Ellipsoid Volume Calculator

Geometry

Ellipsoid volume and Knud Thomsen surface area

Quick Answer

Ellipsoid Volume Calculator: Ellipsoid volume and Knud Thomsen surface area. Volume: V = 4πabc/3 (semi-axes a, b, c).

Enter any one value, the rest auto-solve

Semi-axis a

Semi-axis b

Semi-axis c

Volume Vauto

Surface area S≈auto

Diagram (updates live with input)

Step-by-step

V = (4/3)πabc = (4/3)π × 6.0000 × 4.0000 × 3.0000 = 301.5929

S ≈ 4π·((a^p·b^p + a^p·c^p + b^p·c^p)/3)^(1/p)，p = 1.6075（Knud Thomsen 近似）= 231.2760

同体积球半径 = ∛(abc) = 4.1602

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How to Use

Enter known values: fill sides, radius or angles in the Ellipsoid Volume Calculator.
Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
See formula and steps: the result panel shows the formula used and the substitution.
Try another case: change any known value to solve again.

Key Points

Ellipsoid Volume Calculator is a free online geometry tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Ellipsoid volume and Knud Thomsen surface area.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Ellipsoid math

Volume: V = 4πabc/3 (semi-axes a, b, c)

Surface (Knud Thomsen): S ≈ 4π[(aᵖbᵖ+aᵖcᵖ+bᵖcᵖ)/3]^(1/p), p = 1.6075, error <1.1%

a=b=c=R gives the sphere V = 4πR³/3

Earth is an oblate ellipsoid: a=b≈6378 km, c≈6357 km

Example: egg a=3, b=c=2.2 cm → V ≈ 60.8 cm³; Earth's volume ≈ 1.083×10¹² km³.

FAQ

How do I use the Ellipsoid Volume Calculator?

Open the page and fill in the input fields — results update automatically. Ellipsoid volume and Knud Thomsen surface area.

Are the results accurate?

Yes. Standard formulas and conversion factors are used and verified.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. Everything runs locally in your browser.

Related Guides

Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated: 2026-08-07

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Ellipsoid Volume Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/ellipsoid

Results provided by this tool are for reference only and do not constitute professional advice.