🛢️ Elliptical Tank Calculator
Volume, capacity, axes, and perimeter of oval-shaped tanks
Enter Tank Dimensions
a = semi-major, b =
semi-minor, L = length
📊 Results
Semi-major (a)
40 cm
Semi-minor (b)
25 cm
Full Width (2a)
80 cm
Full Height (2b)
50 cm
Length (L)
150 cm
Volume
471.2 L
Cross-Section
3,142 cm²
Perimeter ≈
206 cm
📝 Step-by-Step Solution
Given: a = 40 cm, b = 25 cm, L = 150 cm
Cross-section area: A = πab = π × 40 × 25 = 3,141.59 cm²
Volume: V = πabL = π × 40 × 25 × 150 = 471,239 cm³
Volume = 471.24 Liters
Perimeter ≈ π(3(a+b) - √((3a+b)(a+3b))) ≈ 206.2 cm
📐 Elliptical Tank Formulas
Volume: V = πabL
Cross-Section Area: A = πab
Perimeter (Ramanujan): P ≈ π(3(a+b) - √((3a+b)(a+3b)))
Find axis: a = V / (πbL), b = V / (πaL), L = V / (πab)
Understanding Elliptical Tanks
🛢️ Oval Cross-Section
Elliptical tanks have oval ends. Common in fuel trucks, storage tanks, septic tanks. Calculated as prism with ellipse base.
📐 Two Axes
a = semi-major (half of wider dimension). b = semi-minor (half of narrower dimension). a ≥ b always.
📏 Volume = πabL
Ellipse area × length. Same principle as cylinder (πr²h) but with two different radii.
⭕ Perimeter
No exact formula for ellipse perimeter. Ramanujan's approximation is accurate to ~0.04% for most shapes.
Frequently Asked Questions
What is the volume formula for an elliptical tank?
V = πabL. Pi times semi-major axis times semi-minor axis times
length. Cross-section area multiplied by length.
What are semi-major and semi-minor axes?
Half the full dimensions. a = half of width (larger), b = half of
height (smaller). If width is 80cm, a = 40cm.
How do I convert to gallons?
1 US gallon = 3.785 liters. Our calculator can output directly in
gallons. Or divide liters by 3.785.
How do I find tank length from volume?
L = V / (πab). Divide volume by ellipse cross-section area. Need
both semi-axes.
How do I calculate ellipse perimeter?
Ramanujan's approximation: P ≈ π(3(a+b) - √((3a+b)(a+3b))).
Accurate within 0.04%.
What if a = b?
It's a cylinder. Ellipse becomes circle. V = πr²L. Our formulas
still work correctly.
Is this for horizontal or vertical tanks?
Horizontal orientation typically. L is along the ground. For
vertical, L becomes height. Formula is same.
How do I measure an elliptical tank?
Measure full width and height at end. Divide each by 2 for
semi-axes. Measure length along the tank.
What is cross-sectional area used for?
The ellipse end face. A = πab. Used for volume, flow calculations,
structural analysis.
How accurate is this calculator?
Volume is exact. Perimeter uses approximation accurate to ~0.04%.
Real tanks may have slight manufacturing variations.
What is an obround tank?
Similar but different. Obround = rectangle with semicircle ends
(like a stadium). Elliptical = true ellipse shape.
Can I calculate partial fill?
More complex. For horizontal elliptical tank partial fill, need
integral calculus. Not a simple formula.
What about tank ends (heads)?
This assumes flat ends. Domed or dished ends add additional
volume. Consult manufacturer specs.
How do I find the major axis from volume?
a = V / (πbL). Need volume, minor axis, and length. Rearrange the
main formula.
What is the eccentricity?
e = √(1 - b²/a²). Measures how elongated the ellipse is. e = 0 is
circle, approaching 1 is very flat.
Where are elliptical tanks used?
Fuel tanker trucks, propane tanks, septic tanks, oil storage.
Lower center of gravity than circular.
How does doubling dimensions affect volume?
Doubling a or b: 2× volume. Doubling L: 2× volume. Doubling all
three: 8× volume.