Volume Formulas Cheat Sheet — Tank, Pipe, Pond & Cube

Look at the cross-section of your tank. If it is a perfect circle, use the cylinder formula πr²H. If it is a rectangle or square box, use L×W×H. If it is an oval or stadium shape (like most heating-oil tanks), you need the ellipsoid or 'stadium cross-section' formula. If the tank sits on legs with a sloped cone bottom, calculate the cylindrical shell and cone bottom separately then add them. The main tank calculator on the home page lets you pick the shape from a dropdown and applies the correct formula automatically, including partial fill for horizontal cylinders where depth-to-volume is non-linear.

One US liquid gallon is defined as exactly 231 cubic inches — this is not an approximation, it is the legal definition. So divide your cubic-inch volume by 231 to get US gallons. For liters, divide by 61.024. For cubic feet, divide by 1,728 (12³) first, then multiply by 7.48. Imperial gallons are slightly larger — 277.42 cubic inches — so an imperial gallon is about 1.2 US gallons. Always confirm which gallon system your supplier or specification sheet is using, because the difference on a large tank can be significant.

The total capacity formula is the same — πr²L for horizontal, πr²H for vertical. But when the tank is partially filled, the cross-section matters. A vertical cylinder has a constant circular cross-section at every height, so fill depth and filled volume are perfectly linear — half depth equals half gallons. A horizontal cylinder has the same circular cross-section, but the depth runs across the diameter instead of along the axis, creating a non-linear partial-fill curve: 25% depth ≈ 19.6% volume, 50% depth = 50% volume (the only symmetric point), and 75% depth ≈ 80% volume. This is why dip charts for horizontal tanks must be computed point by point using the circular-segment formula — you cannot just divide total gallons by diameter.

A cone has a circular base that tapers to a single point (V = πr²H/3). A truncated cone (frustum) is a cone with the tip cut off, leaving two parallel circular faces of different radii (V = πH(R² + Rr + r²)/3). A pyramid has a polygonal base (square, rectangle, triangle) instead of a circle, and also tapers to a point (V = base area × H/3). Tank hoppers and silos are usually truncated cones — the top is open for filling, the bottom narrows to a discharge port. Calculate the frustum for the tapered section and add the cylindrical shell above it for the full tank.

Break the shape into simpler pieces. An oval pond is an ellipse at the surface — V = π × a × b × average_depth where a and b are the semi-major and semi-minor axes. A kidney-shaped pond can be approximated as two circles of different radii connected by straight sides — calculate each section separately. For any irregular shape, the average depth method works: measure depth at a grid of points, average them, multiply by the surface area. For pools with sloped bottoms (deep end + shallow end), calculate the shallow rectangle and the sloped wedge or truncated cone separately. The home page calculator has a pond section that does this math for common shapes.

Yes — compute the volume in gallons or liters, then multiply by the liquid's density in lb/gal or kg/L. Water is exactly 8.34 lb per US gallon and 1 kg per liter. Diesel fuel is about 7.0 lb/gal (SG 0.84), gasoline about 6.2 lb/gal (SG 0.74), and seawater is 8.5 lb/gal. Multiply the total gallons by the density to get the contents weight. The liquid weight calculator on this site does this bidirectionally and handles temperature-corrected water density. Remember the tank itself also weighs — steel runs about 490 lb per cubic foot, stainless about 500 lb/ft³, and aluminum about 169 lb/ft³. The tank weight calculator pairs with this sheet for shell mass.

Always — the formulas give geometric volume, but wall thickness eats into the usable space. For a tank with inner diameter D and wall thickness t, the actual inner diameter is D - 2t. For an aquarium with 6 mm (1/4 in) glass, a 48 × 24 × 18 inch advertised tank has inner dimensions of roughly 47 × 23 × 17.25 inches, yielding about 83 gallons instead of the 90 gallons a pure box formula would suggest. For steel tanks the effect is smaller — a 275 gal heating-oil tank with 3/16 inch steel loses only about 2% of capacity to wall thickness — but it still matters for certified dip charts and fill calculations. Always measure inside dimensions when you can.

231 cubic inches per US gallon is the direct inch-to-gallon conversion. 7.48052 US gallons per cubic foot is the foot-to-gallon conversion. These are related because a cubic foot is 12×12×12 = 1,728 cubic inches, and 1,728 ÷ 231 = 7.48052. Both are exact definitions — 231 cubic inches per gallon has been the US standard since 1707, and the cubic foot is defined as exactly 12³ cubic inches. Use inches for small tanks and lab equipment, feet for large industrial tanks and ponds, and convert between them using these two constants.