Volume of Frustum Cone Calculator: Get the volume in seconds
The volume of a frustum cone is computed from the bottom radius R, top radius r, and vertical height h. Use the formula V = (1/3)·π·h·(R² + Rr + r²) to get cubic units instantly.
This article explains each variable, shows how to avoid unit mistakes, and includes practical examples for real projects.
What is a frustum cone?
A frustum cone is what you get when you cut the top off a cone with a plane parallel to its base. The result has two circular faces: a larger circle at the bottom and a smaller circle at the top.
Because the sides taper smoothly, the volume is not the same as a simple cylinder. The frustum formula accounts for the changing radius along the height.
Core formula for the volume of a frustum cone
Use this exact volume formula:
V = (1/3) · π · h · (R² + Rr + r²)
- V is the volume (in cubic units).
- R is the bottom radius (half the bottom diameter).
- r is the top radius (half the top diameter).
- h is the vertical height between the two circular faces.
- π is pi (≈ 3.14159).
How to choose the right inputs (radii vs. diameters)
The formula requires radii, not diameters. If you only have diameters, convert them by dividing by 2.
- R = Dbottom / 2
- r = Dtop / 2
If you accidentally plug diameters into the radius slots, your volume will be off by a factor of 8 (because the formula uses squares of radii).
Units and conversions (avoid the most common mistakes)
The calculator computes volume in cubic units based on the length unit you select. You must keep all length inputs in the same unit system (for example, all in centimeters).
For example, if you enter h in meters and radii in millimeters, the result will be wrong even if the numbers look reasonable.
Quick unit guidance
| Length unit | Volume unit |
|---|---|
| mm | mm³ |
| cm | cm³ |
| m | m³ |
| in | in³ |
| ft | ft³ |
Using the Volume of Frustum Cone Calculator
Enter the bottom radius R, top radius r, and height h. Choose the length unit, then click Calculate to get the volume.
If you want to work from diameters, first convert to radii (divide by 2) or use your own conversion before entering values.
Practical examples (real-world use-cases)
Example 1: Estimate material for a truncated funnel
You’re making a funnel-shaped insert. The bottom diameter is 20 cm, the top diameter is 10 cm, and the height is 15 cm. Convert diameters to radii: R = 10 cm, r = 5 cm, h = 15 cm.
Plug into the formula to estimate the internal volume. This helps you predict how much liquid or powder the funnel can hold.
Example 2: Calculate volume of a tapered container
A tapered container has a bottom radius of 2.5 in, a top radius of 1 in, and a height of 8 in. Using R = 2.5, r = 1, and h = 8, you compute the container’s volume in cubic inches.
This is useful for packaging, mixing ratios, and material planning when the container shape is not a simple cylinder.
Sanity checks to confirm your result
After you calculate, use these quick checks to catch input errors.
- If R = r, the frustum becomes a cylinder, and the formula reduces to V = π·R²·h.
- If r = 0, the frustum becomes a cone, and the formula becomes V = (1/3)·π·R²·h.
- Increasing h increases volume linearly; doubling h doubles V.
Frequently Asked Questions
How do I find the volume of a frustum cone from diameters?
Convert diameters to radii first: R = Dbottom/2 and r = Dtop/2. Then use V = (1/3)·π·h·(R² + Rr + r²). Keep all lengths in the same unit (cm with cm, inches with inches) for a correct cubic result.
What does “height” mean for a frustum cone?
The height h is the vertical distance between the two parallel circular faces. It is not the slanted side length. If you only have the slant height, you must use geometry to find the vertical height before calculating volume.
Can I use the frustum formula when the top radius is zero?
Yes. When r = 0, the frustum becomes a full cone. The formula simplifies automatically to V = (1/3)·π·R²·h. This is why the frustum equation is a general form covering cones and cylinders as special cases.
Why do my results seem eight times too large?
This usually happens when you enter diameters into the radius inputs. Because the formula uses squared radii, using diameters instead of radii multiplies the squared terms by 4, and the total volume becomes 8× too large. Always divide diameters by 2.
What unit will the calculator output?
The calculator outputs volume in cubic units derived from your chosen length unit. If you select centimeters, it returns cm³. If you select inches, it returns in³. Make sure R, r, and h are all entered in the same unit system.
