What Is the Cone Volume from Diameter Calculator?
This calculator finds the volume of a right circular cone when you know its base diameter and its height. A cone is a 3D shape with a circular base that tapers smoothly to a single point (the apex). Because measurements of round objects are often taken across the full width (the diameter) rather than from the center (the radius), this tool lets you skip the manual halving step.
How to Use It
Enter the base diameter (d) and the height (h) of the cone in the same unit of measurement (e.g. centimeters). Press calculate to see the volume in cubic units, along with the computed radius. Make sure both inputs share the same unit — mixing inches and centimeters will give a meaningless result.
The Formula Explained
The standard cone volume formula is \( V = \frac{1}{3} \pi r^{2} h \). Since the radius equals half the diameter (\( r = d/2 \)), substituting gives \( r^{2} = d^{2}/4 \). Plugging in:
$$ V = \frac{1}{3} \pi \left(\frac{d^{2}}{4}\right) h = \frac{1}{12} \pi d^{2} h $$That is the equation this calculator uses, so you only need the diameter.
Worked Example
Suppose a cone has a base diameter of 10 cm and a height of 12 cm. Then
$$ V = \frac{1}{12} \times \pi \times 10^{2} \times 12 = \frac{1}{12} \times \pi \times 100 \times 12 = \pi \times 100 \approx 314.16 \text{ cubic centimeters} $$The radius is \( 10 \div 2 = 5 \) cm.
FAQ
What units does the result use? The volume comes out in cubic units of whatever length unit you entered — cubic cm if you used cm, cubic inches if you used inches.
Can I use the radius instead? If you only have the radius, simply double it to get the diameter before entering it, or use a radius-based cone calculator.
Does this work for an oblique (slanted) cone? Yes — as long as "height" is the perpendicular height from the base to the apex, the volume formula is the same for right and oblique cones.
