How is a horizontal cylinder's partial fill calculated?

The liquid forms a circular segment in the end view. The area is r² × acos((r−h)/r) − (r−h) × √(2rh − h²), where h is the fill depth, and that area is multiplied by the tank length. This is why a quarter-depth horizontal tank holds far less than a quarter of its volume.

Why use inside dimensions?

Tank capacity is the volume the fluid occupies, so wall thickness must be excluded. Using outside dimensions overstates the volume, which matters for chemical dosing, expansion-tank sizing, and water storage where accuracy counts.

How do gallons and liters convert?

All math is done in cubic inches, then converted: one US gallon is 231 cubic inches, one imperial gallon is 277.419 cubic inches, and one liter is 61.0237 cubic inches. The tool shows all three units at once.

What is the cone formula?

A full cone holds one third of its bounding cylinder: V = (1/3) π r² h. For a point-down cone filled to depth d, the radius scales linearly with depth, so the partial volume is (1/3) π (r d / h)² d.

Can I use this for an expansion tank?

Yes for the geometric volume. Note that diaphragm expansion tanks have an air bladder, so the usable water volume is less than the geometric volume. Use the geometric figure as the tank shell capacity and apply the manufacturer's acceptance factor for water.

Tank Volume Calculator

This calculator finds the exact volume of a storage tank from its shape and dimensions, in US gallons, imperial gallons, and liters. It handles full tanks and partial fills — including the tricky horizontal-cylinder case — so you can size storage, hot-water, and expansion tanks accurately.

How it works

Each shape uses its exact geometric formula. All math runs in cubic inches and is then converted to the three volume units.

Vertical cylinder:  V = π r² h
Rectangular box:    V = L × W × H
Cone (point down):  V = (1/3) π r² h
Sphere:             V = (4/3) π r³

Partial fills are where it gets interesting. For a sphere filled to depth h, the spherical-cap volume is π h² (3r − h) / 3. For a horizontal cylinder, the liquid cross-section is a circular segment:

A = r² · acos((r − h)/r) − (r − h)·√(2rh − h²)
V = A × tank length

This is why a half-full horizontal tank is exactly 50%, but a quarter-depth tank holds noticeably less than 25% of capacity.

Unit conversions

Unit	Cubic inches
1 US gallon	231
1 imperial gallon	277.419
1 liter	61.0237

Notes

Always enter inside dimensions — wall thickness reduces usable capacity. For diaphragm expansion tanks the geometric volume is the shell size, not the usable water volume, which depends on the bladder acceptance factor. The horizontal-cylinder partial fill uses the exact circular-segment area, so it is accurate at any depth from empty to full. All calculation runs locally in your browser.