🛢️ Horizontal Cylinder Fill Calculator
Calculate volume of partially filled horizontal cylinders and tanks
Enter Tank Dimensions & Fill Level
r = radius, L = length, f =
fill height
📊 Results
Tank Radius
50 cm
Tank Diameter
100 cm
Tank Length
200 cm
Fill Height
30 cm
Fill Volume
451 L
Total Capacity
1,571 L
Fill %
28.7%
Empty Space
1,120 L
📝 Step-by-Step Solution
Given: r = 50 cm, L = 200 cm, f = 30 cm
Segment angle: θ = 2 × arccos((r - f) / r)
Segment area: A = r² × (θ - sin(θ)) / 2
Fill volume: V = A × L
Fill volume = 451,327 cm³ = 451.3 L
📐 Horizontal Cylinder Fill Formulas
Segment Angle: θ = 2 × arccos((r - f) / r)
Segment Area: A = r² × (θ - sin(θ)) / 2
Fill Volume: V = A × L = L × r² × (θ - sin(θ)) / 2
Total Capacity: Vtotal = πr²L
Fill %: (Vfill / Vtotal) × 100
Understanding Partial Fill
🛢️ Horizontal Tanks
Lying down cylinders. Common for fuel tanks, water storage, chemical tanks. Fill level measured from bottom.
📐 Circular Segment
Cross-section is a segment. Not a simple rectangle. Uses arccos and segment area formula for accurate volume.
💧 Non-Linear Fill
Volume doesn't scale linearly with height. At 50% height, volume is exactly 50%. At 25% height, less than 25% full.
📏 Measuring Fill Level
Use dipstick or gauge. Measure from tank bottom to liquid surface. Compare to tank diameter.
Frequently Asked Questions
How do I calculate partial cylinder volume?
Use segment formula: V = L × r² × (θ - sin(θ)) / 2, where θ = 2 ×
arccos((r-f)/r). f = fill height from bottom.
Why isn't partial fill linear?
Circular cross-section. At bottom/top, small height changes =
small volume changes. Middle section changes fastest.
What is a circular segment?
Area between chord and arc. When tank is partially filled, liquid
forms a segment shape in cross-section.
How do I find fill height from volume?
Requires iteration. No direct formula. Our calculator uses
numerical methods to find the height that gives your target volume.
Is 50% fill height = 50% volume?
Yes, exactly 50%. This is unique to cylinders. At the center line,
both height and volume are at 50%.
What about tank end caps?
This calculator uses flat ends. For domed/spherical ends,
additional volume calculations are needed.
Can I use diameter instead of radius?
Yes, divide by 2. r = d/2. Our calculator works with radius for
the formula.
How do I convert to gallons?
1 US gallon = 3.785 liters. Our calculator can output in gallons
directly.
What is the dipstick reading?
Fill height (f). Measure from tank bottom to liquid surface. Same
as "fill level" in our calculator.
How accurate is this for fuel tanks?
Very accurate for cylinder portion. Real tanks have end caps,
baffles, that affect actual capacity slightly.
Can f be greater than r?
Yes, up to 2r (diameter). f > r means more than half full. f = 2r
means completely full.
What units should I use?
Consistent units. If radius in cm, length and fill height in cm
too. Volume converts automatically.
How do I measure tank dimensions?
Diameter: measure across end. Length: measure
cylinder length. Divide diameter by 2 for radius.
Why use arccos in the formula?
To find central angle. Arccos((r-f)/r) gives half the angle
subtended by the liquid segment at the center.
Does orientation matter?
Yes. This is for HORIZONTAL tanks. Vertical cylinders use simple
πr²h formula for partial fill.
What is empty space volume?
Total capacity minus fill volume. How much more liquid can be
added before tank is full.
Can I calculate for sloped tanks?
This assumes level surface. Tilted tanks have uneven fill and
require more complex calculations.