What this calculator does
The Radius of a Cylinder Calculator finds the radius r of a right circular cylinder when you already know its volume V and its height h. It rearranges the standard cylinder volume formula so you can solve for the missing dimension instead of the volume.
How to use it
Enter the cylinder's volume and its height in consistent units (for example cubic centimetres for volume and centimetres for height). Press calculate and the tool returns the radius. It also reports the diameter, which is simply twice the radius. Make sure both inputs use compatible length units — if the volume is in cm³, the resulting radius is in cm.
The formula explained
The volume of a cylinder is $$V = \pi \cdot r^2 \cdot h$$ To isolate the radius, divide both sides by \(\pi \cdot h\) to get $$r^2 = \frac{V}{\pi \cdot h}$$ then take the square root: $$r = \sqrt{\frac{V}{\pi \cdot h}}$$ The height must be greater than zero, otherwise the radius is undefined (you cannot divide by zero).
Worked example
Suppose a cylinder has a volume of 1000 cm³ and a height of 10 cm. Then \(\pi \cdot h \approx 31.4159\), so $$r^2 = \frac{1000}{31.4159} \approx 31.831$$ and \(r = \sqrt{31.831} \approx 5.6419\) cm. The diameter is \(2 \times 5.6419 \approx 11.2838\) cm.
FAQ
What units does it use? Any units, as long as they are consistent. Volume should be the cube of the length unit used for height.
Why must height be positive? The formula divides volume by \(\pi \cdot h\). A zero or negative height makes the result undefined.
Can I get the diameter instead? Yes — the calculator also outputs the diameter, which is exactly twice the radius.
