🥚 Ellipsoid Volume Calculator
Calculate volume or axes of ellipsoids, spheroids, and 3D elliptical shapes
Enter Three Semi-Axes
a, b, c
= semi-axes
📊 Results Triaxial Ellipsoid
Semi-axis a
6 cm
Semi-axis b
4 cm
Semi-axis c
3 cm
Volume
301.6 cm³
Surface Area ≈
201 cm²
Dimns (2a×2b×2c)
12×8×6
📝 Step-by-Step Solution
Given: a = 6 cm, b = 4 cm, c = 3 cm
Volume formula: V = (4/3)πabc
V = (4/3) × π × 6 × 4 × 3
V = (4/3) × π × 72 = 301.59 cm³
Type: Triaxial ellipsoid (all axes different)
📐 Ellipsoid Formulas
Volume: V = (4/3)πabc
Find axis: a = 3V / (4πbc)
Surface Area (approx): A ≈
4π((apbp+apcp+bpcp)/3)1/p,
p≈1.6
Sphere (a=b=c=r): V = (4/3)πr³
Ellipsoid Types
🔵 Sphere
a = b = c. All axes equal. Special case. V = (4/3)πr³. Most symmetric ellipsoid.
🥏 Oblate Spheroid
a = b > c. Flattened at poles like Earth. Equatorial axes equal, polar axis shorter.
🏈 Prolate Spheroid
a = b < c. Elongated like rugby ball. Equatorial axes equal, polar axis longer.
🥚 Triaxial Ellipsoid
a ≠ b ≠ c. All three axes different. Most general case. Egg-like shapes.
Frequently Asked Questions
What is the volume formula for an ellipsoid?
V = (4/3)πabc. Product of semi-axes times (4/3)π. Same structure
as sphere formula but with three different radii.
What are semi-axes a, b, c?
Half the full dimensions. Like radii in each direction. a = half
of x-width, b = half of y-width, c = half of z-height.
How do I find a semi-axis from volume?
a = 3V / (4πbc). Rearrange the formula. Need volume and the other
two axes.
What is a spheroid vs ellipsoid?
Spheroid = two axes equal. Special case of ellipsoid. Oblate
(flat) or prolate (elongated). Ellipsoid = general term for all three.
What is an oblate spheroid?
Flattened sphere. a = b > c. Equator bulges, poles flattened.
Example: Earth is slightly oblate.
What is a prolate spheroid?
Elongated sphere. a = b < c. Stretched along one axis. Examples:
rugby ball, watermelon.
How do I calculate surface area?
No simple exact formula. Approximation: A ≈ 4π((a^p·b^p + a^p·c^p
+ b^p·c^p)/3)^(1/p), where p ≈ 1.6075.
Is Earth an ellipsoid?
Yes, oblate spheroid. Equatorial radius ~6378 km, polar radius
~6357 km. Flattening ratio about 1:298.
What if all axes are equal?
It's a sphere. V = (4/3)πr³. Most symmetric 3D shape. Special case
of ellipsoid.
How do I convert to liters?
1 L = 1000 cm³. Our calculator can output in liters, gallons, or
other units.
What is triaxial ellipsoid?
All three axes different. a ≠ b ≠ c. Most general form. Scalene
ellipsoid. Example: irregular egg.
How does doubling an axis affect volume?
Doubles volume. V is proportional to each axis. Double all three =
8× volume.
What are real-world ellipsoid examples?
Eggs, planets, cells, pebbles, pills. Many natural and
manufactured objects approximate ellipsoids.
How accurate is the surface area formula?
Within ~1% for most ellipsoids. Exact formula requires elliptic
integrals. Approximation is sufficient for practical use.
Can I use full axes instead of semi-axes?
Yes, divide by 2. If given full dimensions (length, width,
height), each semi-axis = dimension / 2.
What is eccentricity of ellipsoid?
Measures deviation from sphere. e = √(1 - c²/a²) for oblate. Value
0 = sphere, approaching 1 = very flat.
How accurate is this calculator?
Volume is exact. Surface area uses approximation formula accurate
to ~1%. Uses π to full precision.