Cone Volume Calculator
Enter cone dimensions below to calculate volume instantly. Use either radius or diameter.
What is conical volume?
Conical volume is the amount of three-dimensional space inside a cone. A cone is a solid shape with one circular base and a single point (the apex). You see cone-like shapes in funnels, traffic cones, ice cream cones, silos, and some tanks.
If you know the radius of the base and the vertical height, you can calculate the volume quickly with a standard geometry formula.
Cone volume formula
where:
V = volume, r = radius of the circular base, h = vertical height, and π ≈ 3.14159.
- The radius is half of the diameter: r = d/2.
- Height must be perpendicular from base to apex (not slant height).
- Units matter: if dimensions are in centimeters, volume is in cubic centimeters (cm3).
How to use this calculator
- Enter the radius or diameter of the cone base.
- Enter the height.
- Optionally type a unit label (like cm or m).
- Choose desired decimal precision.
- Click Calculate Volume.
In addition to volume, the calculator also returns base area, lateral surface area, and total surface area.
Worked example
Example values
Suppose a cone has radius r = 3 m and height h = 8 m.
V = (1/3) × π × 3² × 8
V = (1/3) × π × 9 × 8
V = 24π ≈ 75.398 m3
Quick comparison with a cylinder
A cone with the same base and height as a cylinder has exactly one-third of the cylinder’s volume. That relationship is why the cone formula includes the factor 1/3.
Real-world uses
- Estimating capacity of conical hoppers and bins
- Designing packaging and molded parts
- Determining fill levels in conical tanks
- Construction and architecture measurements
- Math homework, exam prep, and engineering checks
Common mistakes to avoid
- Using diameter as radius by accident
- Entering slant height instead of vertical height
- Mixing units (for example, inches for radius and feet for height)
- Rounding too early in multi-step calculations
FAQ
Can I use diameter directly?
Yes. Enter diameter and the calculator converts it to radius automatically if radius is blank.
What if my cone is truncated (frustum)?
A frustum requires a different formula using two radii and a height. This calculator is for a full right circular cone.
Why are units cubic?
Volume measures 3D space, so units are always raised to the third power (for example, cm3, m3, in3).