Cone Volume Calculator
Calculate the volume of a cone from its radius and height
Volume
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Cone Volume Calculator Formula
Volume of a cone:
V = (1/3) × π × r² × h
r = base radius, h = height
How to Use This Calculator
- Enter the radius of the circular base.
- Enter the height of the cone (perpendicular distance from base to apex).
- Click Calculate Volume to see the result.
Frequently Asked Questions
Why does the cone formula have a 1/3?
A cone's volume is exactly one-third of the cylinder with the same base and height (V = ⅓πr²h vs. πr²h for the cylinder). You can verify this with our cylinder volume calculator. This relationship can be proven by calculus or by Cavalieri's principle.
What is the height of a cone?
The height is the perpendicular distance from the center of the base to the apex (tip). It is not the slant height along the side of the cone. If you only know the slant height l, use h = √(l² − r²).
What units does this calculator use?
This calculator is unit-agnostic. If you enter radius in cm and height in cm, the result is in cm³. Always use the same unit for both inputs.
What is the surface area of a cone?
The total surface area is SA = πr² + πrl, where l is the slant height (l = sqrt(r² + h²)). The first term is the base area and the second is the lateral (side) area.
Does this formula work for truncated cones (frustums)?
No. A truncated cone (frustum) has the top cut off and uses a different formula: V = (πh/3)(R² + Rr + r²), where R and r are the radii of the two circular faces. This calculator is for complete cones only.
Can I share my calculation?
Yes. After clicking Calculate, the URL updates with your input values. Copy and share the URL to let anyone else see the same pre-filled form and result.