Conical Frustum Volume CalculatorFree online math calculator — instant results, no sign-up
Calculate a conical frustum's volume from two radii and height.
Sign in to save results and favorites.
About the Conical Frustum Volume Calculator
The Conical Frustum Volume Calculator finds the volume of a truncated cone from its bottom radius, top radius, and perpendicular height. Use it for a solid with parallel circular ends and a straight, tapered side. With bottom radius 5, top radius 3, and height 8, the calculated volume is 410.5014400691 cubic units.
- Bottom radius
- The distance from the center of the bottom circular face to its edge, entered in the same length unit as the top radius and height.
- Top radius
- The distance from the center of the top circular face to its edge, entered in the same length unit as the bottom radius and height.
- Height
- The perpendicular distance between the two circular faces, not the slant height, entered in the same length unit as both radii.
Formula and method
V = (πh/3)(R² + Rr + r²); with the default inputs, V = (π × 8/3)(5² + 5 × 3 + 3²) = 392π/3 ≈ 410.5014400691.
- VVolume of the conical frustum, in cubic units.
- RBottom radius, in length units.
- rTop radius, in length units.
- hPerpendicular height between the circular faces, in length units.
- πPi, the constant ratio of a circle's circumference to its diameter.
Square each radius and multiply the two radii together, then add those three terms. Multiply the sum by π and the height, and divide by 3. For the default inputs, the radius terms total 25 + 15 + 9 = 49, so the volume is 49 × π × 8 ÷ 3 = 392π/3, displayed as 410.5014400691.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Bottom radius5
- Top radius3
- Height8
Results
- Result410.5014400691
How to use the Conical Frustum Volume Calculator
- 1Choose one length unit for all measurements and convert any measurements that use a different unit.
- 2Enter the Bottom radius; the default is 5. If you measured a diameter, divide it by 2 first.
- 3Enter the Top radius; the default is 3.
- 4Enter the perpendicular Height; the default is 8. Do not use the length along the sloping side.
- 5Read the calculated volume: the default inputs give 410.5014400691 cubic units.
Reading your result
The Result row reports the frustum's volume. With the default inputs, 410.5014400691 means the solid occupies approximately 410.5014400691 cubic units. The output unit is the cube of the input length unit: centimeters produce cubic centimeters, and meters produce cubic meters. The displayed decimal is an approximation of the exact value 392π/3.
Limitations
The calculation assumes an ideal conical frustum with parallel circular faces and a radius that changes linearly along its height. Use nonnegative radii and a positive height for a nondegenerate solid; negative dimensions are not physically meaningful. The tool does not account for wall thickness, rounded edges, or irregular shapes. For container capacity, use internal dimensions rather than external dimensions. Displayed decimal precision does not guarantee equivalent accuracy in measured inputs.
Common questions
Does the bottom radius have to be larger than the top radius?+
No. Swapping the two radii leaves R² + Rr + r² unchanged, so reversing the frustum's orientation does not change its volume.
Can I enter diameters instead of radii for a conical frustum?+
Not directly. Divide each circular face's diameter by 2 before entering it in the corresponding radius field.
Can I use the sloping side length as the height?+
No. The formula needs the perpendicular separation of the circular faces. For a right conical frustum with slant height s, first find h = √(s² − (R − r)²).
What happens if the radii are equal or one radius is zero?+
Equal radii describe a cylinder, and the formula becomes V = πR²h. If one radius is zero, the shape is a cone, and the formula becomes V = πh times the remaining radius squared, divided by 3.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
You might also like
Slope Calculator
Slope, angle and line equation through two points.
Area Calculator
Area of common 2D shapes.
Volume Calculator
Volume of common 3D shapes.
Surface Area Calculator
Surface area of 3D shapes.
Circle Calculator
Radius, diameter, circumference and area.
Triangle Calculator
Solve a triangle from three sides.
Results are estimates for informational purposes and are not financial, medical or legal advice.