Ellipsoid Volume Calculator

Online ellipsoid volume calculator supporting input of three semi-axis parameters and dynamic 3D ellipsoid display, suitable for advanced geometry calculations.

Bug report

Browser execution mode: Your data is processed in your browser and is not uploaded to the server.

Speed and Stability: Processing speed depends on your device and browser. For large batch work, the desktop version may be more stable.

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If the online tool fails to load or run, try the desktop tool.https://tools.yikeaigc.com/

Tool Usage

Return to old version

Set semi-axis values, then calculate volume and view the diagram

Enter the three perpendicular ellipsoid semi-axes a, b, and c to calculate volume, approximate surface area, axis ratios, equivalent sphere radius, and copyable steps.

Volume formula: V = 4/3 x pi x a x b x c Supports spheres and spheroids Settings can be saved locally

Common formulas

体积：V = (4 / 3) x pi x a x b x c
三轴表面积：Knud Thomsen 近似公式
旋转椭球表面积：按长扁旋转椭球分别计算

Note: A general ellipsoid has no simple elementary closed-form surface area. For unequal axes, this tool gives a common engineering approximation and marks it in the results.

Parameters

Choose unit and precision first, then enter the three semi-axis lengths. Values must be greater than 0.

Awaiting input

Semi-axis a

Radius along X axis

Semi-axis b

Radius along Y axis

Semi-axis c

Radius along Z axis

Units and display

Length unit

Decimal places

Assist mode Sphere mode, keep a = b = c Spheroid, keep b = c Show formulas and steps

Sample data

a = 6 cm b = 4 cm c = 3 cm

Ellipsoid volume -

Surface area -

Axis ratio a:b:c -

Diameters 2a, 2b, 2c -

Equivalent sphere radius -

Calculation steps

Enter parameters and click Calculate.

Conversion item	Result
Awaiting calculation	-

计算结果将在这里生成，便于复制到作业、论文或记录表。

Instructions

Software Usage Instructions

Set the semi-axis parameters: Enter the three semi-axes a, b, and c of the ellipsoid in the parameter area. The values must be greater than 0 and use the same length unit.
Select the unit and precision: Choose mm, cm, m, in, ft, or yd, and control the result display with the number of decimal places.
Select an auxiliary mode: Sphere mode keeps a=b=c; spheroid mode keeps b=c; for a general triaxial ellipsoid, you can directly enter the three semi-axes separately.
Use sample data: Click the sphere, prolate ellipsoid, oblate ellipsoid, or triaxial ellipsoid examples to quickly view calculation results for different shapes.
Start calculating: After clicking “Calculate Volume,” the tool will generate the volume, surface area, axis ratios, diameters, equivalent sphere radius, and unit conversion results.
View and export: Drag the 3D diagram to view the shape, copy the calculation results, or download the ellipsoid diagram.
Save settings: Click “Save Settings” to keep the current semi-axes, unit, precision, and display options for continued use next time.

FAQ

A: The ellipsoid volume formula is V=(4/3)×π×a×b×c, where a, b, and c are the semi-axis lengths in three mutually perpendicular directions.

A: A semi-axis is half of the diameter in the corresponding direction. The volume formula uses semi-axes. If you have measured the diameters in three directions, divide each by 2 before entering them.

A: A general triaxial ellipsoid usually has no simple elementary formula for surface area, so the tool uses the Knud Thomsen approximation; when the shape is a sphere or a spheroid, it is calculated using the corresponding formula.

A: No. The volume is determined by the product of a, b, and c, so changing their order does not change the volume; however, the order affects how each direction is displayed in the 3D diagram.

A: The equivalent sphere radius represents the radius of a sphere with the same volume as the current ellipsoid. It is calculated as r=∛(a×b×c), making it easier to compare ellipsoids and spheres.

A: Common causes include entering diameters instead of semi-axes, using inconsistent units for the three parameters, or displaying too few decimal places. It is recommended to first confirm what the measured values represent, then convert them to consistent units before calculating.