to calculate Roman pool volume step by step

You will need these measurements:

  1. Measure the straight length, width, and depth. A Roman pool is a rectangle with two semicircular ends. Measure the straight rectangular run (length), the width, and the average depth.
  2. Add the rectangle and the two end caps. The two semicircular ends together form one full circle of diameter = width. Surface area = (Length × Width) + π × (Width ÷ 2)².
  3. Multiply by depth, then convert. Volume in cubic feet = surface area × depth. Multiply by 7.48 for US gallons.
Worked example

A Roman pool 28 ft long, 16 ft wide, 5 ft deep: (28 × 16) + π × 8² = surface area, × 5 = 3,245 cubic feet, then × 7.48 ≈ 24,277 US gallons.

How a Roman pool's curved ends are calculated

A Roman pool is a rectangle with two semicircular ends — the classic 'stadium' or discorectangle outline. The two semicircular ends together make one full circle whose diameter equals the pool width, so the area is the rectangle (straight length × width) plus a full circle of radius width ÷ 2. The measurement to get right is the straight length: measure only the rectangular run between where the curves begin, not the overall length including the rounded ends, or you'll double-count the curved area. The width doubles as the diameter of each semicircular end. Don't confuse a Roman with a Grecian (straight cut corners) or a true oval (a continuous ellipse) — all three use different formulas.

Questions

Common answered

A Roman pool is a rectangle with two semicircular ends, also called a stadium shape. The curved ends together form a full circle of diameter equal to the pool width.
Add the rectangle (straight length × width) to a full circle of radius equal to half the width. The two semicircular ends combine into that one circle.
Measure only the straight rectangular run between where the curves begin. The curved ends are added separately as a circle, so including them in the length would double-count.
A Roman has a straight middle section with semicircular ends; an oval is a continuous ellipse with no straight sides. Their area formulas are different.
It depends on the straight length and width, but a 28 ft × 16 ft Roman holds roughly 17,000 gallons at 5 ft average depth. Enter your dimensions above for an exact figure.