Calculate Cone Volume Instantly
Enter a radius (or diameter) and height to find the cone volume using the formula V = (1/3)πr²h.
What Is the Volume of a Cone?
The volume of a cone tells you how much space is inside it. Think of an ice cream cone, a traffic cone, or a funnel-shaped container. If you know the radius of the circular base and the vertical height, the volume is straightforward to calculate.
- V = volume
- r = radius of the base
- h = perpendicular height
- π ≈ 3.14159
How to Use This Cone Volume Calculator
Step-by-step
- Enter the radius of the cone base. If you only know diameter, enter that instead.
- Enter the cone height (vertical height, not slant height).
- Select a unit and decimal precision if needed.
- Click Calculate Volume.
The tool also shows base area and the substituted formula values so you can verify each step.
Example Calculation
Suppose a cone has radius r = 3 cm and height h = 10 cm.
V = (1/3) × π × 3² × 10 = (1/3) × π × 9 × 10 = 30π ≈ 94.25 cm³
That means the cone can hold about 94.25 cubic centimeters.
Radius vs. Diameter: Common Confusion
A frequent mistake is entering diameter as radius. Remember:
- Diameter = 2 × Radius
- Radius = Diameter ÷ 2
If your answer seems too large, check whether you accidentally used diameter in place of radius.
Real-World Uses for Cone Volume
- Estimating material in conical molds and castings
- Measuring storage capacity of hopper bottoms and funnels
- Calculating portions in food packaging (cone cups, wafers)
- Solving geometry homework and exam problems quickly
Common Mistakes to Avoid
- Using slant height instead of vertical height
- Mixing units (for example radius in cm and height in m)
- Forgetting the 1/3 in the cone formula
- Rounding too early in multi-step calculations
Quick FAQ
Can I use this for truncated cones (frustums)?
No. This calculator is for a full right circular cone. A frustum needs a different formula.
What if I only know diameter?
Enter diameter and leave radius blank; the calculator converts automatically.
What unit is returned?
Volume is returned in cubic units based on your selected unit, such as cm³, m³, in³, or ft³.