Frustum Volume Calculator

Online frustum volume calculator that supports input of the upper and lower base radii and height, with 3D frustum visualization and surface area calculation.

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.

Loading tool, please wait...

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

Tool Usage

Return to old version

Set parameters first, then view results and net

Enter top radius, bottom radius, and height for live results. For engineering estimates, add material density, batch data, and export options.

Calculation mode

Select known values; the tool will switch the required inputs.

Parameter settings

Enter the frustum top/bottom radii and vertical height.

Length unit

Result precision

Top radius r1

Bottom radius r2

Height h

Cylinder modeKeep r1 = r2 Cone modeFix r1 = 0

Material & Display

For weight estimates and formula display; does not affect geometry.

Material Density

Angle Display

Main Volume Unit

Show Calculation StepsIncludes formula substitution, lateral area, and net derivation

Drag to Rotate Scroll to Zoom Live Preview

Frustum Volume -

Lateral area-

Total surface area-

Slant height-

Weight estimate-

Waiting for input.

Net & unit conversion

The side unfolds into an annular sector for cardboard, sheet metal, container design, and more.

Waiting to calculate

Batch calculate

Enter per line: top radius, bottom radius, height.

Calculation history

Saves the latest 20. Click a record to refill.

No history yet.

Instructions

Software Usage Instructions

Select calculation mode: Choose forward calculation, reverse height calculation, or reverse bottom radius calculation, and the tool will automatically switch the required parameters.
Enter frustum parameters: For forward calculation, enter the top radius r1, bottom radius r2, and height h; for reverse calculation, enter the target volume and the corresponding known conditions.
Set units and precision: Choose millimeters, centimeters, meters, inches, feet, or yards, and set the number of decimal places for the result.
Use special shapes: Cylinder mode keeps r1=r2, while cone mode fixes r1 at 0, suitable for handling special cases of cylinders or cones.
View calculation results: The tool displays volume, lateral surface area, total surface area, slant height, base area difference, multi-unit conversions, and lateral net parameters.
Estimate material weight: Select materials such as water, steel, aluminum, copper, concrete, glass, plastic, or pine, or enter a custom density.
Use example parameters: Click examples such as bucket, flowerpot, funnel, chimney, or paper cup to quickly load common dimensions.
Batch calculation: In the batch area, enter multiple sets of data in the format “top radius,bottom radius,height” on each line, then click batch calculation to export CSV.
Save and export: You can save the current settings, save history records, copy the result text, or export a PNG image containing the main results.

FAQ

A: The volume formula for a frustum is V = (π/3) × h × (r1² + r1r2 + r2²), where r1 is the top radius, r2 is the bottom radius, and h is the vertical height.

A: The slant height is the inclined height of the frustum’s lateral surface, calculated as l = √(h² + (r2-r1)²). It is used to calculate lateral surface area and net parameters.

A: After unfolding, the lateral surface of a frustum is usually an annular sector. The inner radius, outer radius, central angle, and arc length can be used for cardboard cutting, sheet metal layout, container making, and educational drawing.

A: When the target volume is known and the top and bottom radii are known, you can use the reverse height calculation feature to calculate the required height. It is commonly used in container capacity design.

A: The weight estimate is based on volume multiplied by density. The preset density is a reference value; actual materials may vary due to formula, moisture content, temperature, or porosity. For engineering quantities, it is recommended to enter the measured density.

A: Enter one set of parameters per line, in the format top radius,bottom radius,height. English commas, Chinese commas, spaces, or tabs can all be used as separators.