Volume to Cylinder

Horizontal Cylinder Volume

A horizontal cylinder lies on its side — the circular cross-section is vertical and the length runs left to right. Total volume is the same as any cylinder: V = πr²L. But partial fill calculations are different from vertical tanks, and this tool handles both.

Horizontal Cylinder Volume

V = πr²L
L (Length) r

What is Horizontal Cylinder Volume?

V = πr²L (total)

Horizontal Cylinder Volume is a calculator for cylinders that lie on their side — where the circular cross-section is vertical and the length runs horizontally. This tool exists because while total volume is the same regardless of orientation (V = πr²L), partial fill calculations for horizontal tanks are significantly more complex than for vertical ones.

When a horizontal cylinder is partially filled, the liquid forms a circular segment shape, not a simple rectangle. Calculating this requires trigonometry (arccos) and the circular segment formula. This calculator handles that complexity automatically.

This tool is essential for fuel tank operators, propane tank owners, tanker truck drivers, and anyone with a horizontal storage tank who needs to know how much liquid is inside at any given fill level.

Horizontal Cylinder Volume Formula

Partial fill is complex

When a horizontal cylinder is partially filled, the liquid forms a circular segment in the cross-section. The volume of liquid at depth h (measured from the bottom) is:

V = L × [r² × arccos((r−h)/r) − (r−h) × √(2rh − h²)]

This is more complex than a vertical tank (where partial volume is simply πr²h). The curved bottom means the fill rate is nonlinear — the tank fills slowly at the bottom and top, and fastest in the middle.

At h = r (half full), the volume is exactly πr²L / 2.

Applications of Horizontal Cylinders

r Propane • Fuel • Water

Horizontal cylindrical tanks are common for fuel storage (propane, diesel, gasoline), water transport, and industrial liquid storage. They're chosen over vertical tanks when head clearance is limited or when the tank needs to sit on a trailer.

Hot water cylinders in some countries are mounted horizontally. Tanker trucks carry liquid in horizontal cylindrical tanks. Underground fuel storage tanks at gas stations are typically horizontal.

The lower center of gravity of a horizontal tank makes it more stable during transport.

Cylinder Volume Calculators

Specialized tools for every cylinder volume scenario — pick the one that matches your measurement.

🧪 Volume in Litres ⛽ Volume in Gallons 💉 Volume in Milliliters 🥤 Volume to Ounces 📏 Using Diameter 📐 Using Radius 🔵 By Circumference ⬡ From Area 🎨 From Surface Area 📝 Derivation ∫ Using Integration 🔧 Measurement Guide 🛢️ Tank Calculator ⭕ Hollow Cylinder 🔷 Right Cylinder ↔️ Horizontal Cylinder ↕️ Vertical Cylinder 🔺 Cylinder vs Cone 🌐 Cylinder vs Sphere ⚖️ Volume to Weight ❓ Without Height ❔ Without Radius 🔲 Without Top & Bottom

Frequently Asked Questions

Is the volume of a horizontal cylinder different from a vertical one?
No. Total volume is V = πr²L regardless of orientation. Only partial fill calculations differ.
How do I calculate how much liquid is in a horizontal tank?
Measure the liquid depth h from the bottom. Use V = L × [r² × arccos((r−h)/r) − (r−h) × √(2rh − h²)]. This calculator does it for you.
At what depth is a horizontal cylinder half full?
At h = r (the liquid level equals the radius). At this point, the cross-section is a semicircle and the volume is exactly half the total.
Why do fuel tanks lie horizontally?
Horizontal tanks have a lower center of gravity (safer for transport), fit under low clearances, and can be partially buried underground. They're also easier to load onto trailers.
How do I measure the liquid level in a horizontal tank?
Use a dipstick inserted vertically through the top of the tank. The wetted length is the liquid depth h. Some tanks have sight glasses or electronic level sensors.